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January, 2017

ASACUSA STATUS REPORT

Recent progress and plans for 2017

ASACUSA collaboration

H. Aghai-Khozanih, C. Amslerg, S. Arguedas Cuendisg, D. BarnaI , H. Breukerf , M. Corradinik,A. Daxi, M. Diermaierg, P. Duprea, M. Fleckg, R. Hayanoi, H. Higakib, M. Horih, D. Horvathj

Y. Kanaia, T. Kobayashic, T. Kobayashii, B. Kolbingerg, N. Kurodac, M. Lealik, E. Lodi-Rizzinik,V. Mackelg, C. Malbrunotf,g, V. Mascagnak, O. Massiczekg, Y. Matsudac, T. Matsudatec, Y. Murakamii,Y. Nagatad, M. Nicolicsg, B. Radicsa C. Sauerzopfg, M. Simong, A. Soterh, H. Spitzerg, M. Tajimaa,c,K. Todorokii, H.A. Toriic, S. Ulmere, S. Vamosig, L. Venturellik E. Widmanng, M. Wiesingerg,H. Yamadai, Y. Yamazakia J. Zmeskalg

aAtomic Physics Research Unit, RIKEN, bGraduate School of Advanced Sciecnces of Matter, Hi-roshima University, cInstitute of Physics, the University of Tokyo, dDepartment of Applied Physics,Tokyo University of Agriculture and Technology, eUlmer Initiative Research Unit, RIKEN, fCERN,gStefan-Meyer Institute, hMax-Planck-Institut fur Quantenoptik, iDepartment of Physics, The Uni-versity of Tokyo, jWigner Research Centre for Physics, kUniversita di Brescia

Executive summary

• Antiprotonic helium spectroscopy (for Mp

/me

determination)In 2016, we achieved the following:

– In 2016, we published the results of precision laser spectroscopy of bu↵er-gas cooled an-tiprotonic helium (pHe+) based on the experimental results of previous years (publishedin Science). We determined the ratio M

p

/me

with a fractional precision of 8⇥ 10�10.

– We continued precision two-photon laser spectroscopy of pHe+ cooled to T ⇠ 1.5 K tofurther improve the experimental precision on the antiproton-to-electron mass ratio.

The goals for 2017 are to measure two two-photon p4He+

transitions (n, `) = (36, 34)!(34, 32)and (33, 32)!(31, 30), and the p3He

+

transition (n, `) = (35, 33)!(33, 31) for atoms cooledto T ⇠ 1.5 K. This in principle may lead to a determination of the M

p

/me

value with arelative precision of better than 3⇥ 10�10.

• Toward the H ground-state hyperfine spectroscopyIn 2016, we achieved the following:

– successful transport of 1.5-eV monoenergetic pulsed antiproton beams from the MUSASHItrap to the double cusp trap,

– synthesis of antihydrogen atoms in the double cusp trap by injecting the 1.5-eV ps intothe positron plasma; around 60% of FIC (field ionizer in the cusp) events were localizedwithin the first 0.7 s, implying a quick separation of 80–90% of trapped antiprotons fromthe positrons,

– quantum states of antihydrogen atoms were studied with the downstream field ionizer(FID) and the H detector; analyses indicate the production of n < 14 H atoms.

The goal in 2017 is like in 2016 to optimize the antihydrogen beam for hyperfine spectroscopy.

• Experiments with a polarized (ordinary) hydrogen beam

– the final results of the �1

-transition, showing an achieved experimental precision of 2.7ppb and an agreement with the maser results within 1 � are available,

– setup modifications have been completed for measuring both �1

and ⇡1

transitions withinthe same setup.

• p-nuclei annihilation cross section measurement at 5.3 MeVAnalysis of the data collected in 2015 for the p-carbon annihilation cross section at 5.3 MeVhas been finalized. This will serve as a benchmark to understand energy and mass numberdependence of antinucleon annihilations at low energies

Contents

I Antiprotonic Helium 1

1 Antiprotonic helium 11.1 Single-photon spectroscopy of bu↵er-gas cooled pHe+, and antiproton-to-electron mass ratio . 11.2 Two-photon spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Plans for 2017: Continuation of two-photon laser spectroscopy experiments on cold pHe+

atoms 7

II CUSP experiment for H Spectroscopy 9

1 CUSP experiment for H Spectroscopy 91.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Adiabatic transport of antiprotons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.3 CUSP experiment for Antihydrogen Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 281.4 Summary of the 2016 run and Plan for 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

III Experiments with a polarized hydrogen beam 36

1 Experiments with a polarized hydrogen beam 361.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361.2 The remeasurement of the hydrogen hyperfine structure . . . . . . . . . . . . . . . . . . . . . 361.3 New spin-state analysing sextupole magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371.4 Spin-flip microwave cavity for ⇡1-transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381.5 Ring apertures for a hollow hydrogen beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401.6 Plans for 2017 . . . and beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

IV Antiproton-nuclei cross section measurement at 5.3 MeV 43

1 Introduction 43

2 The measurement 43

3 The results 47

Part I

Antiprotonic Helium

1 Antiprotonic helium

1.1 Single-photon spectroscopy of bu↵er-gas cooled pHe+, and antiproton-to-electron mass ratio

In 2016, the ASACUSA collaboration published the results of precision laser spectroscopy of bu↵er-gas cooled antiprotonic helium (pHe+) based on the experimental results of previous years [1].The antiproton-to-electron mass ratio M

p

/me

can be precisely determined from the single-photontransition frequencies of this atom. We measured thirteen such frequencies by laser spectroscopyto a fractional precision of (2.5 � 16) ⇥ 10�9. About 2 ⇥ 109 pHe+ were cooled to temperaturesbetween T = 1.5 and 1.7 K by utilizing bu↵er-gas cooling in cryogenic low-pressure helium gas. Thenarrow thermal distribution led to the observation of sharp spectral lines of small thermal Dopplerwidth. The deviation between the experimental frequencies and the results of three-body quantumelectrodynamics calculations was reduced by a factor 1.4–10 compared to previous single-photonexperiments carried out by ASACUSA. From this we determined the ratio [1] as,

Mp

/me

= 1836.1526734(15), (1)

which agrees with the recent proton [2] value of,

Mp

/me

= 1836.15267377(17), (2)

within 8⇥ 10�10.Prior to this experiment, it was not known whether collisions with normal matter atoms would

cool pHe+ to such low (T ⇠ 1.5 K) temperatures, as the corresponding multi-body calculations werecomplicated. In fact, other exotic atoms such as pionic hydrogen [3] were heated by collisions thatdeexcite the atom; pHe+ colliding with other helium atoms annihilated the antiprotons occupyingsome states [4]. We adjusted the density of the bu↵er helium gas so that the pHe+ atoms, onceformed, rapidly underwent a few hundred or more cooling collisions before being interrogated bythe laser beam. The 1s electron protected most of the pHe+ atoms during this cooling.

The transition frequencies of pHe+ have recently been calculated to a precision of ⇠ 10�10 byevaluating the complete set of quantum electrodynamics (QED) corrections up to order m

e

↵7 inatomic units [6–8]. These a priori calculations used the CODATA2010 recommended values [5] of thefundamental constants, including the fine structure constant ↵, the 3He- and 4He-to-electron massratios, the Bohr radius, and the Rydberg constant. By comparing the calculated and experimentalpHe+ frequencies, the ratio can in principle be determined to a fractional precision of < 1⇥ 10�10,which may rival the best measurements of M

p

/me

[2, 9–12].

The newly published data represents > 1.5⇥ 109 cold p4He+

atoms and > 5⇥ 108 cold p3He+

atoms that were collected over a 3-year period.Figure 2 shows the profile of the p4He+ transition (n, l) = (37, 35)!(38, 34) obtained by plot-

ting the intensities of the annihilation signals induced at laser frequencies between �1 and 1 GHzaround the resonance centroid. Each data point was collected from 6–10 antiproton pulses. Pairs offine structure sublines arise from the dominant interaction between the orbital angular momentumof the antiproton and the electron spin; the positions of the four hyperfine sublines that arise fromthe additional spin-spin interaction between the antiproton and electron are indicated by arrows.

1

Figure 1: Schematics of the experiment. Top: Drawing of the experimental setup used to synthesizeantiprotonic helium atoms and cool them by bu↵er gas cooling to T=1.5 K. Bottom: drawing ofthe laser systems used for spectroscopy.

This single-photon resolution exceeds those of previous sub-Doppler two-photon spectroscopy ex-periments, and is consistent with the Doppler width �⌫ = 160 � 170 MHz of p4He+ thermalizedto T = 1.5� 1.7 K when the contributions of power broadening (< 30 MHz), natural width (⇠ 20MHz), laser linewidth which include the Fourier transform limit due to the pulse length of the laser(6 MHz), and the hyperfine structure (< 30 MHz) are subtracted. Collisional broadening e↵ectsare small. The strong signal intensity (3⇥ larger than in the previous high-resolution single-photonexperiment relative to the total number of p4He+ atoms formed in the target) arises from the highdensity of cold p4He+ that lie within the thermal velocity class excited by the laser. Figure 2C showsthe profile of a previously undetected p4He+ resonance (38, 35)!(39, 34). Its spectral resolution islimited by the > 1-GHz Auger width of the daughter state. Previous experiments could not resolvethe fine structure in favored transitions of the type (n, `)!(n�1, `�1), but it is now revealed in the(39, 35)!(38, 34) resonance of cold p4He+ [Fig. 2B]. We also resolved the three-peak structure inthe p3He+ resonance (36, 34)!(37, 33) [Fig. 2D] arising from the eight unequally-spaced hyperfinesublines caused by the additional interaction of the 3He nuclear spin. The fact that they were muchnarrower than the single-photon resonances measured previously with inferred Doppler widths of�⌫ = 160–470 MHz relative to their transition frequencies of ⌫ = 356–1133 THz, and no significantbroadened background component indicates that nearly all of the atoms had cooled to T = 1.5–1.7

2

K.

0

1

2

3

4

-2 0 2

(A)

Sig

na

l in

ten

sity

(

arb

.u.)

-2 0 2

(B)

-2 0 2

Laser frequency offset (GHz)

(C)

-2 0

(D)

2

Figure 2: Resonance profiles of the single-photon transitions (A) (n, l) = (37, 35)!(38, 34), (B)(39, 35)!(38, 34), and (C) (38, 35)!(39, 34) of bu↵er-gas cooled p4He

+

atoms. The narrow, intensespectral lines are compatible with the Doppler widths of atoms cooled to T = 1.5�1.7 K, relative tothe corresponding transition frequencies between ⌫ = 356 and 502 THz and when the Auger widthsof the resonance daughter states are subtracted. The arrows indicate the theoretical positions ofthe hyperfine lines caused by the spin-spin interaction between the antiproton and electron [13];the (B) and (C) splittings had not been observed previously (D) The profile (36, 34)!(37, 33) ofcooled p3He

+

shows a further splitting due to the 3He nuclear spin. The x-abscissa indicates theo↵set of the optical frequency of the laser relative to the resonance centroid. Blue curves indicatethe best fit of an ab initio model based on the optical Bloch equation [18].

The spin-independent transition frequencies ⌫exp

(Table 1) were determined by fitting the pro-files with a theoretical lineshape (Fig. 2, blue lines). The lineshape was obtained by solving theoptical Bloch equations of the single-photon transitions between the (2` + 1) ⇠ 70 magnetic sub-states, and taking into account power broadening e↵ects, thermal motion of the atoms, the spuriousfrequency modulation in the laser, and the spatial and temporal profiles of the laser beam. Thepositions of the hyperfine sublines were fixed to the theoretical values [13], the uncertainty of whicha↵ects ⌫

exp

by 0.1 MHz (Table 2).Cold collisions with helium atoms deform the pHe+ orbitals and shift the resonance frequencies

[14,15]. Figures 4, A and C show the frequency shifts of two p4He+

transitions (38, 35)!(39, 34) and(37, 35)!(38, 34) having the largest observed gradients , measured at target densities between ⇢ =1.8⇥1018 and 8⇥1018 cm�3. The much smaller shifts of other transitions such as (32, 31)!(31, 30)were not resolvable within the 2 MHz experimental uncertainty. The measured shifts agree withquantum chemistry calculations [14] within ⇠ 20%. A linear extrapolation to ⇢ = 0 yielded the zero-density frequencies; for transitions with small d⌫/d⇢, the gradients measured at higher densities⇢ > 1⇥ 1020 cm�3 were used [16].

The strong resonance signal from the large density of cold pHe+ occupying the thermal distri-bution depopulated by the laser yielded a small statistical uncertainty �

stat

= ±1 MHz on ⌫exp

of

the p4He+

transition (37, 35)!(38, 34), and �stat

= ±10 MHz for (34, 33)!(35, 32), which has adaughter state of large (1 GHz) natural width (see Table 2). A systematic uncertainty of 0.4–3MHz arose from the fitting function [18] itself. The magnetic Zeeman shifts in these transitionsbetween Rydberg states are small (< 0.1 MHz) under our experimental conditions. The spuriousfrequency modulation of the laser pulses (24,25) were measured with a precision of 0.4–1.0 MHz.The shift in ⌫

exp

arising from laser fields that induce a.c. Stark e↵ects [18] were 5 MHz inour earlier two-photon experiment carried out at higher laser fluences [17]; the shifts were smaller(< 0.2 MHz) for the single-photon transitions studied here.

