Summary of Working Group 4 - Intense Muon Physics -

Marco Grassi a, Katsuhiko Ishida b and Yannis K. Semertzidis c

aIstituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy

bAdvanced Meson Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

cBrookhaven National Laboratory, Physics Dept., Bldg 510A, Upton, NY 11973-5000, USA

Various topics of muon physics were discussed in the Working Group 4 (WG4) of the NuFact04 workshop. Thissummary will survey various lepton flavor violation (LFV) studies and high precision measurement that could bebenefited from higher fluxes of muon beams. Also discussed were muon’s applications and future prospects forintense muon beams.

1. Introduction

Muon’s importance is recognized not only inparticle physics but also in nuclear, atomic andcondensed matter studies and is ever increasing.When the high intensity muon beams are real-ized for the neutrino factory, further progress isexpected in various fields of muon physics. Thisworking group was organized to discuss topics onthe following aspects of muon science:

• lepton flavor violation,

• high precision measurement of muon prop-erties,

• muon’s applications,

• development of intense muon beams.

2. Lepton Flavor Violation

In the Standard Model (SM), the muon num-ber is exactly conserved. In any simple exten-sion of the SM, obtained with the introduction ofDirac neutrino masses and neutrino mixing, lep-ton number violating processes with charged lep-tons become possible as well. However, becauseof the smallness of neutrino masses, the rates forthese processes are immeasurably small. On theother hand, super-symmetric unification theories(SUSY-GUT) generically predict LFV processes

in the charged sector at levels close to experimen-tal limits. Lepton number violating processes aretherefore not contaminated by the background ofany simple extension of the Standard Model andconstitute unambiguous and clean signals of pro-found new physics.

2.1. Lepton Flavor Violation theory

We had five talks on theoretical aspects relatedto the Lepton Flavor Violation.

In the first talk, C.S.Lim of Kobe Universitydiscussed the relation between a class of LFV pro-cesses and the possible Majorana nature of neu-trinos. The Majorana nature of neutrino massmatrix could be verified by L-violating processes,and, though the rates are extremely small, thepredictions in terms of the mass matrix are welldefined, and strong enhancement are expected incase of new Physics beyond the SM.

E. Takasugi of Osaka University presented aSuper Symmetric unification scheme where thebi-maximal mixing was assumed. Various aspectsand predictions of this scheme were discussed.

In the third presentation K. Tsumura of Os-aka University clearly reviewed the mechanismthrough which sizable LFV processes are fore-seen in Minimal SUSY extension of the StandardModel. The dependence of the branching ratioson the SUSY mass scale and the hierarchy amongthe µ → eγ and the τ → µγ processes were dis-cussed.

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In the following talk S. Kanemura of OsakaUniversity described aspects of LFV in the µ− τsector embedded in a SUSY framework. In par-ticular he examined the contribution of higgs me-diated LFV process in deep inelastic µN → τN

′

scattering. S. Kanemura concluded his presenta-tion noticing that, even if the background needsto be better estimated, the computed cross sec-tions for this specific process are large enough tobe seriously considered at new high-energy high-intensity muon beams.

In the last theoretical presentation T. Shindoufrom KEK examined three SUSY models, differ-ing on the mixing matrix and the Yukawa cou-pling. The predictions of these models for severalLFV process were also shown. T. Shindou con-cluded his talk remarking how the comparison ofµ → eγ, τ → µγ, τ → eγ and µ − EDM measure-ments constitutes a powerful tool to discriminateamong various models.

2.2. Lepton Flavor Violation experiments

There were three presentations on LFV exper-iments, one on MEG by M. Grassi of INFN Pisa,the second on MECO by Y. Semertzidis and thelast on PRISM/PRIME by Y. Kuno of OsakaUniversity.