3

All measured transition frequencies ⌫exp

(Fig. 3A, open circles with error bars) agree with the-oretical ⌫

th

values (filled squares) within the experimental uncertainties of (2.5� 15)⇥ 10�9. Thisagreement is 1.4–10 times better than in previous single-photon experiments [16]. The uncertain-ties for most of the theoretical frequencies ⌫

th

are due to uncalculated QED contributions of ordershigher than m

e

↵7, whereas for some transitions (i.e., (37, 35)!(38, 34) of p4He+

) numerical uncer-tainties in the calculation of the relativistic Bethe logarithm (Table 2) dominate. The correctionson ⌫

th

due to the finite charge radii [6, 19] of the helium nucleus (4–7 MHz) and of the antipro-ton (< 1 MHz) are small, because the Rydberg antiproton orbital has negligible overlap with thenucleus, and is polarized away from the 1s electron.

The frequencies ⌫th

for the unfavoured (n, `)!(n + 1, ` � 1) transitions with low transitionprobabilities [18] between the n � 36 states changed by (2.6 � 2.7) ⇥ 10�9 when the M

p

/me

ratio used in the calculations was changed by 1 ⇥ 10�9. These sensitivities M

= 2.6–2.7 (Ta-ble 1) of the transitions [4] measured here are > 2⇥ larger than those of the low-n or two-photontransitions studied earlier. The value that yielded the best agreement between ⌫

th

and ⌫exp

of

the p4He+

transition (37, 35)!(38, 34) deviated from the CODATA2010 recommended value forM

p

/me

by �Mp/me

= (7± 10)⇥ 10�10. By minimizing ⌃ [⌫th

(Mp

/me

)� ⌫exp

]2p

/�2

stat

over the thir-

teen p4He+

frequencies, and considering the above systematic errors, �sys

, we obtained the ratioM

p

/me

= 1836.1526734(15). The 1-standard deviation uncertainty in the parenthesis includes thecontributions 9 ⇥ 10�7, 11 ⇥ 10�7, and 3 ⇥ 10�7 of the experimental statistical and systematicuncertainties, and the theoretical uncertainty, respectively.

The atomic mass of the electron was recently determined [2] with a precision of 3 ⇥ 10�11, bymeasuring the ratio between the cyclotron frequency and the precession frequency of the electronspin of a 12C5+ ion confined in a Penning trap, and comparing the results with QED calculationsof its g-factor. From this and the known proton mass, the proton-to-electron mass ratio wasdetermined as M

p

/me

= 1836.15267377(17), which is larger by 4 ⇥ 10�9 and 8 ⇥ 10�10 than theratios determined by comparing the cyclotron frequencies of protons and electrons in a Penning trap,and the CODATA2010 recommended value. Our value agrees with the result from Ref. [2] (Fig. 3B).The precision of our measurements here is a factor of 3.5 better than the recent determination ofM

p

/me

by laser spectroscopy of HD+ molecules [12].We use the analysis method of Hughes and Deutch [20–24] to constrain the equality between

antiproton and proton masses �M

= (Mp

� Mp

)/Mp

and charges �Q

= (Qp

+ Qp

)/Qp

from these

measured p4He+

transition frequencies. The p4He+

transition frequencies are proportional to Q2

p

Mp

and have linear dependencies �M

M

+ �Q

Q

< |⌫exp

� ⌫th

|/⌫th

, where the calculated sensitivitiesM

and Q

are shown in Table 1. The right side of the equation was evaluated as < (3±15)⇥10�10

by averaging over the transitions and considering the statistical and systematic uncertainties. TheTRAP and BASE collaborations [22–24] have on the other hand measured the cyclotron frequency(/ Q

p

/Mp

) of antiprotons confined in Penning traps as (Qp

/Mp

)/(Qp

/Mp

) + 1 = 1.6(9) ⇥ 10�10

[22, 23] and 1(69) ⇥ 10�12 [24] which implies that �Q

⇠ �M

. By combining the two types ofexperimental results, we conclude that any deviation between the proton and antiproton massesand charges are < 5 ⇥ 10�10 at the 90% confidence level. Recently the ALPHA experiment hasprovided a limit < 7⇥10�10 on any residual charge of antihydrogen [25], by analyzing its movementin a magnetic bottle trap; when combined with the pHe+ results, this constrains the equality ofthe electron and positron charges to a similar level.

4

Figure 3: Comparison of experimental and calculated transition frequencies (A). Shown are thefractional di↵erences between the experimental (open circles) and theoretical (squares) values of 13transition frequencies of p4He

+

and p3He+

atoms cooled to T = 1.5�1.7 K. Antiproton-to-electronmass ratio compared with proton-to-electron mass ratios (B). Top to bottom: the most precisedirect measurement [9] of the proton-to-electron mass ratio obtained by contrasting the cyclotronfrequencies of a proton and an electron confined in a Penning trap; indirect determinations [2,10,11]by measuring the magnetic moment of the bound electron in 12C5+ and 16O7+ ions in a Penningtrap; laser spectroscopy of HD+ molecules [3]; antiproton-to-electron mass ratio obtained fromtwo-photon laser spectroscopy of p4He+ [17] and single-photon spectroscopy of cold atoms in thiswork. Yellow band represents the CODATA2010 recommended value [5]. The CODATA2014 valueis similar to the value of Ref. [2].

5

Figure 4: Transition frequency shifts of the (n, `) = (37, 35)!(38, 34) resonance in p4He+ measuredat target densities between ⇢ = 1.8⇥1018 and 8⇥1018 cm�3 (A), and higher densities up to 1.6⇥1021

cm�3 (B). The data are fit with a common linear function. Frequency shift of (38, 35)!(39, 34) inp4He+ (C).

Table 1: Spin-averaged transition frequencies of pHe+. Experimental values show respective total,statistical, and systematic errors in parentheses; theoretical values show respective uncertaintiesfrom uncalculated QED terms and numerical errors in parentheses.

transition transition frequency (MHz)(n, `) ! (n0, `0) Expt. Korobov [?]

p4He+

transitions(40, 35) ! (39, 34) 445608573(5)(4)(1) 445608572.3(4)(38, 35) ! (39, 34) 356155990.1(2.1)(2.0)(0.8) 356155990.5(4)(39, 35) ! (38, 34) 501948753.4(2.1)(1.9)(0.8) 501948755.1(2)(37, 35) ! (38, 34) 412885133.1(1.0)(0.8)(0.6) 412885132.4(2)(37, 34) ! (36, 33) 636878154.3(2.2)(1.9)(1.1) 636878152.09(5)(34, 33) ! (35, 32) 655062100(10)(10)(1) 655062101.92(7)(35, 33) ! (34, 32) 804633058.2(2.1)(1.8)(1.2) 804633058.46(6)(32, 31) ! (31, 30) 1132609226.7(2.8)(2.5)(1.4) 1132609224.01(8)

p3He+

transitions(38, 34) ! (37, 33) 505222282(4)(4)(1) 505222281.0(3)(36, 34) ! (37, 33) 414147510.4(2.6)(2.3)(1.2) 414147508.9(3)(36, 33) ! (35, 32) 646180416(5)(4)(1) 646180412.58(5)(34, 32) ! (33, 31) 822809167(5)(5)(1) 822809172.30(7)(32, 31) ! (31, 30) 1043128581(5)(4)(1) 1043128580.64(8)

6

Table 2: Experimental and theoretical one standard deviation errors associated with transition(n, `) = (36, 34) ! (34, 32) of p4He

+

.

Error (MHz)Transition (37, 35) ! (38, 34) (32, 31) ! (31, 30)

Statistical error, �stat

0.8 2.5Collisional shift error 0.4 0.1A.c. Stark shift error 0.2 0.2

Zeeman shift < 0.1 < 0.1Frequency chirp error 0.4 1.0

Seed laser frequency calibration < 0.1 < 0.1Hyperfine structure 0.1 0.1

Line profile simulation 0.3 0.8Total systematic error, �

sys

0.7 1.3Total experimental error, �

exp

1.0 2.8

Uncertainties from uncalculated QED terms < 0.10 < 0.05Numerical uncertainty in calculation 0.20 0.08

Charge radii uncertainties < 0.01 < 0.01Total theoretical uncertainty, �

th

0.2 0.08

1.2 Two-photon spectroscopy

In 2016 the collaboration continued precision two-photon laser spectroscopy of pHe+ cooled toT ⇠ 1.5 K to further improve the experimental precision on the antiproton-to-electron mass ratio.Lowering the temperature of pHe+ reduce this broadening, while also enhancing the signal-to-noise ratio of the laser resonance. The atoms were irradiated with two counter-propagating laserbeams of wavelengths 417.8 and 372.6 nm. This excited a non-linear two-photon transition of theantiproton (n, `) = (36, 34)!(34, 32). The 75-keV antiproton beam ejected from the radiofrequencyquadrupole decelerator (RFQD) was stopped in a helium target and synthesizing the p4He+. Aseries of electrostatic quadrupole lenses reduced the background from beam halos. In 2015 weinstalled a new femtosecond frequency comb based on an erbium fiber laser and a so-called figure-nine laser cavity with a nonlinear cavity mirror, that produced laser pulses of repetition ratefr

= 250 MHz and wavelength � = 1560 nm. We acquired data corresponding to 5 ⇥ 108 atoms.The collaboration is currently analyzing this new data, and we are on track to further improve theM

p

/me

precision by adding further data in 2018–2019.

2 Plans for 2017: Continuation of two-photon laser spectroscopyexperiments on cold pHe+ atoms

Our 2017 plans are identical to the 2016 ones: we plan to continue measuring two two-photon p4He+

transitions (n, `) = (36, 34)!(34, 32) and (33, 32)!(31, 30), and the p3He+

transition (n, `) =(35, 33)!(33, 31) for atoms cooled to T ⇠ 1.5 K. This in principle may lead to a determinationof the M

p

/me

value with a relative precision of better than 3 ⇥ 10�10, after extensive systematicstudies and measurements.

7

References

[1] M. Hori et al., Science 354, 610 (2016).

[2] S. Sturm et al., Nature 506, 468 (2014).

[3] A. Badertscher et al., Phys. Lett. B 392, 278 (1997).

[4] R.S. Hayano, M. Hori, D. Horvath, E. Widmann, Rep. Prof. Phys. 70, 1995 (2007).

[5] P.J. Mohr, B.N. Taylor, and D.B. Newell, Rev. Mod. Phys. 84, 1527 (2012).

[6] V.I. Korobov, L. Hilico, and J.-P. Karr, Phys. Rev. Lett. 112, 103003 (2014).

[7] V.I. Korobov, L. Hilico, and J.-P. Karr, Phys. Rev. A 89, 032511 (2014).

[8] V.I. Korobov, Phys. Rev. A 89, 014501 (2014).

[9] D.L. Farnham, R.S. Van Dyck Jr., P.B. Schwinberg, Phys. Rev. Lett. 75 3598 (1995).

[10] T. Beier et al., Phys. Rev. Lett. 88, 011603 (2002).

[11] J. Verdu et al., Phys. Rev. Lett. 92, 093002 (2004).

[12] J. Biesheuvel et al., Nature Communications 7 10385 (2016).

[13] V.I. Korobov, Phys. Rev. A 73 022509 (2006).

[14] D. Bakalov et al., Phys. Rev. Lett. 84 2350 (2000).

[15] V.I. Korobov, Z.-X. Zhong, Q.-L. Tian, Phys. Rev. A 92 052517 (2015).

[16] M. Hori et al., Phys. Rev. Lett. 96, 243401 (2006).

[17] M. Hori et al., Nature 475, 484 (2011).

[18] M. Hori, V.I. Korobov, Phys. Rev. A 81 062508 (2010).

[19] R. Pohl, Nature 466, 213 (2010).

[20] R.J. Hughes, B.I. Deutch, Phys. Rev. Lett. 69, 578 (1992).

[21] K.A. Olive et al., (Particle Data Group), Chin. Phys. C 38 090001 (2014).

[22] G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999).

[23] J.K. Thompson, S. Rainville, D.E. Pritchard, Nature 430, 58 (2004).

[24] S. Ulmer et al., Nature 524, 196 (2015).

[25] M. Ahmadi et al., Nature 529, 373 (2016).

[26] V.I. Korobov, Phys. Rev. A77, 042506 (2008).

[27] D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev. Lett. 100, 120801 (2008).

8

Part II

CUSP experiment for H Spectroscopy

1 CUSP experiment for H Spectroscopy

.

Double Cusp Magnet

Microwave Cavity

Sextupole MagnetH Detector

Figure 5: A schematic drawing of the CUSP experiment with the double cusp magnet for H groundstate hyperfine spectroscopy.

Figure 5 shows the basic concept of the CUSP experiment to perform the ground state hyperfinetransition spectroscopy of H atoms. Cold H atoms are synthesized in the double cusp magnet anda spin-polarized H beam in low field seeking states (LFS) is guided along the axis, passing themicrowave cavity, the sextupole magnet, and finally being detected by the H detector.