In the first talk the status of the MEG exper-iment has been reviewed. The MEG Collabora-tion is presently building a detector to search forµ → eγ decay with a single event sensitivity of∼ 5 × 10−14 on the branching ratio. The exper-iment will be conducted at the Paul Scherrer In-stitut (PSI), Switzerland. A schematic view ofthe detector concept is shown in Figure 1. Themomentum and the emission direction of the e+

are measured by a magnetic spectrometer, com-posed of a quasi-solenoidal magnetic field and aset of ultra-thin drift chambers. An array of plas-tic scintillators is placed on each side of the spec-trometer to measure the e+ emission time. Theγ-rays penetrate through the thin superconduct-ing coil of the spectrometer and are detected byan innovative liquid Xenon scintillation detector.Various sub-detector prototypes have been pro-duced and their results were already within thedesign requests, or near by. The detector is in theconstruction phase and the data taking is foreseen

Figure 1. Schematic view of the MEG detector

starting in 2006.Y. Semertzidis reported on the status of the

MECO project. The MECO collaboration wasformed to look for the µ−

→ e− coherent con-version in the field of an Al nucleus with a sin-gle event sensitivity of 2 × 10−17. A schematicview of the beam line and the detector is shownin Figure 2. The signal is given by a single e−

of ∼ 105 MeV emerging from the target. Highenergy electrons may originate from the muondecays in orbit or from beam related processes,like radiative pion capture. The first backgroundis reduced to acceptable levels by measuring thee− momentum with a resolution of ∼ 200 KeVFWHM, while the second one is handled by re-ducing the number of pions entering the stoppingtarget during measurement time. For this pur-pose a new pulsed high-intensity beam line hasbeen designed at Brookhaven National Lab. Aproton extinction factor at the level of ∼ 10−9,between beam-on and beam-off, has to be ob-tained.

The collaboration is considering to use an in-strument, with a very large dynamic range, tomeasure this extinction factor in the AGS ringdown to 10−10. The instrument is based onelectro-optics techniques. The beam line is ex-pected to be completed at the end of 2008.

Y. Kuno reported on the PRISM/PRIME

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Proton Beam

Straw Tracker

Crystal

Calorimeter

Muon Stopping

Target

Muon Beam

Stop

Superconducting

Production Solenoid

(5.0 T – 2.5 T)

Superconducting

Detector Solenoid

(2.0 T – 1.0 T)

Superconducting

Transport Solenoid

(2.5 T – 2.1 T)

Collimators

Primary proton

beam

Figure 2. The MECO project: a schematic viewof the beam line and the detector.

project at J-PARC. The project is designed tosearch for µ−

→ e− conversion with enhancedsensitivity with respect to MECO. The goal isa single event sensitivity of 5× 10−19. The beamline, PRISM, is designed around a Fixed FieldAlternating Gradient Synchrotron ring (FFAG),which reduces the beam energy spread to 2%level, allowing thinner target, maintains the beamintensity, ∼ 1012µ/s for 1 MW proton power, andenhances the pion suppression. The layout of thePRISM beam line is shown in Figure 3. Althoughthe complete muon beam line is not yet approvedat J-PARC, the construction of the FFAG wasfunded by the Osaka University in 2003. The ringconstruction will last 5 years, and the technicalissues related to the FFAG operation will be ad-dressed.The design of the PRIME detector, that will beoperated with the PRISM beam line, is still pre-liminary. The reduced muon energy spread wouldpermit a thinner target and consequently an en-ergy resolution of ∼ 350KeV at 100 MeV. Such agood resolution will keep the muon decay in orbitbackground at adequate level for the experimentsensitivity.

Figure 3. The layout of the PRISM muon source.)

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3. High precision experiments

The very exciting presentations on high in-tensity muon physics demonstrates the need fora high power proton driver facility. Precisionphysics experiments with muons, a second gen-eration particle, are very sensitive to physics be-yond the standard model (SM). In those exper-iments belong the muon g-2, the muon EDM,the µ+

→ e+γ and µ−

→ e− conversion exper-iments, and the T-violation experiments. Theyalso provide important input on the accuracy ofthe SM parameters, like the muon lifetime, andmuon capture experiments. All of those exper-iments are statistics limited and would benefitwith the availability of a higher intensity facility.The beam parameter requirement is very differentdepending on the application.

3.1. Muon g-2

We had two talks on the muon g-2, one on thetheory by K. Hagiwara of KEK, and one on theexperiment by J. Miller of Boston University.

The theoretical talk was focused on the accu-racy of the SM value of the muon anomalous mag-netic moment dominated by the uncertainty onthe hadronic correction [1]. The current level ofaccuracy as well as the possible future level of ac-curacy were presented. The values presented are

aSMµ = 11659183(6.7)× 10−10 (1)

with

aQEDµ = 11658471.9(0.14)× 10−10, (2)

aEWµ = 15.4(0.2)× 10−10, (3)

ahad,LOµ = 691.8(6.1)× 10−10, (4)

ahad,NLOµ = −9.8(0.1)× 10−10, (5)

ahad,LBLµ = 13.6(2.5)× 10−10. (6)

The experimental value [2] is

aSMµ = 11659208(6)× 10−10, (7)

which results to

aexpµ − aSM

µ = (25 ± 9) × 10−10 (8)

or 2.7 times the stated uncertainty.The prospects of the error reduction in the SM

were discussed concluding that a further reduc-tion by a factor of two to three is still possible.For the hadronic contribution only the e+e− dataare used [3].

Since the difference between experiment andtheory is in the range of two to three sigma andsince the accuracy of the muon g-2 value is stillstatistics limited the obvious next step was torun further with increased muon flux. J. Millerdescribed the status of the proposal to BNL toupgrade the muon g-2 experiment. The goal isto reduce the experimental error by a factor ofabout 2.5 bringing it down to 0.2 ppm from thecurrent 0.5 ppm. This will be achieved by up-grading the muon beam line with an estimatedincrease in the muon flux of about a factor offive. Other improvements include opening up theinflector ends to increase the injection efficiencyinto the g-2 ring and upgrading the detectors totake the flux and reduce pulse overlapping. Theproposal has been unanimously approved by theBNL PAC and next it needs funding approval. Ifapproved it is expected to start taking data inabout two years.

As an example of the potential power of the de-creased error we show Figures 4, 5. The first fig-ure shows [4] the area of SUSY parameters as con-straint by various measurements, including thecurrent g-2 results. The second figure assumes areduction by a factor of two in both theory andexperiment for g-2 while keeping the differencebetween theory and experiment the same for il-lustrative purposes.

3.2. Electric Dipole Moments

There were two presentations on electric dipolemoments (EDM), one on theory by J. Hisano ofTokyo University and one on experiment by J.Miller of Boston University.

The theory talk was focused on color EDMs inthe frame of SUSY SU(5) with right-handed neu-trinos. The improved sensitivity by about two or-ders of magnitude of the planned deuteron EDMexperiment, even at 10−27 e · cm level, over thepresent best limits from neutron and Hg was em-phasized (see Figure 6).

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Figure 4. The SUSY parameter space as con-straint by various measurements, including thepresent muon g-2 results.

On the experimental presentation the new sen-sitive technique of measuring EDMs in storagerings was emphasized. This technique, applicableto both muon and deuteron, was described in de-tail. In a magnetic storage ring the particle feels astrong E-field in its own rest frame due to specialrelativity (Lorentz field). This field is always inthe radial direction and if the particle possessesan EDM it will precess along this axis. A majorlimitation is the g-2 precession since the spin onlymoves vertically for half of the g-2 cycle. The newidea is the implementation of a radial E-field tocancel the g-2 precession of the particles and letthe spin accumulate in the vertical direction.

For the muon, the expected sensitivity is10−24 e · cm as is described in the LOI submit-ted to J-PARC [5]. The EDM is the imaginarypart and the anomalous magnetic moment thereal part of the same matrix element and are re-lated as

dµ = 2 × 10−22e · cmaSUSY

µ

25 × 10−10tanφCP (9)

The muon EDM experiment is therefore going to

Figure 5. The SUSY parameter space as con-straint by various measurements, including theprojected reduction of the errors by a factor oftwo in the muon g-2 results for both theory andexperiment. For illustration purposes the currentdifference between theory and experiment is as-sumed.

probe the CP-violating phase at a fraction of a1%.

3.3. Precision Measurement of Muon

Properties

Next we had three talks on precision measure-ments of muon properties. W. Fetscher of ETH(Zurich) presented the time reversal invariance(TRI) experiment, D. Tomono of KEK presentedthe progress in the muon lifetime experiment andF. Gray of Berkeley presented the muon captureand muon lifetime experiments at PSI.