1.1 Experimental Setup

In order to realize this project, we have constructed the experimental setup shown in fig. 6. An-tiprotons from the AD is injected and trapped in MUSASHI (antiproton accumulator) via theRFQD (Radio Frequency Quadrupole Decelerator), which decelerates 5.3 MeV antiprotons downto ⇠100 keV with the e�cincy of ⇠30%. In MUSASHI, trapped antiprotons are cooled, radiallycompressed, and finally transported to the double cusp maget. In the double cusp magnet, an-tiprotons are mixed with preloaded positrons to synthesize H atoms. The ASACUSA micromegastracker (AMT) is installed in the double cusp magnet to reconstruct the annihilation position ofantiprotons inside the cusp magnet. The field ionizer in the downstream of the double cusp magnet(to be referred to as FID hereafter) can field-ionize H atoms as low as n⇠12. The microwave (MW)cavity induces spin-flip transitions coverting H atoms in LFS to high field seeking states (HFS),which is analysed by the sextupole magnet. The antihydrogen detector monitors H atoms arrivingat the end of the equipment.

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Figure 6: The whole view of the CUSP experiment setup.

1.1.1 Double cusp magnet

In 2014, we developed a new superconducting magnet called “double cusp” magnet which increasesthe intensity and the spin-polarization of the H beam and also reduces the leak field near themicrowave cavity. The new magnet has a large bore diameter so that the AMT (see Sec.1.1.2) isinstalled between the magnet bore and the cold bore where the cusp MRE is housed.

Figure 7 (a) schematically shows the configuration of the MRE and the double cusp magnet,which consists of two sets of the anti-Helmholtz coils. The current directions of two coils at thecenter are the same, and the current directions of the other two coils on both sides are oppositefrom the central ones. Figure 7 (b) shows the on-axis magnetic field distribution of the double cuspmagnetic field. The double cusp magnet yields an octupolar magnetic field, and so the magneticfield decreases quickly outside of the magnet. The magnetic field on axis has one positive maximumpeak at the center, two small negative peaks on both sides, and two points of ~B = 0.

1.1.2 ASACUSA Micromegas Tracker - AMT

In 2014, the Asacusa collaboration installed and commissioned a tracking new detector, the ASACUSAMicromegas Tracker (AMT, Micromegas = Micro-MEshGaseous Structure), for detecting and re-constructing the antiproton and antihydrogen annihilations in the cusp trap in three dimensionswith a resolution of � ⇡ 1 cm.

The AMT detector is described in detail in [8]. Shortly, it consists out of two curved gaseousdetector layers using micromegas technology. Each layer is formed as a half cylinder, with a length

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Figure 7: (a) A schematic configuration of the double cusp magnet and the MRE. (b) The on-axismagnetic field distribution along z-direction.

of 413 mm and radii of 78.5 mm and 88.5 mm, respectively. They are mounted concentrically withthe multi-ring electrodes (MRE) of the CUSP trap, covering the upper half of the trapping region.A schematic overview of the cylindrical AMT detector is shown in Figure 8.

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Figure 8: Schematic view of the ASACUSA Micromegas tracker detector.

Test and z-axis calibration of the AMT In order to calibrate the z-axis of the AMT withthe position of the CUSP trap, antiprotons have been trapped on-axis at di↵erent z-positions byapplying corresponding electrostatic potentials to the MRE. A fraction of the trapped antiprotonsannihilate with the rest gas in the trap. The AMT recorded the annihilation events occuring duringthe trapping. Figure 9 shows the z-positions of the reconstructed annihilation events seen by theAMT (lower graph), together with the corresponding MRE potentials (upper graph).

By fitting the AMT-data with Gaussians, an agreement with the potential minima within thefit error is found.

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Test of the XY-resolution of the AMT We also tested XY-resolution of the AMT. i.e. ifannihilations at the MRE wall can be discriminated from annihilations at the trap center.

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During the so called ”slow extraction”, antiprotons trapped, cooled and extracted from theMUSASHI trap were transported towards and through the double-CUSP trap, while being guidedby the double-cusp magnetic field. During this procedure the MRE electrodes were held at groundwhile the double-CUSP magnetic field was at nominal strength. Depending on their initial condi-

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tions, a fraction of the antiprotons would stay on axis and another fraction of antiprotons wouldbe guided towards the B

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= 0 T point of the double-cusp magnetic field lines until they reach theMRE electrodes which leads to annihilation events at Z ' �12 cm axial coordinate. Figure 10ashows the summed up XY postions of the annihilation events of 41 slow extractions. The annihi-lations form a circular band along the ring electrodes. Because of the AMT shape (half-cylinder),annihilation events taking place on the upper half of the MRE are preferentially detected.

In contrast, figure 10b shows the reconstructed annihilation events of a antiproton life timemeasurement. Antiprotons were trapped on-axis inside the MRE electrode for 300 seconds using aharmonic potential.

1.1.3 Field Ionizer Downstream FID

The field ionizer downstream of the double cusp magnet (FID) is installed to evaluate the principalquantum number of H atoms. The FID consists of two parallel meshes orientated perpendicular tothe beam propagation axis and separated by a gap of 10 mm. They have been tested with a voltagedi↵erence of up to �U=20 kV (±10 kV) under ultra high vacuum conditions. The generatedelectrical field is su�ciently homogeneous across the full acceptance of the HFS spectrometer (opendiameter of 100 mm) in order to allow for the unambiguous suppression of quantum states above achosen principal quantum number (n). For instance, a bias of ⇡ ±8.7 kV produces a field strengthof 17.4 kV/cm, which is su�cient to ionize states with n �12. A picture of the two meshes of thefield ionizer is shown in Fig. 11.

Additionally, two retractable blockers for the central beam component have been installed afew centimeters downstream of the field ionizer. The central beam component is expected to beless polarized, and also the selection strength of the superconducting sextupole magnet is weakestat the centre, where the B-field gradients are smallest. One of the blockers consists of a silicondetector (planar implanted passivated silicon) which is sensitive to antihydrogen annihilations.This new active beam blocker has not been used during antihydrogen production in the 2014 run,however, during an antiproton life-time measurement a decay curve, by pion detection, could berecorded. This indicated that this new device is well suited to improve the e�ciency for providinga normalization count rate for the antihydrogen beam production.

Figure 11: Picture of the field ionizer meshes in the new vacuum chamber between cusp trap andcavity.

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1.1.4 H Detector

Figure 12 shows the drawing of the antihydrogen beam detector which consists of a 2D positionsensitive BGO calorimeter and a hodoscope. The BGO calorimeter consists of a 90 mm� and 5 mmthick BGO crystal, 4 ⇥ 64 channel multi-anode PMTs and QDCs. The hodoscope consists of twolayers of 32 plastic scintillator bars with SiPMs mounted on both ends. When an H atom hits theBGO, energetic pions are emitted from its annihilation point. The BGO calorimeter measures thedeposited energy of these pions to the BGO crystal. The inner and outer layers of the hodoscopecombined with the annihilation point on the BGO determine the pion tracks.

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Figure 12: The drawing of the antihydrogen beam detector.

2D position sensitive BGO calorimeter The deposited energy E to the BGO was calibratedby comparing the measured energy deposition spectrum of cosmics with that obtained with theGeant4 simulation.

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Figure 13 (a) shows a typical cosmic event with two tracks. We defined the hit position inthe BGO as the center of the channel measuring the maximum charge. The red colored bars inthe hodoscope shows the hit bars. We define two angles, one is the angle from the horizontal line(labeled A) to the first track, ✓, and the other is the angle between the first and the second tracks,�✓. Fig. 13 (b) shows the correlation between ✓ and �✓. It is seen that there are strong correlationsfor �✓ ⇠180 degree, which is a peculiar feature for cosmics. By selectively remove such events, onecan remove the contribution of cosmics quite e�ciently. It is noted that the small peak appears ataround ✓ = 270� and �✓ = 30�. The cosmic gamma rays make this peak which is identified by theGeant4 simulation.

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Figure 14: (a) The count rate of cosmic ray events as a function of the energy deposition threshoudto the BGO calorimeter. The black and red symbols are without and with cut of the spheroidal“muon events” region in fig. 13(b). (b) The detection e�ciency of antiprotons as a function of thedeposition energy deposition threshould. It is seen that the detection e�ciency is ⇠60% with theenergy deposition threshould of 20 MeV and the “muon events”cut.

Figure 14 (a) shows the count rate of cosmic ray events measured by the antihydrogen beamdetector as a function of the energy threshold in the BGO. Blue and red symbols are the resultswithout and with the event cut, respectively. For example, it is 0.004 counts/s at 20 MeV. Fig-ure 14 (b) shows the detection e�ciency of antiprotons arriving at the BGO crystal. as a functionof the energy threshold in the BGO. Symbols are the same as in Fig. 14 (a). At 20 MeV, thedetection e�ciency is 0.6.

Tracking Detector The 2D position sensitive BGO calorimeter is surrounded by a two layeredhodoscope for tracking the charged annihilation products (mainly pions). The tracking detectoris supported by a 1 mm thick stainless steel pipe (see fig. 12). Both layers are composed ofeight removable panels containing four 5 mm thick scintillating bars (material EJ-200) each. Thediameter of the inner layer is 200 mm, the outer one is 350 mm. The inner bars have a length of

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Figure 15: Preliminary time of flight distributions for the outer hodoscope (right) and for thecombined time of flight information of inner and outer hodoscope (left) for cosmic background andantiproton data. The peak of the antiproton distribution is not centered exactly around zero dueto the o↵ center hit position of the abtiprotons on the BGO.

30 cm and a width of 2 cm, while the outer ones have a length of 45 cm and are 3.5 cm wide. Thehodoscope detector covers 50% of the solid angle for annihilation products coming from the centerof the BGO disc.

Light guides are glued to both ends of the scintillating bars matching the detecting area of thetwo attached KETEK 3350TS silicon photomultipliers (SiPMs) which are operated in series to in-crease light collection. The SiPM detectors are read out using self developed front-end electronics [6]and CAEN V1742 waveform digitisers.

The individual bars are wrapped in aluminium foil before being wrapped together in light-blocking foil to ensure light tightness. The ends of the bars are covered in black tape and anadditional layer of black latex paint to secure the tape and fill small possible holes in the wrapping.

Before the beam time 2016, several upgrades of the hodoscope detector have been carried outat the SMI lab, most importantly, the improvement of the time of flight resolution. A relativisticparticle with a velocity close to the speed of light needs approximately 1 ns to travel a distanceof 30 cm. With a time of flight resolution of < 600 ps it is therefore possible to separate eventsstemming from the inside of the hodoscope from those passing the detector from outside such ascosmic particles, the main background source.

A detailed study of light guide wrapping materials has been done, resulting in the removal ofthe reflective paint on the light guides used in the 2015 setup which attenuated the signals heavily.Finally, the light guides where wrapped in aluminium foil. Compared to 2015, approximately tentimes higher signals were achieved.

The time of flight resolution was measured with cosmic particles in the laboratory by calculatingthe mean time (between up and downstream SiPM timestamps) di↵erence of two bars resulting in551±75 ps FWHM for outer bars and 497±73 ps for inner bars [7]. This was remeasured in thecomplete setup at the AD during beam time this year, see figure 15. The results show a slightlyhigher FWHM of about 900 ps which is under investigation but can most likely be explained bythe longer signal cables in the full setup and di↵erences in the data acquisition system compared tothe laboratory setup. The mean time di↵erence between pions and cosmics amounts to 0.90± 0.01ns in accordance with a relativistic particle traversing the hodoscope vertically.

The two sided read-out of the scintillating bars also allows the determination of the hit positionin beam direction. For the outer hodoscope bars the resolution was determined to be 73±3 mmFWHM and for the inner bars 59±4 mm FWHM [7]. This enables the possibility of rudimentarytracking in 3D in order to discriminate between straight tracks created by cosmics and tracks witha kink due to antiproton annihilations.

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Figure 16: Picture of the new amplifier read-out boards for the hodsocope.

Furthermore, an update of the self-developed read-out electronics [6] has been done resultingin a more compact and more robust setup, see figure 16. Instead of only two channel per boardand therefore 64 amplifier boards for the whole hodoscope as in the previous setup, there are noweight bigger modules with 16 channels each with a protecting safeguard. The signal cables havebeen equipped with more stable connectors and the twisted power cables of the SiPMs have beenreplaced by longer ones, allowing the electronics to be further away from the detector and easieraccess. The slow control of the amplifier boards, i.e. the settings of the gain and threshold, is nowdone by an on-board Arduino microcontroller on each module, making it more e�cient and robust.

The data acquisition system has been improved by retrieving a more accurate event timestamp inrespect to the mixing signal using the CAEN waveform digitizers. The resolution of the timestampsis about 10 ns.

Analysis The previous, simple analysis consisted of hard cuts on the energy deposit in the BGO(energy deposit > 20 MeV) and on the number of hodoscope bar hits. It has been improved byincorporating two dimensional tracking and the time of flight information of the hodoscope.

First, cuts on the mean time between up- and downstream timestamps and on the z-positionfor all hodoscope hits are applied in order to remove random coincidences. Then the most probabletracks based on the event hit patterns are found, excluding ”orphan” hits i.e. a hit in only one ofthe two layers. Found events with just one track are rejected as background.

Subsequently, the time of flight of the event is calculated as follows: for each track the average ofthe mean times of outer and inner hodoscope are calculated and the mean of di↵erences between alltracks is determined. This is then compared via P-value test with the time of flight distributionsdeduced from cosmic background measurements during ASACUSA beam time breaks and slowextractions of antiprotons from the MUSASHI to the detector. By combining the timing informationof outer and inner layer instead of only using the outer one, the overlap of the distributions becomessmaller by a factor of ⇡0.6.

Background rejection has been tested with two weeks of cosmic data, resulting in 0.4% falsepositives which corresponds to an estimated background rate of 0.004/s on the H detector.

Three dimensional tracking has been tested but the improvement in cosmic rejection turnedout to be almost negligible due to the poor resolution in z-direction mentioned above. A better z-resolution would enable more e�cient tracking in 3D and therefore also the possibility to distinguishbetween annihilations on the BGO and those in its direct vicinity. Thus, a possible hardwareupgrade is under investigation (see section 1.1.5).

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1.1.5 Antihydrogen Detector upgrade and antiproton annihilation studies

The position resolution of the annihilation detector along the beam axis will be improved byadding a scintillating fiber detector which will suppress the background from H annihilation on thebeam pipe. We also plan to conduct a systematic study of the charged multiplicity distributionin antiproton-nucleus annihilation on various materials, for which the slow extracted beam fromMUSASHI is ideally suited. The current BGO detector will be replaced by a high resolutionannihilation vertex detector for these measurements.

Antiproton-nucleus annihilation The multiplicity distribution of charged annihilation prod-ucts (such as pions, protons and nuclear fragments) is not well known for antiprotons annihilatingat rest on nuclei. This information is an essential ingredient to Monte Carlo simulations (such asGEANT4), to model the background contribution in antihydrogen and low energy antiproton expe-riments. The current Monte Carlo simulations are performed with the CHIPS [9], the FRITIOF [10]or the FLUKA [11] packages. The former two were developed for high energy hadronic interactions.They are based on the interaction between parton constituents and are extrapolated to low energyantiproton annihilation (in spite of the fact that the low energy annihilation mechanism is still notunderstood in detail). FLUKA models the hadronic interaction at a higher level, i.e. in terms ofresonance production and decay

Figure 17: Left: charged annihilation multiplicities for stopping antiprotons in copper and gold(dots with error bars), compared with Monte Carlo predictions from CHIPS, FTFP (FRITIOF) andFLUKA. Right: average multiplicities of minimum ionizing particles (top) and nuclear fragments(bottom) for copper, silver and gold, compared with Monte Carlo predictions (data obtained withnuclear emulsions, see [14]).

Until very recently these models could not be verified, due to the absence of annihilation data.A few data points on antiproton annihilation at rest from experiments at the AD are now available[12–14]. It is fair to say that none of the models is able to reproduce the data. For example, fig. 17(left) shows the charged multiplicity distribution for copper and gold, and fig. 17 (right) the averagecharged multiplicity for copper, silver and gold, for minimum ionizing particles (essentially pions)and heavily ionizing annihilation products (p, ↵ and nuclear fragments). FRITIOF (also calledFTFP) is in clear disagreement and in particular grossly underestimates the number of nuclearfragments (also observed in [12]), CHIPS does not reproduce the distribution of heavy products.

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FLUKA performs somewhat better, which is perhaps not surprising since it models the interactionat the level of hadrons.

We intend to measure the multiplicity of minimum ionizing particles and that of nuclear frag-ments for antiprotons annihilating at rest on various elements across the periodic table. This will beperformed by annihilating very low energy antiprotons on thin (⇠ 5 µm) foils of various materials,such as Be (Z = 4), C (12), Ti (22), Cu (29), Mo (42), Sn (50), W (74) and Pb (82). The position ofthe annihilation vertex will be determined with a precision in the 10 µm range by a high resolutionpixel detector capable of reconstructing the tracks of the annihilation pions and of measuring theenergy deposited by nuclear fragments. We plan to use the Timepix3 detector obtained from theMedipix3 Collaboration, such as the one recently tested by AEgIS [15]. The Timepix3 is an ASIChybrid detector module made of 256 ⇥ 256 square 55 ⇥ 55 µm2 pixels. The detector thickness is675 µm, the dynamic range 4 – 500 keV/pixel and the time resolution 1.6 ns.

Figure 18: Left: annihilation of a 1 keV antiproton on the surface of the Timepix3 detector. Thepicture shows the emission of three minimum ionizing particles (pions) and of a nuclear fragment.The large energy deposit (Bragg peak) is clearly visible at the end of the track [15]. Right: re-construction of the annihilation vertex on the surface of a foil located in front of the Timepix3detector [16].

Figure 18 shows the typical energy deposited by a 1 keV antiproton annihilating on the surfaceof the detector. Annihilation on a thin foil placed close to the detector has also been tested byAEgIS and data are currently being analyzed. Preliminary results show that the annihilation vertexcan be located with a precision of 25 µm. Operation in vacuum has been tested at the level of10�7 mbar. For the operation in our experiment, the detector will be placed in an OVC enclosureseparated from the UHV region by the foil under investigation (fig. 19 below). An antiprotonrate of a few 100 sub-keV antiprotons, extracted from the MUSASHI trap during 10 s after everyAD cycle, should be su�cient to obtain large statistical samples, even with the modest size of thecurrent detector (14 ⇥ 14 mm2. One of our collaborators is initiating discussions with the Medipix3collaboration to design the readout board suited for insertion into our apparatus, and to perhapsprocure a larger detector than the current one. Swapping material sheets requires to break thelocal vacuum and hence 8 AD shifts will be needed to complete these measurements, together withthe overall setup change a total of 2 weeks of beam time will be necessary.

Scintillating fiber detector As mentioned earlier, the current bars of the annihilation detectorprovide a modest position resolution of about 7 and 6 cm for the outer and inner layers, respectively.We therefore intend to upgrade the annihilation detector by adding two layers of scintillating fibers,

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providing a resolution of typically 2 mm along the beam direction. This is su�cient to identifythe annihilation of H atoms on the carbon layer of the BGO detector. A sketch of the layout isshown in fig. 19. We plan to use square fibers from Kuraray (SCSF-78) with the light emissionpeaked at 450 nm, a decay time of 2.8 ns and an attenuation length in the order of 4 m. Thefibers are wound in spirals around the detector axis with an outer spiral detector diameter of 250mm (made of 2 ⇥ 2 mm2 fibers) placed behind the inner scintillator array and a diameter of 150mm (made of 1 ⇥ 1 mm2 fibers) placed around the beam pipe. We estimate that we would need32 fibers (each covering 5 turns) for the outer layer and 32 fibers (each covering 8 turns) for theinner layer. Each fiber will be read out by SiPMs at each end and is digitized with the SMI-IFES(intelligent front-end electronics ) board [6] resulting in an LVDS (low voltage di↵erential signal)time-over-threshold output to allow for time walk corrections in order to obtain an accurate hitposition along the fiber.

Figure 19: Upgraded annihilation hodoscope equipped with fibers and the Timepix3 detector forannihilation studies. (The Timepix will be replaced by the current BGO detector for H studies.)1-Timepix3 detector, 2-thin foil to study the annihilation multiplicity, 3-vacuum pipe, 4-outerscintillator array, 5-inner scintillator array, 6-2 mm and 1mm diameter fiber detectors.

Antiproton extraction results As mentioned in the previous section, direct extractions ofsingle stacks of antiprotons with 150 eV from the MUSASHI trap to the antihydrogen detectorhave been carried out during beam time. Two shifts were spent and a total number of about 13100events were recorded with roughly 160 events per extraction.

Figure 20 shows the angular distributions for cosmic data (left) and antiproton data (right) incomparison with Geant4 simulations. The distribution for antiprotons is not flat as expected dueto the o↵ center hit position of the antiprotons on the BGO.

Figure 21 shows a comparison of number of tracks and bar hits per event for antiproton extrac-tion data and cosmic background data where a track is defined as a hit on the BGO and a hit inthe inner and outer hodoscope layer.

1.2 Adiabatic transport of antiprotons

The MUSASHI trap upstream of the double cusp trap (see fig. 6) accumulates, cools, and com-presses antiprotons. After stacking several AD shots, the cooled antiprotons are pulse-extractedand transported toward the double cusp trap to be mixed with a preloaded positron plasma tosynthesize H atoms. In order to prepare a large number of cold H atoms, the following conditionsshould be fulfilled, i.e.,

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Figure 20: Angular distribution: bar number versus normalized counts for cosmic runs (left) andantiproton extractions (right) in comparison with simulations.

Figure 21: Preliminary histograms of number of tracks (blue) and bar multiplicity (green) perevent for antiproton (left) and cosmic events (right). A track is defined as one hit in BGO, innerand outer hodoscope.

1. preparation of a cold antiproton cloud in the MUSASHI trap,

2. minimization of the antiproton heatup during its extraction from the MUSASHI trap,

3. realization of an adiabatic transport of antiprotons from the MUSASHI trap to the doublecusp trap,

4. minimization of the antiproton heatup during its retrapping in the double cusp trap,

5. minimization of the kinetic energy of antirpotons in the positron plasma by tuning the po-tential level of the positron cloud.

One of the most important achievements in 2016 was the realization of the item 3, adiabatictransport. At the same time, we have also succeeded in improving the situation of the other items.

In order to synthesize cold H atoms, a monoenergetic antiproton beam is injected in a positroncloud with its energy high enough so that antiprotons can be mixed but low enough so that it doesnot heat up the positron cloud.

1.2.1 Optimization of extraction scheme for better initial energy distribution

Antiprotons from the AD via the RFQD are accumulated in the MUSASHI trap for cooling andhandling of antiprotons. Typically, 3⇥ 106 antiprotons by stacking 4 AD shots were accumulated,cooled by 108 electrons which are self-cooled via synchrotron radiation. After trapped antiprotons

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are cooled, electrons are kicked out by opening the trap for 200 ns still keeping antiprotons intact.By repeating this process two times, the number of electrons were reduced to 5 ⇥ 106. Then thecooled antiprotons are radially compressed with a rotating electric field at 247 kHz [3].

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Figure 22: (a), (b) Potential configurations to extract 20 eV antiprotons used in 2015 and 2016,respectively. The black dotted lines show potentials to trap antiprotons, and the solid purple linesshow potentials to extract antiprotons. Trapped antiprotons were extracted as a pulsed antiprotonbeam by quickly switching the potential from the black dotted line to the purple solid line. (c) Azoomed view of the region where antiprotons are trapped. In 2016, the potential variation in theantiproton trapping region during the switching where trapped antiprotons locate is comparable toor even smaller than the antiproton temperature.

The potential distribution was modified from the catching well to an ”extraction” well, whichwas kept for 10 s so that remaining electrons still in the trap cooled antiprotons which could havebeen heated by the RF for antiproton compression and the potential manipulation. The remainingelectrons were removed by quickly switching the potential from trapping to extraction for 500 nsfor 6 times before the antiproton extraction. This procedure is essential to stably synthesize Hatoms. Actually, electrons contaminating antiprotons in the nested trap accelerate the separationof antiprotons from positrons.

The energy of the extracted antiproton beam is varied by varying the float voltage applied tothe extraction well keeping the well shape of the antiproton trapping region. Figures 22(a) and (b)show examples of the potential distributions for the float voltage of -20 V used in 2015 and 2016,respectively. The black dotted lines and the purple solid lines show configurations for trappingand extraction, respectively. As is seen in fig. 22(c), the potential di↵erence for the 2016 potentialbetween the trapping and extraction modes is much less than the antiproton temperature in theMUSASHI trap, i.e., the extraction step does not a↵ect the antiproton temperature in the cusptrap (Item 2). On the other hand, if we use the 2015 potential, the energy width the extractedantiprotons can be as large as ⇠ 1 eV even if the antiproton temperature in the MUSASHI trap isassumed to be 0.2 eV.

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Figure 23: The electric potential and magnetic field distribution on axis to measure the energydistribution of antiprotons. Antiprotons which overcome the potential barriers at z ⇠ 700 mmreach a gate valve at z ⇠ 1925 mm and annihilate.

1.2.2 Energy distribution at the exit of the MUSASHI trap

The axial energy distribution of antiprotons extracted from the MUSASHI trap was measured⇠700 mm downsream from the trapping region. Figures 23 (a) and (b) show the distributions ofthe electrostatic potential and the magnetic field strength, respectively. Antiprotons overcome thebarrier at ⇠700 mm reached a gate valve (z ⇠ 1925 mm) and annihilated. Charged pions emittedduring the antiproton annihilations were detected by a plastic scintillator located near the gatevalve. An integrated axial energy distribution of antiprotons was obtained by counting the numberof annihilations as a function of the barrier height. Figure 24 shows such distributions for the floatvoltages of -1.5 V, -2.5 V, -10 V, and -20 V.