W. Fetscher described the TRI experimentwhich is a measurement of the transverse e+ po-larization from the decay of µ+ with the appara-tus of Figure 7. The overall improvement in theTRI measurement is a factor of three over presentlimits.

D. Tomono presented the current status of themuon lifetime measurement at the Rutherford

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Figure 6. The d-quark color EDM as predictedby the SUSY model (see text). Also shown arethe current limits from the neutron and Hg EDMsas well as the sensitivity of the planned deuteronEDM experiment at the 3 × 10−27 e · cm level.

Lab. The uncertainty in the Fermi constant of9 ppm is coming from the uncertainty in the muonlifetime. The technique chosen to improve themuon lifetime accuracy (see Figure 8) is to usea 50 Hz muon beam structure. After the arrivalof the muon beam and after a detector short re-covery time, the muon decay is followed for 70µs.It is expected to improve the muon lifetime mea-surement by about a factor of 10.

F. Gray described two experiments presentlyin the construction/running phase at PSI. One isthe muon capture experiment and the other themuon lifetime. For the muon lifetime the aim isto get more than 1012 muon statistics in orderto reduce the Fermi constant uncertainty to lessthan 0.5 ppm.

4. Application of muons

Muon’s unique properties (charge, spin, massetc) with its rather long lifetime for an unstableelementary particle have brought many interest-ing and important applications. In materials, thepositively charged muon behaves like a light pro-

Figure 7. The TRI experimental apparatus withthe coordinate system used in the muon decaymeasurements.

ton and a negatively charged muon behaves like aheavy electron. Such a characteristic behavior ofmuons can be monitored through Michel decays,atomic x-rays and so on.

4.1. Positive muon programs

Among the various applications of muons,the best known is µSR (muon spin rota-tion/relaxation/resonance). In the µSR methodbeams of muons (µ+ in most cases) with all theirspins polarized are implanted in various typesof condensed matter. The subsequent precessionand relaxation of their spins is determined fromthe direction of the emitted positrons when theydecay.

Y. J. Uemura of Columbia University presentedthe study of the superconductors as one of themost successful applications of µSR. When a vor-tex lattice is formed in type II superconductors,there appears a field distribution dependent onthe penetration depth λ, which is one of the twobasic parameters of superconductors. The muonswill randomly sample the field distribution andthe field spread was clearly observed as a spread

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Figure 8. The muon lifetime muon beam struc-ture at Rutherford Lab.

in muon spin precession frequency.µSR has been applied to bulk samples because

of the rather broad stopping distribution of MeVenergy muon beams. Recently, µSR has acquirednew advantage with the introduction of low en-ergy muon beams in the keV range as was pre-sented by E. Morenzoni of PSI in the plenary ses-sion. The cryogenic moderator method generatedkeV muons with a rate of 103/s at PSI. This al-lows to vary the implantation depth in thin sam-ples. The low energy muons have been used asnovel probe to study magnetic properties of thinfilms, near surface regions and multilayered struc-tures. The depth distribution of magnetic fieldnear the surface of superconductors, magnetiza-tion of thin nonmagnetic layers between magneticlayers were mapped for the first time.

Y. Matsuda of RIKEN presented an alternativemethod to produce ultra slow muon beam by us-ing lasers to ionize thermally emitted muoniumsfrom the surface of a hot tungsten metal. Therehas been rapid progress in these years and a con-version efficiency of 4 × 10−5 was achieved start-ing from a surface muon beam. The efficiencywould be improved further with the increase oflaser power.

4.2. Negative muon programs

A number of programs making use of largefluxes of negative muons were presented. Muoncatalyzed fusion is a unique phenomenon wherethe muons implanted in hydrogen makes muonicatoms and molecules, and a nuclear fusion occur,while the muon is released right after and triggerfurther fusions. The fusion yield is close to thescientific break-even and studies towards higherfusion yield is continuing by introducing new tar-get conditions (density, temperature, molecularmixture etc). Present topics were reported byK. Ishida of RIKEN such as the magnetic-fieldeffect and low temperature solid effect. Also,control of muonic molecular formation rate withnon-equilibrium molecular states composition bymethods such as ortho-para control may con-tribute to the enhancement of µCF efficiency.