To evaluate the energy spread of the antiproton beam, the antiproton cloud in the MUSASHItrap was assumed to be in a thermal equilibrium at its temperature T , i.e.,

fp

(px

, py

, pz

) =1

(2⇡mkB

T )3/2exp

✓� 1

2mkB

T(p2

x

+ p2y

+ p2z

)

◆(3)

where kB

is the Boltzmann’s constant. The energy distribution is then given by

f✏

(✏)d✏ = 2

r✏

⇡

✓1

kB

T

◆3/2

exp

✓� ✏

kB

T

◆d✏ (4)

where ✏ = p2/2m. As is seen in fig.23, antiprotons trapped in a magnetic field of ⇠2.5 T areextracted toward the region with much weaker magnetic field, i.e., the transverse thermal motion isconverted to the longitudinal direction. Because of this, the energy distribution of the antiprotoncloud can be determinied by measuring the axial energy distribution at z ⇠ 700 mm.

23

1.5 V float

2.5 V float

10 V float

20 V float

1.2

1.0

0.8

0.6

0.4

0.2

00 5 10 15 20 25 30

Nor

mal

ized

ann

ihila

tion

coun

t [a.

u.]

On axis barrier potential [V]

1.5 V floatsimulation

Figure 24: Axial energy distributions of antiprotons measured at ⇠700 mm downstream for thecenter of the MUSASHI trap (see fig. 23(a) for various float voltages of -1.5, -2.5, 10, and -20 V.Filled circles, open circles, filled squares, open squares correspond to 1.5, 2.5, 10, and 20 V, respec-tively. The red starts are the result of the simulation assuming the antiproton temperature in theMUSASHI trap to be 0.4 eV. Curves fitted using eq.5 are also shown.

When the float voltage of the MUSASHI trap is Vfl

, the energy distribution given by eq. 4 isshifted by the corresponding amount. The integrated energy distribution, F (E), of the extractedantiprotons is then given by

F (E) = C

1�

Erf

sE � eV

fl

kB

T

!� 2

sE � eV

fl

⇡kB

Texp

✓�E � eV

fl

kB

T

◆!!(5)

where C is a normalization factor. The best fitted results are shown by solid lines in fig. 24, andthe fitted parameters are summarized in Tab. 3. It is seen that the measured energy widths getlarger for �10 V and �20 V extractions as compared with �1.5 V and �2.5 V extractions.

Float voltage [V] 3kB

T/2 [eV] �2 / ndf

�1.5 0.6± 0.1 0.85�2.5 0.6± 0.1 0.85�10 0.8± 0.2 11.7�20 0.9± 0.2 2.55

Table 3: Summary of fitting results for various float voltages.

In order to evaluate the temperature of the antiproton cloud in the MUSASHI trap, antipro-

24

ton trajectories were simulated by varying the barrier height for the fixed float voltage of �1.5 V.In the simulations, the initial position is assumed to be uniformly distributed in an spheroid ofminor radius of 5 mm and major radius of 50 mm. Trajectories of 10,000 particles were simu-lated ignoring the interaction between particles. The radial barrier height variation is taken intoaccount automatically. Likelihood function is calculated by multiplying probability at each datapoint, assuming Gauss distribution whose mean and sigma correspond to measured value and itsuncertainty, respectively. The normalization factor C and the float voltage V

fl

and the temperatureT were the fit parameters. The best fitted simulation results are shown by the red stars in fig. 24,which reproduces the observation quite well. By this way, the temperature of the antiproton cloudin the MUSASHI trap is estimated to be

3

2kB

T = 0.4+0.1

�0.1

eV (68%C.L.). (6)

1.2.3 Adiabatic transportation of ps

In order to transport antiprotons from the MUSASHI trap to the cusp trap adiabatically, threepulsed coils, the coil T, coil A and coil B were installed along the beamline, the locations of whichare shown in fig. 25 by the vertical blue and light blue strips, the widths of which correspond to thecoil lengths. The thin colored curves in fig. 25 show the magnetic field lines from the MUSASHImagnet to the double cusp magnet, the center of which is located at ⇠3000 mm. It is seen thatthe magnetic field lines are parallel to the beamline in the MUSASHI magnet and also almostparallel around the antihydrogen production region where positrons are confined (⇠2750 mm, seealso fig. 28). The thick black lines show calculated trajectories of 1.5 eV antiprotons with their initalradial positions of 0.4, 0.8, 1.2, 1.6, and 2.0 mm from the axis. It is clearly seen that antiprotonsfollow the magnetic field lines for all the trajectories, and are transported into the double cuspmagnet.

distance from the center of the MUSASHI trap [mm]2000 2100 2200 2300 2400 2500 2600 2700 2800

pote

ntia

l on

axis

[V]

-8

-6

-4

-2

0

2

4

distance from the center of the MUSASHI trap [mm]2000 2100 2200 2300 2400 2500 2600 2700 2800

Bz o

n ax

is [T

]

0

0.4

0.8

1.2

1.6

2

(a)

(b)

Figure 26: (a) potential and (b) magnetic field distributions used to measure the energy distributionof antiprotons in the double cusp trap. Antiprotons overcoming the potential barrier at z ⇠ 2600mm are trapped.

25

Figure 25: The thin colored lines show the magnetic field lines for 0 < r < 3 mm The black solidlines are calculated trajectories of antiprotons at 1.5 eV. Vertical highlighted strips show the axialpositions of the MUSASHI magnet, coil T, coil A, and coil B from left to right.

The axial energy distribution of antiprotons in the double cusp trap located 2.6 m downstreamfrom the antiproton trap was measured to inspect the transport feature of antiprotons. Figure 26shows the potential and magnetic field configurations used to measure the axial energy distributionof antiprotons extracted with the float voltage of 1.5 V. About 10 s after the trapping, antiprotonswere slowly extracted to downstream. Most of them are guided along the diverging magnetic fieldline, and annihilated on the innerwall of the MRE electrode located at the B

z

=0 plane located at⇠2880 mm. The annihilation signals were detected by the AMT scintillators surrounding the doublecusp trap. The axial energy distribution was obtained from the trapped number of antiprotonscounted by AMT scintillators as a function of the potential barrier.

26

- barrier voltage on axis [V]0 5 10 15 20 25 30

norm

aliz

ed a

nnih

ilatio

n co

unt [

a.u.

]

0

0.2

0.4

0.6

0.8

1

1.21.5 V float

2.5 V float

10 V float

20 V float

Figure 27: The integrated axial energy distributions for various float voltages of -1.5, -2.5, -10, -20V at z ⇠ 2640 mm. Filled circles, open circles, filled squares, and open squares correspond to -1.5,-2.5, -10, and -20 V, respectively. Fitted curves with eq. 5 are also shown.

Float voltage [V] 3kB

T/2 [eV] �2 / ndf

-1.5 0.3± 0.1 1.31-2.5 0.3± 0.1 0.18-10 2.1± 0.3 2.57-20 4.4± 0.4 5.74

Table 4: Summary of fitting results for various float voltages.

Figure 27 shows the number of trapped antiprotons as a function of the barrier depth forantiprotons transported with four di↵erent float voltages. Fitting results are summarized in Tab. 4.It is noted that antiproton clouds with the kinetic energy as low as ⇠1.5 eV were successfullytransported from the MUSASHI magnet to the double cusp magnet traveling more than 2.5 m, andtrapped with no axial energy broadening. As can be imagined also from fig. 24, the axial energydistribution of antiprtons with the float voltages of -10 V and -20 V antiprotons are found to bemuch broader than the antiproton temperature in the MUSASHI trap, i.e., the transports are notat all adiabatic, and the measured axial energies are much lower than the total energies. On theother hand, the axial energy spreads of the antiprotons with the float voltages of -1.5 V and -2.5 Vwere comparable to the evaluated antiproton temperature in the MUSASHI trap (see eq. 6).

The temperature of antiprotons in the MUSASHI trap was evaluated using the same simulationcode trying to reproduce fig. 27 and Table 4 for the float voltage of -1.5 V. In doing so, the antiprotoncatching timing used for the simulation was selected to be the same as the experimental one. Thepotential barrier shown in fig. 26(a) was closed 155 µs after the extraction from the MUSASHItrap.

Using the maximum likelihood method, the antiproton temperature in the MUSASHI trap wasevaluated to be

3

2kB

T = 0.3+0.1

�0.1

eV (68%C.L.), (7)

which is consistent with eq. 6.

27

In other words, we can now inject antiprotons with high e�ciency into the positron cloudwithout heating the positron cloud very much. Actually, the axial energy spread was reduced abouta factor of 10 as compared with the results in 2015. The typical number of trapped antiprotons inthe double cusp trap was 6⇥ 105 with the trapping e�ciency of about 20% at this very low energyof 1.5 eV.

1.3 CUSP experiment for Antihydrogen Spectroscopy

1.3.1 Synthesis of H in the double-cusp trap

After the successful transport of ⇠1.5 eV antiprotons, we proceeded to the H atom synthesisin the double-cusp magnet. Figure 28(a) schematically shows the cross section of the multiplering electrode (MRE) which is housed in an ultra-high vacuum bore. A 3D tracking detector,ASACUSA Micromegas Tracker (AMT), surrounds the bore, which consists of two half-cylinderlayers of Micromegas and one full cylindrical layer of scintillator bars.

Figures 28(b) and (c) show distributions of electrostatic potential and field strength for synthesisand detection of H atoms, respectively. We prepared an electrostatic well with an electric field muchstronger than the field around the nested trap near the center of the double cusp where the on-axismagnetic field reaches its maximum (see Fig. 28(d)). This field ionizer in the double cusp mangetis referred to as FIC (field ionizer in the cusp). The electric field here can field-ionize H atomswith n > 44 [4, 5]. Field-ionized antiprotons were accumulated in the field ionization (FI) well,and were released from time to time to monitor how the H atom production rate varies since themixing of antiprotons and positrons. Antiprotons released from the FI trap annihilated and weremonitored by scintillators of the AMT. Due to a geometrical constraint, the active area of theAMT covers only the mixing region and the FI well as shown in Fig. 28(a). After several cyclesof field-ionization and dumping of antiprotons, the nested trap configuration was transformed asimple trap configuration so that antiprotons remained in the nested trap were extracted slowlytoward the B

z

=0 plane and the annihilation number was counted by the AMT scintillators.In the following experiments, 6 ⇥ 105 antiprotons were trapped in the nested well where a

positron plasma with a density of 6⇥ 108cm�3 was preloaded.

28

z [m]-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

B [T

]

-2-10123

[V]

φ

-300

-200

-100

0

100

200

300

p beam from the MUSASHI

_

AMT scintillators

H detector_

(a)

(b)

(d)

(c)

z [m]0-0.4 -0.2 0.40.2

Mixing Region

FIC

0

40

80

E [V

/cm

]

×ÓÏ

×ÓÔ

×Ï

Ô

Ï

0

5

-5

-10

-15

Figure 28: (a) The MRE of the double cusp trap is schematically shown. The axial position of theAMT detector is also shown. (b) The distribution of electrostatic potential on the axis is shown.The mixing region (the nested trap) and the FIC are shown. An enlarged view of the nested trappotential distribution is shown on the left top corner. (c) The blue line shows electric field strengthalong the axis with the FIC on. The black line corresponds to the case with the FIC o↵. (d) Thedistribution of magnetic field strength by the double cusp magnet. Corresponding regions to themixing region and the field ionization well are also shown.

The time evolution of the number of field ionized antiprotons is shown in Figs. 29(a) and (b)for the antiproton transport energies of 20 eV and 1.5 eV, respectively. Figures 29(c) and (d) showcount rates corresponding to (a) and (b). The positron densities were almost the same, around6 ⇥ 108cm�3 for both cases. It is seen that the H production rate is quite high immediately afterthe mixing in both cases (t < 0.7 s). In Fig. 29(c) for the 20 eV injection, the second peak followsat around 5 s. On the other hand, the production rate for the 1.5 eV case (Figure 29(d)) decreasedmonotonically. As is discussed in Sec. 1.2, the 1.5 eV antiprotons were successfully transportedfrom the MUSASHI trap to the double cusp trap without increasing the axial energy width, whichsuppressed heating of the positron plasma. Around 60% of the field-ionized H events was observed

29

(a) (b)

Fiel

d Io

nize

d co

unts

Time after injection [s]5 15 2510 200

100

50

200

150

250

Rat

e of

fiel

d Io

nize

d co

unt [

/s]

Time after injection [s]5 15 2510 200

100

50

200

150

250

Rat

e of

fiel

d Io

nize

d co

unt [

/s]

Time after injection [s]5 15 2510 200

100

50

200

150

250

Fiel

d Io

nize

d co

unts

Time after injection [s]5 15 2510 200

100

50

200

150

250

(c) (d)

Figure 29: (a) and (b) show the number of H atoms field-ionized during the time interval shownby the width of the histogram for the transport energy of 20 eV (data from 2015) and 1.5 eV (datafrom 2016), respectively. The positron densities (n

e

+) were 6 ⇥ 108cm�3 for both cases. (c) and(d) replot the data of (a) and (b) converting the vertical axis into the production rate of (a) and(b), respectively.

in the first 0.7 s. In the case of 20 eV transportation, this number was about 20%. This temporallocalization improves the signal-to-noise (S/N) ratio of the H detector considerably.

Figure 30(a) plots the number of annihilations counted by the AMT scintillators (two or morecoincidences between scintillator bars were required) with the same bin size as in fig. 29. Backgrounddue to antiproton annihilations with residual gas atoms/molecules were subtracted from the data.Figure 30(b) plots the same results converting the vertical axis into the count rate. The blue lineis the result when the FIC well was on, while red dotted line shows the case without the FIC well.Time profiles of these results are qualitatively similar to those shown in Fig. 29, i.e., a sharp peakat the first bin (t < 0.7 s), followed by long and continuous H production. It is noted however thatthe number of events in the first bin was 35–40% of the H events integrated over 25 s, which is 60%in the case of the FI measurement discussed above. The count of the AMT scintillator providedan additional information. When the FIC well was on, the count at the first bin decreased by 20%against the condition without the FI well, while counts in both cases were in good agreement att >0.7 s. It is noted that H atoms with n>61 or so would also be field ionized around z = -0.2 to-0.1 m before they reached the FIC well (see Fig. 28(c)), and most of the re-ionized antiprotons areexpected to escape toward the upstream and annihilate. The di↵erence of annihilation count atthe first bin might be due to antihydrogen atoms at higher n state at the beginning of the mixing.

In order to investigate the reason of the quick decrease of the H production, the upstreambarrier of the nested well was opened to the level of the e+ plasma potential as a function of thewaiting time since the start of the mixing. By this way, antiprotons interacting with positrons inthe nested trap were released during the well opening, and those which were kept in the nested

30

time [s]0 5 10 15 20 25

Cou

nt /

mix

ing

0

2000

4000

6000

8000

10000

12000

14000 w/o FI well

w/ FI well

time [s] 0 5 10 15 20 25

Cou

nt ra

te /

mix

ing

[s]

2000

4000

6000

8000

10000

12000

14000

16000

18000

0

w/o FI well

w/ FI well

(a) (b)

Figure 30: (a) Count per mixing by the AMT scintillators with double coincidence condition. Blueline is when the field ionization well was prepared. Red dotted line shows the case without the fieldionization well. (b) Count rate per mixing by the AMT scintillators.

trap had already localized either in the upper or lower part of the mixing region in the nested trap.The number of localized (separated) antiprotons were counted later. To our surprise, the ratio ofthe localized antiprotons were quite high as high as 90% even when the mixing time is 0.6 s, inaddition this ratio stayed almost constant for more than seveal seconds. The result implies that80–90% of antiprotons was quickly separated within 1 s or so, while 10–20% of antiprotons wascontinuously contacting with the e+ plasma.

As discussed in Sec. 1.1.4, an H detector was developed. Under the present analysis condition,the detection e�ciency was ⇠60%. The H detector was installed downstream of the double cusptrap via the external field ionizer in 2016. In this configuration, the solid angle coverage of thedetector was 0.02% of 4⇡.

Figure 31 shows the time evolution of counts by the H detector per mixing. During the mea-surement with the H detector, there was no FI well in the cusp. We applied a weak potential onthe FID in front of the H detector to reflect antiprotons escaping from the mixing region if any.The corresponding strength of the field will ionize antihydrogen atoms of n > 53. Backgroundwas estimated from runs with antiprotons trapped and cooled in the double cusp trap. Cosmicsand secondary particles produced by antiproton annihilation consisted background. As discussedin Sec. 1.1.4, the background rate was (4.3 ± 0.7) ⇥ 10�3 s�1. The red line in the figure indicatescorresponding expected background count. No strong peak at the first bin was recognized by theH detector like in the case of the AMT.

Assuming isotropic distribution of antihydrogen atoms in the nested trap, the expected numberof H atoms reaching the H detector was estimated using the number of antiprotons in the FIC,which is shown by the green solid line in Fig. 31. The black dashed line corresponds to the estimatednumber of H atoms by the AMT scintillators. Considering the fact that the detection e�ciencyof the H detector is ⇠60% (see sec. 1.1.4) when the energy deposition on the BGO is higher than20 MeV, both the FIC and AMT data were multiplied by 0.6. It is seen that the FIC measurementpredicts more count on the H detector in the first bin. Only 27% of the predicted count, however,were measured by the H detector. On the other hand, the number of events for t > 0.7s were moreor less consistent with each other.

The reason of the discrepancy at the first bin is under discussion.

AMT data during mixing The following two figures 32 and 33 show the annihilation eventsrecorded by the AMT during mixing, i.e. where antiprotons were injected into a previously prepared

31

time [s]0 5 10 15 20 25

Cou

nt /

mix

ing

0

0.2

0.4

0.6

0.8

1

1.2

1.4FIAMT sci.H det._

B.G.

Figure 31: Solid histogram shows count obtained by the H detector. Expected background areshown as red line. Green solid line shows count estimated from the FI measurement. Black dashedline is estimated count from the annihilation signals observed the AMT scintillators.

positron plasma. Fig. 32 shows the first three seconds of 108 accumulated mixing runs with similarconditions. The left part shows the XY-coordinate. The annihilations take place around r = 4 cm,which is consistent with annihilations at the MRE wall. The z positions range between z = -25 and-20 cm, thus overlapping with the region of the positron plasma.

-8

-6

-4

-2

0

2

4

6

8

yposi

tion

(cm

)

-8 -6 -4 -2 0 2 4 6 8

x position (cm)

0

5

10

15

20

0

1

2

3

4

5

6

7

radiu

s(c

m)

-35 -30 -25 -20 -15 -10 -5 0

z position (cm)

0

10

20

30

40

50

60

70

Figure 32: Annihilation events during the first three seconds of mixing. The left part shows thedistribution of the annihilation positions in the XY plane, the right part in the RZ plane.

15 seconds after injection, the annihilation is localized at z - 20 cm, where the downstreampotential minimum for the antiprotons is located (the upsteam potential minimum is outside of the

32

view of the AMT). Radially, the annihilation area is extended from 0 to 4 cm. This indicates, thatthe antiprotons are trapped at the potential minima, but are still interacting with the positroncloud to form antihydrogen.

-8

-6

-4

-2

0

2

4

6

8

yposi

tion

(cm

)

-8 -6 -4 -2 0 2 4 6 8

x position (cm)

0

5

10

15

20

0

1

2

3

4

5

6

7

radiu

s(c

m)

-35 -30 -25 -20 -15 -10 -5 0

z position (cm)

0

20

40

60

80

100

120

Figure 33: Annihilation events during t=15-30 s of the mixing cycle. The left part shows thedistribution of the annihilation positions in the XY plane, the right part in the RZ plane.

1.3.2 Measurement of principal quantum number distribution of H

By varying the strength of the electric field applied on the external field ionizer, n distribution of Hatoms reaching the H detector was studied. The density of the positron plasma was 6⇥ 108cm�3.

Figure 34 shows a preliminary result of the number of H atoms detected with di↵erent potentialon the FID. At the strongest electric field which field-ionizes H at n � 14, the count for the first5 s was 0.14 per mixing on the average (using 43 mixings). The statistical significance in one-sidedGaussian standard deviations for the ratio of Poisson means becomes 3.2 �. Here the backgroundwas observed 32 counts in total for 7,500 s. This result implies the observation of H atoms atn < 14. The detection of H atoms with n<14 is important considering the fact that the lifetime ofsuch states have only short lifetime, and can reach their ground state on the way to the cavity.

1.4 Summary of the 2016 run and Plan for 2017

We have succeeded to transport monoenergetic pulsed antiproton beams from the MUSASHI trapto the double cusp trap with its kinetic energy as low as 1.5 eV. Synthesis of antihydrogen atomsin the double cusp trap was studied by directly injecting such ultra slow p beams with the narrowenergy width into the positron plasma. Around 60% of FIC events were localized within the first0.7 s, which is expected to contribute a better S/N ratio for detection at the end of the spectrometerline.

Our observations implied a quick separation of charged particles, 80–90% of trapped antiprotons.The experiment, however, implies that the rest of antiprotons stayed long at around the level ofpotential of the positron plasma.

Time spectra of FIC count, antiproton annihilation count, and H candidate count show thediscrepancy at t < 0.7 s, the reason of which is under discussion.

33

< n

Coun

t / m

ixin

g

0

0.4

0.8

1.2

1.6

2.0t < 25s

t < 5st < 1s

t < 25s

t < 5st < 1s

< n202010 104030 6050 30 40 50 60 70 80

Coun

t / m

ixin

g

-210

-110

1

Figure 34: Averaged number of H atoms per mixing detected by the H detector as a function ofthe highest principal quantum number. The blue, red and green solid circles are the numbers fort<1 s, <5 s, and <25 s, respectively.

Quantum states of antihydrogen atoms were studied with the FID and the H detector. Theanalysis indicates that H atoms with its principal quantum number smaller than n=14 were syn-thesized.

The goal in 2017 is like in 2016 to optimize the antihydrogen beam for hyperfine spectroscopy.To realize this,

• Optimize conditions of antiproton trapping, manipulation, transpoirt, and retrapping in thecusp: 3 weeks

• Direct injection of coler antiproton beam into temperature and density controlled positronclouds: 2 weeks

• Developments of a static merging scheme to synthesize H atoms: 4 weeks

• Measurements and optimization of n-distribution and polarization: 2 weeks

• Antiproton annihilation experiment: 2 weeks:

References

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34

[2] N. Kuroda, H. A. Torii, Y. Nagata, M. Shibata, Y. Enomoto, H. Imao, Y. Kanai, M. Hori, H.Saitoh, H. Higaki, A. Mohri, K. Fujii, C. H. Kim, Y. Matsuda, K. Michishio, Y. Nagashima,M. Ohtsuka, K. Tanaka, and Y. Yamazaki. Phys. Rev. ST Accel. Beams, 15, 024702 (2012).

[3] N. Kuroda, H.A. Torii, M. Shibata, Y. Nagata, D. Barna, M. Hori, D. Horvth, A. Mohri, J.Eades, K. Komaki, and Y. Yamazaki. Phys. Rev. Lett., 100 203402 (2008).

[4] G. Gabrielse, N.S. Bowden, P. Oxley, A. Speck, C.H. Storry, J.N. Tan, M. Wessels, D. Grzonka,W. Oelert, G. Schepers, T. Sefzick, J. Waltz, H. Pittner, T.W. Hansch, and E.A. Hessels(ATRAP Collaboration), Phys. Rev. Lett., 89 213401 (2002).

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[6] C. Sauerzopf et al., NIM A 819, 163166 (2016).

[7] C. Sauerzopf et al., NIM A http://dx.doi.org/10.1016/j.nima.2016.06.023 (2016).

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[11] T. T. Bohlen et al., Nuclear Data Sheets 120 (2014) 211

[12] B. Kolbinger et al. (ASACUSA Collaboration), J. of Instrumentation, in preparation

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[15] N. Pacifico et al. (AEgIS collaboration), Nucl. Instr. Meth. A 831 (2016) 17

[16] Picture kindly provided by N. Pacifico.

35

Part III

Experiments with a polarized hydrogen beam

1 Experiments with a polarized hydrogen beam

1.1 Synopsis

ASACUSA is operating an atomic hydrogen beam setup for the initial purpose of testing thecomponents of the antihydrogen hyperfine spectroscopy apparatus. In previous years we reportedon the remeasurement of the hydrogen hyperfine structure in a beam based on the �

1

-transition(F = 1,M

F

= 0 ! F = 0,MF

= 0) and on the necessary in-depth analysis. In October 2016 amanuscript with the final results of this experiment has been submitted and is available on pre-print servers [1, 2], showing an achieved experimental precision of 2.7 ppb and an agreement withthe maser results within 1 �. Last year we reported on necessary developments to move toward themore challenging but also more interesting ⇡

1

-transition (F =1,MF

=1 ! F =0,MF

=0). In 2016these modifications have been completed and the hydrogen beam setup is now ready to investigateboth transitions within the same setup. The primary task is the characterisation of the upgradedspin-flip cavity and its preparation for the antihydrogen experiment. In addition the improvedhydrogen setup opens up the opportunity to constrain certain coe�cients of Lorentz-invarianceviolating terms in the non-minimal standard model extension by Kostelecky et al. [3] even withouta comparison to antihydrogen.

1.2 The remeasurement of the hydrogen hyperfine structure

The source of cold, polarized, and modulated atomic hydrogen and a quadrupole mass spectrometerfor selective hydrogen-rate detection have been assembled and tested at the Stefan Meyer Institutein Vienna. End of 2013 the source and detector were transported to CERN and installed at theCryolab. In 2014 the spin-flip-driving microwave cavity for �

1

-transitions (equipped with Helmholtzcoils and cubical two-layer magnetic shielding) and the spin-state-analysing superconduncting sex-tupole magnet have been incorporated into the hydrogen beam setup. Figure 35 gives a sketchof the key components with some details in the caption and figure 36 shows a photograph of thehydrogen beam setup at the Cryolab from 2014.