X-rays from muonic atoms provide a method tostudy the nuclear properties and nuclear sizes. Itwould be possible to study unstable nuclei if wecan make muonic atoms of unstable nuclei withgood efficiency. P. Strasser of KEK has presenteda feasibility study at the RIKEN-RAL muon fa-cility in order to produce muonic atoms of unsta-ble nuclei using the cold hydrogen film method.Good progress was achieved with stable argonions implanted in solid deuterium films. Evenwith an inhomogeneous target corresponding toan average Ar concentration of 0.5 ppm, strongmuon transfer µAr(2-1) X-rays were observed.

4.3. Radiography

Another unique property of the muon is thehigh penetration power of high energy muons.Muons do not interact strongly, unlike hadrons,and muons do not easily make showers, unlikeelectrons and photons. Muon has 100% detectionefficiency and easy track determination. Thusmuon radiography is useful for very thick sub-stances that were beyond investigation by anypresent methods. K. Nagamine of KEK describedthe study of the inner structure of mountains suchas Mt. Tsukuba and Mt. Asama with cosmic-raymuons. This may be applied to the predictionof volcanic eruption by monitoring the densitychange along the movement of channel inside thevolcano. When a high intensity and high energy

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muon beam is realized by future accelerators, itwould even be possible to do element selectivemuon radiography by detecting both muon en-ergy loss and multiple scattering.

5. Intense muon beams: progress and re-

quirements

Concerning a development towards intensemuon beams, H. Miyadera of University of Tokyopresented Dai Omega, which is the first makingmodel of an axially symmetric surface muon chan-nel. Dai Omega consists of four large aperturesuperconducting coils with a design solid angleof 1.3 srad. and was first operated in Dec 2001.Recently, a particle separator with axisymmetricelectrode was installed and was proved to be ef-fective in eliminating positron contamination inthe beam.

Y. Miyake of KEK presented the progress ofthe Muon Science Facility at J-PARC. The fa-cility uses the pulsed proton beam from 3 GeVproton synchrotron. The budget for phase 1 wasalready approved and the first beam is expectedin 2007. Various progress was made in the de-sign and manufacture of the components aroundthe production target. These muon beams willbe used for precision measurements as well as forvarious applications such as µSR.

A. Sato of Osaka University reported the fastextraction facility at J-PARC 50 GeV. The muonphysics part of the fast extraction facility plansto use the PRISM for LFV and EDM and g-2 ex-periments. LOI (Letter of Intent) was submitted.

There were discussions about the requirementof muon beam properties after short presentationsby Y. Semertzdis (MECO), Y. Arimoto of OsakaUniversity (PRIME), J. Miller (g-2 and edm), K.Ishida (other experiments) and A. Blondel of Uni-versity of Geneva (neutrino factory scenarios).

6. Conclusion

After the review of the recent muon physicsprograms, it is clear that the muon itself is anideal elementary particle for precision tests offundamental physics. In particular, muon lep-ton flavor violation, muon g-2 and edm are pow-

erful tools to explore physics beyond the Stan-dard Model. There are also wide areas of ap-plications of muons to nuclear/atomic/materialstudies. Most of these experiments are statisticslimited and they can greatly benefit by the avail-ability of much higher intensity sources. Also sig-nificant background reduction can be expected bymuon beams of characteristic energy, space andtime structure. New high intensity and high pu-rity muon beam lines are under construction, orunder planning, and will contribute to the devel-opment of these exciting physics programs.

REFERENCES

1. K. Hagiwara et al., Phys. Lett. B557, 69(2003), and Phy. Lett.D69, 093003 (2004).

2. G.W. Bennett et al., (Muon g-2 Collabora-tion), Phys. Rev. Lett. 92, 161802 (2004).

3. M. Davier and W. Marciano, Ann. Rev. Nucl.Part. Sci. 54, 115 (2004); M. Passera, hep-ph/0411168, 2004.

4. The plots were provided by K. Olive and arebased on work by Ellis, Olive, Santoso, andSpanos.

5. The Muon EDM LOI at J-PARC: http://www-ps.kek.jp/jhf-np/LOIlist/pdf/L22.pdf

M. Grassi et al. / Nuclear Physics B (Proc. Suppl.) 149 (2005) 329–336336