Extensive characterisations of the antihydrogen spectroscopy components were conducted andcompleted with a remeasurement of the zero-field hydrogen hyperfine splitting. Experimental set-tings and arrangements have been varied in order to study systematic e↵ects. Consequently a largeamount of data was available to determine the hyperfine splitting. On one hand this lead to a finalstatistical uncertainty of only 3.4 Hz (one standard deviation). On the other hand no systematice↵ects could be revealed at the achieved level of precision, apart from a systematic uncertaintyof 1.6 Hz introduced by the time standard (rubidium clock). The total uncertainty of the finalresult is 3.8 Hz and presents an improvement by more than an order of magnitude compared to theprevious best value by Rabi-type spectroscopy [4]. The corresponding relative precision is 2.7 ppb.The anticipated precision for the first measurements on antihydrogen is closer to 1 ppm. Therefore,systematic shifts caused by the spectroscopy method can be safely excluded.

The microwave cavity and the superconducting sextupole magnet have been returned to theAD to be available during all antihydrogen runs of ASACUSA after LS1. The hydrogen source anddetector have been relocated to the building 275.

36

Figure 35: Main components of the Rabi-type hydrogen beam setup as it has been in operation atthe Cryolab in 2014. Molecular hydrogen H

2

gets dissociated by a microwave driven plasma; atomichydrogen H enters the vacuum region through a PTFE tubing kept on cryogenic temperatures bya coldhead and is thereby slowed down; the atomic hydrogen beam gets polarised and velocityselected by a doublet of permanent sextupole magnets mounted in vacuum; a tuning fork choppermodulates the beam at 180 Hz and 50% duty cycle and adds time-of-flight measurements and lock-in amplifaction to the diagnostic tools. The hyperfine spectrometer is taken from the antihydrogenexperiment and consists of a microwave cavity of strip-line geometry surrounded by Helmholtzcoils and a magnetich shielding and followed by a superconducting sextupole magnet for spin-stateanalysis. A quadrupole mass spectrometer serves as a mass-selective detector of the hydrogen beamrate based on single ion counting.

1.3 New spin-state analysing sextupole magnets

The design and construction of a spin-state analyser using commercial permanent magnets arrangedin a sextupole Halbach configuration have been reported last year. Since the superconductingsextupole magnet has returned permanently to the antihydrogen experiment such a replacementwas required for the hydrogen setup. In total nine individual sextupole magnets of 50 mm me-chanical length each have been built and six are required to achieve the same integral gradient(Rgs

dz ⇠500 T/m, gs

defined below) as the superconducting sextupole running at the maximalcurrent of 400 A. Magnetic field measurements showed better properties in terms of field-symmetryand alignment of magnetic and mechanic axes as had been expected for this cost-e�cient solution.For an ideal sextupole field the absolute value of the magnetic field scales with the square of the

distance from the axis (radius r in cylinder coordinates):��� ~B(r)

��� = gs2

r2. The following function

has been applied to fit��� ~B��� for every xy-plane of the 3-dimensional field maps to determine the

aforementioned properties:

37

Figure 36: Photograph of the hydrogen setup at the cryolab in 2014.

Table 5: Results for the fit parameters of equation 8 applied to the measured field maps of the ninepermanent sextupole magnets (measurements and fits by M. Huzan, CERN summer student).

magnet-ID gs

(mT/m2) x0

(mm) y0

(mm) a b

A 1.68 -0.0191±0.0003 -0.0065±0.0003 1.0039±0.0003 1.0015±0.0005B 1.68 0.0032±0.0057 -0.0017±0.0058 1.0027±0.0005 0.9981±0.0005C 1.68 -0.0545±0.0066 0.0416±0.0066 1.0301±0.0006 1.0362±0.0006D 1.72 0.0547±0.0040 0.0412±0.0037 1.0003±0.0003 1.0067±0.0003E 1.72 0.0076±0.0036 0.0170±0.0036 1.0055±0.0003 0.9995±0.0003F 1.72 -0.1096±0.0045 -0.0987±0.0046 1.0067±0.0004 1.0005±0.0004G 1.72 -0.0387±0.0041 0.0769±0.0042 1.0045±0.0003 1.0020±0.0003H 1.67 0.0133±0.0037 -0.0273±0.0036 0.9969±0.0003 1.0084±0.0003I 1.68 0.1508±0.0062 -0.2192±0.0063 1.0060±0.0005 1.0007±0.0005

��� ~B(r)��� =

gs

2

"✓x� x

0

a

◆2

+

✓y � y

0

b

◆2

#. (8)

Results for the fit parameters are given in the table 5. x0

and y0

are a measure for the alignmentof magnetic and mechanical axes, while a and b should be equal (and close to unity), if the fieldfollows the cylinder symmetry for | ~B|.

1.4 Spin-flip microwave cavity for ⇡1

-transitions

Measurements of the ⇡1

-transition are more challenging as a static magnetic guiding field of higheruniformity is required in comparison to the case of the �

1

-transition. This is caused by the linear

38

Test%Stand% Hydrogen%Beam%Setup%

Figure 37: Left: Test stand for magnetic field measurements inside the cavity. Right: Installationof the new cavity and shielding (only bottom parts) at the hydrogen setup.

Table 6: Geometry of the big and small coils of the McKeehan-like coil configuration. The conductoris a strip wire of dimension 10⇥1 mm2. At a current of 10 A approximately 30 W of power areconsumed in the coils and a field of ⇠23 Gauss is generated at the centre.

coil-pair turns mean radius distance from centre conductor area h⇥ b

big 38 (2x19) 252 mm 86 mm 19⇥20 mm2

small 23 159 mm 230 mm 23⇥10 mm2

Zeeman shift of the state F =1,MF

=1. A double coil pair inspired by the McKeehan configura-tion [5] has been shown to meet the demand on the field uniformity using finite element simulations.The coil dimensions have been optimized in conjunction with the geometry of a magnetic shieldingand a uniformity defined as �|B|/|B| of 100 ppm could be achieved, which is about a factor of 10better than required. A three-layer cylindrical shielding combined good performance and reason-able technical complexity. The coils from CERN’s normal conducting magnet laboratory and theshielding from an external company arrived in the second half of 2016. Thorough magnetic fieldmeasurements in a test setup confirmed uniformities of ⇠500 ppm, which is worse than expectedfrom simulations but still a factor of 2 better than required. Figure 37 shows the test stand on theleft and the installation within the hydrogen beam setup on the right. The final coil parametersand shielding geometry are summarized in the tables 6 and 7.

An additional distinction between �1

- and ⇡1

-transitions comes from the respective directions ofthe static magnetic field (produced by the coils) and the oscillating microwave field. The componentof the oscillating field parallel or perpendicular to the static field drives the �

1

or ⇡1

-transition,respectively. The new coils can be mounted to provide a horizontal (as in the figure) or verticalstatic field and the cavity can be rotated in steps of 45�. Choosing an orientation between paralleland perpendicular allows for the measurement of �

1

- and ⇡1

-transitions in the same setup. However,

39

Table 7: Geometry of the three-layer cylindrical shielding. The µ-metal has a thickness of 2 mm.The shielding-factor was measured at 1 Hz (quasi static) by the manufacturer (Sekels) to be >45000in radial and >2000 in axial direction. The large di↵erence originates from the axial openings forthe beam pipe of d > 100mm.

layer diameter lengthinner 640 mm 540 mmmiddle 700 mm 580 mmouter 760 mm 620 mm

especially close to the beam axis the sextupole magnets feature di↵erent beam optical propertiesfor the F =1,M

F

=0 and the F =1,MF

=1 states. The simplest way of providing similar beamoptical e↵ects for both states is operating at larger radii. The required change to the beam opticsis discussed in the next paragraph.

1.5 Ring apertures for a hollow hydrogen beam

The magnetic moment of the low-field-seeking state involved in the �1

-transition (F =1,MF

=0)depends on the strength of the external magnetic field, as illustrated in figure 38. Above a criticalfield of B

c

⇠0.05 T (which appears naturally in the Breit-Rabi formula) the magnetic momentabecome more similar. The field inside sextupole magnets vanish on centre and lead to a region ofB < B

c

around the axis. For the new spin-state analyser the radius of this region is roughly 8 mm.By forming a hollow beam using ring apertures as shown on the right of figure 39 this regionis avoided. The polarisation and velocity selection as produced in such a geometry have beensimulated in a straight-forward trajectory code assuimg cylinder symmetry. First measurements ofthe velocity agree well with simulations. Simulated trajectories are presented on the left of figure 39.Blocking the central beam component also removes high field seeker, which could pass the analyserfields close to the axis. Eventually, the antihydrogen measurement will be performed with a hollowbeam for this reason. The blocked beam rate will also be used to provide a normalization countrate, which provides an important cross check in a low statistic experiment using a count rate dropas signature for the hyperfine transition.

Both transitions have been observed in the Earth’s magnetic field and confirm that similarvelocities and polarisations are selected and achieved with the new beam optics (see figure 40).

1.6 Plans for 2017 . . . and beyond

The capability to investigate the ⇡1

-transition opens up several new possibilities. By measuringthe transition frequency at various static external fields the zero-field value can be determinedby extrapolation (equivalently as it has been done for the �

1

-transition [1, 2]). Alternatively ameasurement of the frequencies of the �

1

- and ⇡1

-transition at the same external field alreadyallows for the determination of the zero-field value. Exploring systemtic and statistical uncertaintiesrelated to this method is of special relevance to ASACUSA’s antihydrogen campaign, as a zero-fieldvalue can be extracted from only two resonances. Moreover, as both transitions are involved thismethod is potentially sensitive to shifts in either of them.

Another goal is the complete automation of the measurements to enable long-term measure-ments. For instance, a search for sidereal or annual variations could then be started. In such acampaign the �

1

-transition, which is not expected to be sensitive to CPT-violation according to

40

µ!(µ

B)!

magne)c!field!(T)!

high!field!seeking!states!

low!field!seeking!states!

Figure 38: magnetic moment of the singlet (F = 0,MF

= 0) and triplett states (F = 1,MF

=+1, 0,�1) of ground-state hydrogen. (figure from the master thesis of M. Wiesinger).

Ring%%Apertures%

#2%

#1%

#2%#1%

Figure 39: Left top: Simulated trajectories for the hollow beam setup with ring apertures. Leftbottom: field gradient of the permanent sextupoles. Right: fotographs of the two ring apertures(figures from the master thesis of M. Wiesinger).

41

300#

500#

700#

900#

beam

#rate#(H

z)#

500#

700#

900#

excita4on#frequency#(MHz)#–#1420.4#0.00#A0.02# 0.02# 0.04#0.02# 0.06# 0.08#

excita4on#frequency#(MHz)#–#1420.8#

σ1" π1"

Figure 40: Resonanes recorded using the Earth’s magnetic field as static guiding field. Left: �1

-transition. Right: ⇡

1

-transition. Both resonances show similar width and strength indicatingsimilar velocities and polarisations of the respective hyperfine states.

theory [3], would serve as the reference when looking for shifts of the ⇡1

-transition. A bipolar high-precision current supply for the McKeehan-like coils has been purchased, as switching the magneticfield direction will increase the number of coe�cients, that can be restricted. A GPS antenna hasbeen installed to provide long-term stability of the frequency standard and exclude this source ofsystematic errors in future measurements.

A separate task is the investigation of methods to increase the precision of in-beam spectroscopy.Higher precision would lead to increased sensitivity in long-term measurement campaigns. Forinstance a reduction of the beam velocity would result in a proportional precision increase, asthe interaction time of the atoms with the microwave field scales inversely with the velocity. Aresolution increase, which can be directly transferred to the antihydrogen measurements is providedby the Ramsey-method of separated oscillatory fields. This task will form the Ph.D project availableat the Stefan Meyer Institute through the AVA (Accelerators Validating Antimatter) Marie-CurieInnovative Training Network recently approved.

References

[1] Preprint on CERN document server: http://cds.cern.ch/record/2222328

[2] Preprint on arXiv: http://arxiv.org/abs/1610.06392

[3] V. A. Kostelecky and A.J. Vargas, Phys. Rev. D 92, 056002 (2015).

[4] P. Kusch, Phys. Rev. 100, 1188 (1955)

[5] L.W. McKeehan, Review of Scientific Instruments, 7, 150 (1936).

42

Part IV

Antiproton-nuclei cross section measurementat 5.3 MeV

1 Introduction

The knowledge of the annihilation cross section (�ann

) of low-energy antinucleons with nucleonsand nuclei is of interest both in fundamental cosmology, to study the matter-antimatter asymmetryin the Universe [1], and in nuclear physics, to determine the parameters of the strong interactionboth in the quark models and in the optical potential models. Most of the measurements in theprojectile momentum below 400 MeV/c were performed at CERN during the 80’s and 90’s withthe LEAR facility and more recently with the Antiproton Decelerator (AD), see fig. 41 and Ref. [2].Unfortunately the existing data are incomplete and show some discrepancies when compared withthe expectations.

One of these anomalies concerns the quasi-nuclear bound states or resonances which were pre-dicted both by quark and by potential models but not yet discovered. There is only one indi-cation for a dip in the antiproton-proton annihilation cross section data at momentum around130 MeV/c [3]. A resonance, but sub-threshold, was discovered in the total e+e� ! hadronscross-section by the FENICE Collaboration [4].

In addition in the 200–400 MeV/c region, the antiproton (p) and antineutron (n) annihilationcross sections are similar (see, e.g., fig.11 in [5]), as expected, but their values result to be larger thanthose calculated by the optical potential models that fit well the existing data at higher energiesand the measurements with the antiprotonic atoms [6].

Recently Friedman has highlighted that the antineutron data at low energies have an abnormalbehaviour [6]: in the momentum range 70–400 MeV/c, the annihilation cross sections of n on severalnuclei (C, Al, Cu, Ag, Sn, Pb) measured at LEAR [5] show a steep rise at the lowest energies thatis actually expected for charged particles (like p) as a consequence of the electrostatic focussing oftheir trajectories towards the target nucleus.

To try to solve these anomalies a direct comparison between the p and n experimental �ann

’sat the same energies on the same nuclei could help to estimate the relative strength of antiprotonand antineutron interaction with nuclei. The existing data allow direct comparison at low energiesonly for hydrogen and tin targets [2] due to the lack of p data.

Since the existing antineutron data are more systematic than the antiproton ones, more data onantiproton annihilations on nuclei at low energy are required and for example a precise measurement(10%) on one-two targets at 100 MeV/c of the antiproton �

ann

’s would allow a stringent comparisonwith the antineutron �

ann

’s with nuclei. For this reason the ASACUSA Collaboration has performeda measurement of the �

ann

of 5.3 MeV antiprotons on carbon. The results of the analysis of thedata acquired during the 2015 AD runs are here presented.

2 The measurement

The measurement is performed by counting the antiproton annihilations Ntarget

on a solid thincarbon target in respect of the annihilations N

ring

of the antiprotons scattered by the target on aring (called ”2nd ring”) placed downstream (see Fig. 42).

The experimental apparatus, shown in Fig. 43, has been designed with a particular care to

43

[MeV/c]LAB

p210 310

[mb]

σ

210

310

410

antinucleon reaction/annihilation cross section on nuclei

He3 Ne

Pt

SnNi

Pb

CuCa

Al

CHe4

D

p

C

Pd

Pt

pn

Cn

Aln

Cun

AgnSnn

Pbn

antinucleon reaction/annihilation cross section on nuclei

Figure 41: Published measurements of the antinucleon annihilation cross sections for kinetic energybelow 500 MeV. The antineutron data are in ocher.

separate in time the signal of the p annihilations on the target and on the 2nd ring from thebackground of the p annihilations on the rest of the apparatus.

The target and the 2nd ring are placed in a vacuum chamber made by two cylinders (the firstone is 120 cm in diameter and 130 cm in length, the second one is 60 cm in diameter and 130 cmin length). The first cylinder is directly connected with the AD beam line.

A detector (”DET1”), made of scintillating bars, already used for the �ann

measurement at 125keV and in the antihydrogen experiment with the Cusp Trap [7], counts the annihilations comingfrom the target and, when inserted, from the 2nd ring by detecting the produced pions. DET1consists of 7 modules with di↵erent numbers of bars (from 24 to 62): 3 modules are placed closeto the target position just around the first cylinder (sideways and below), while 4 modules are

44

p

SIGNAL

� � targetNAp � �

ring

target

NvApannV

me

pti p

p

p

p2° ringtarget

p

Figure 42: Scheme of the technique to measure the antiproton annihilation cross section.

positioned more externally. The signal from the bars (1.5⇥1.9 cm2 section and 96 cm of length)are read by Hamamatsu 64 channels PMTs and acquired by dedicated front–end boards.

The antiproton beam intensity is monitored by a Cherenkov detector (”BIM”) placed at theend of the apparatus where almost the totality of the annihilations occurs.

A second Cherenkov detector (”CHER”) is positioned close to the target and outside the firstcylinder to measure the time shape of the antiproton beam. This is done in specific runs by rotatingthe target in such a way that the whole antiproton beam annihilates on the target frame.

The targets are carbon self-supporting films (700 nm and 1000 nm thick) mounted on circularrings (internal diameter = 10 cm, external diameter = 13 cm). Their thickness is known with highprecision (better than 2-3%) and also the uniformity is assured to be better than 2%. However,as discussed later, the used technique allows the measurement of the �

ann

value to be independentfrom the uncertainty of the target thickness.

Thanks to the large diameter of the target foils the background events due to the annihilationsof the p beam halo hitting the target frame is strongly reduced. The target is placed around 45 cmfar from the entrance of the first cylinder.

The 2nd ring (inner diameter = 6 cm, outer diameter = 11 cm) is placed 15 cm downstreamthe target. It is devoted to intercept the antiprotons scattered by the target in a selected solid

45

Figure 43: Picture of the experimental apparatus: the 2 cylinders (in light blue) are surroundedby the inner (orange) and the outer (yellow) modules of the scintillator bars detector; the twoCherenkov detectors are in violet.

angle. The di↵usion angles are in the range (11.3�–20.1�) where, for the 5.3 MeV antiproton, thethe scattering elastic cross section (�

scatt

) is expected to be due to the Coulomb interaction whilethe contribution from the nuclear elastic scattering is negligible.

The annihilation cross section �ann

of 5.3 MeV antiprotons on the carbon target can be deter-mined by:

�ann

=N

target

Nring

�scatt

(9)

where, as previously said, Ntarget

is the number of the annihilations in the target and Nring

is the number of the antiprotons di↵used from the target on the 2nd ring with a scattering crosssection �

scatt

.The N

target

and Nring

events can be determined by DET1 through the counting of the annihi-lations vertices on the target and on the 2nd ring, respectively, by reconstructing the trajectoriesof the annihilations products (mostly pions). Since this procedure has a very poor e�ciency, inorder to get more statistics we prefer just to count the pions hitting DET1 whose number is pro-portional to the annihilations events. One of the advantages of the present technique is that the�ann

measurement is independent from the detection e�ciency since both Ntarget

and Nring

are

46

measured by the same detector (DET1) and �ann

depends on their ratio. The same applies for theuncertainty on the target thickness.

The target and the 2nd ring events can be e�ciently separated from the background due tothe p annihilations on the vacuum chamber walls by using just the time information of the DET1signals if the the time duration of the p bunches is enough small. For this we have exploited the socalled Multiple Extraction mode of AD where each antiproton bunch is divided in 6 bunches withshorter time length. A further reduction has been achieved by tuning the AD kicker time. Thefinal time duration, as detected by CHER, becomes 50 ns long with a rise time of 15 ns. This result(achieved only for the first of the 6 bunches, while the remaining are discarded) satisfies very wellthe experiment requirements, as discussed in the next paragraph.

3 The results

Fig. 44 shows the time distributions of the hits recorded by the inner modules of DET1 for thethree di↵erent experimental conditions performed in one day of data acquisition (i.e. 8-hours shift).The back line is for the data achieved when the 1000 nm thick C-target is put on the p beam line(”only-target runs”), the red line when both the C-target and the 2nd ring are present (”2nd-ringruns”), the blue line when only the 2nd ring is on the beam (”empty-target runs”). The threehistograms have been normalized at the same number of incident antiprotons by means of thesignals recorded by the BIM detector.

The peak at around 535 ns in the black histogram is mainly due to the annihilations on thetarget while that in the red histogram comes from both the target and the 2nd ring annihilations.The plateaus after the peaks are due to the p annihilations on the vacuum chamber walls. Thedepletion in the 560–590 region of the red distribution in respect to the black one can be explainedif we consider that the antiprotons di↵used by the target in the 11�–20� angular range, insteadof hitting the downstream part of the first cylinder, are intercepted by the second ring that istemporally only 5 ns far from the target annihilations. The huge peaks starting at t = 600 ns comefrom the annihilations occurring on the end walls of the two cylinders.

It must be noted that the signal from the target appears clearly in the region between 515 nsand 550 ns thanks to the reduced time length of the antiproton bunch (50 ns).

The annihilations on the vessel walls coming from the antiprotons scattered from the targetare delayed of at least 20 ns in respect of the annihilations on the target and so they are expectedto start at around 540 ns. The region before t = 540 ns is then free from the background of theannihilations on the wall of the vacuum chamber.

The few events in the blue distribution show that the background coming from the halo of thebeam hitting the target frame is very low.

The annihilations on the target and on the 2nd ring are determined with the counts of the hitsmeasured by DET1 in fiducial time intervals which are selected to be free from the background ofthe walls annihilations as described below. The e↵ect of the detector saturation is corrected bymultiplying the counts of each run with coe�cients, that depend on the hit number, calculated byMonte Carlo simulations.

To evaluate the annihilations on the target, we count the hits detected in the fiducial interval�T = 520–535 ns of the only-target runs, to which we subtract the estimated events on the targetframe obtained from the empty-target runs. The achieved count is called M

ann

.The corresponding count of the events on the 2nd ring, M

0ring

, must be performed in the time

interval �T0delayed by 5 ns in respect of �T (�T

0=525-540 ns) since 5 ns is the p time-of-flight

from the target to the 2nd ring. The M0ring

value is obtained by subtracting the events of the

47

time [ns]480 500 520 540 560 580 600 620

norm

aliz

ed c

ount

s

0

50

100

150

200

250

300

350

400

Figure 44: Time distributions of the hits recorded by the inner modules of DET1 for di↵erentconditions in one day: the black line corresponds to the case when the 1000 nm thick C-target ison the beam (only-target runs); the red line is for the events when in addition to the carbon targeta second ring has been placed downstream (2nd-ring runs); the blue line represents the case wherethe target is removed and only the second ring is present (empty-target runs).

only-target runs from those of the 2nd-ring runs, both evaluated in �T0.

The normalization of the di↵erent counts is done by using the BIM signal of the p beam intensityTaking into account that M

ann

/M0ring

⇡ Ntarget

/Nring

it is possible to use Equation 9 todetermine �

ann

once �scatt

is known.The M

ann

/M0ring

value results to be 0.87 ± 0.04 where the error is only the statistical one.The �

scatt

value can be calculated with the Moliere-Bethe formulation which well describes themultiple scattering of MeV protons (see, e.g., Ref.. [9]). By means of Monte Carlo simulations withthe GEANT package, it has been possible to determine the �

scatt

value for di↵erent geometries ofthe p beam.

The final result of the annihilation cross section of antiprotons with 5.3 MeV kinetic energy inthe laboratory reference system is �

scatt

= (1.49 ± 0.15) barn. The error is the quadratic sum of thestatistical error and the systematic error. The latter has several contributions. The normalizationof the events counts is a↵ected by 2.1% error coming from the uncertainty on the BIM signals. Thecorrection of the saturation e↵ect of DET1 is estimated to have 5% error. The finite time resolutionof DET1 produces a 4% error. The ±1 mm uncertainty of the distance between the target and the2nd ring yields a 1.5% error on �

scatt

while the uncertainty on the radial extension of the p beam,which is estimated of few mm, causes a 6% error.

48

In Fig. 45 the present result with p and n �ann

on carbon from Ref. [5, 8] are shown togetherwith the calculations from Ref. [6]

Our measurement does fit the trend of the n–C �ann

. This qualitatively conflicts with theexpectations on the focussing e↵ect of slow charged projectile from target nucleus which foreseethat p �

ann

should be larger than n �ann

. For example in the Friedman’s calculations based on theoptical potential the p �

ann

value is around 40–50% larger than the n �ann

at 5.3 MeV.The present result is higher than the Friedman’s prediction of around 30%, which corresponds to

3 standard deviation uncertainty of the measured value. It should be noted, as discussed in section 1,that the same model foresees �

ann

values which are systematically below the measurements withboth p and n at higher energies, while the comparison with the p values on Ni, Sn and Pt is notdiscriminating due to the large uncertainties of the measured data.

A clear explanation of the disagreement between experimental data and theory is not availableto us.

[MeV/c]LAB

p0 100 200 300 400 500 600 700 800 900

[mb]

σ

0

500

1000

1500

2000

2500

3000

3500

4000

Figure 45: Antinucleon �ann

at low energies on carbon. The blue points are the experimental valuesfor p: the present measurement is the value at p

lab

= 100 MeV/c while the data for plab

> 400MeV/c come from Ref. [8] (p

lab

is the projectile momentum in the laboratory reference system).The yellow points are the experimental n data [5]. The continuous and dashed lines represent thecalculations with the optical potential model from Ref. [6] for n and p, respectively.

49

The measurement can be extended to medium-heavy targets by means of the same apparatusand the same technique, as demonstrated by Monte Carlo simulations [10]. In addition also themeasurement of the antiproton nuclear elastic cross section on di↵erent nuclei could be performedby changing the distance of the 2nd ring from the target to explore di↵erent angular di↵usionregions. So far no data exist at these energies.

In the near future with the ELENA facility, the p �ann

’s can be measured even at 100 keV, asalready demonstrated by ASACUSA [11,12].

References

[1] A. G. Cohen, A. de Rujula and S. L. Glashow, The Astrophys. Journ. 495 (1998) 539.

[2] A. Bianconi et al, Phys. Lett. B 704 (2011) 461.

[3] F. Iazzi, et al., Phys. Lett. B 475 (2000) 378.

[4] A. Antonelli et al., Nucl. Phys. B 517 (1998) 3

[5] M. Astrua et al., Nucl. Phys. A 697 (2002) 209

[6] E. Friedman, Nucl. Phys. A 925 (2014) 141.

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[8] K.Nakamura et al., Phys. Rev. Lett. 52 731 (1984)

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