Lamb shift in muonic hydrogen - Boston Universityg2pc1.bu.edu/lept14/talks/Pohl_LM14_V3.pdf ·...

Muonic news

Muonic hydrogen and deuterium

Randolf Pohl

Lamb shift inmuonic hydrogen

The Proton Radius Puzzle

Muonic deuterium

and helium

Randolf Pohl

Max-Planck-Institut für

Quantenoptik

Garching

[fm]Proton charge radius R0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

H spectroscopy

scatt. Mainz

scatt. JLab

p 2010

p 2013 electron avg.

7.9

1

There is the muon g-2 puzzle.

Randolf Pohl Lepton Moments, July 22 2014 2

There is the muon g-2 puzzle.– – – – – – – – – – – – – – – –


There are TWO muon puzzles.


Two muon puzzles

•Anomalous magnetic moment of the muon ∼ 3.6σ

J. Phys. G 38, 085003 (2011).


Two muon puzzles


• Proton radius from muonic hydrogen


Two muon puzzles


•Proton radius from muonic hydrogen ∼ 7.9σThe measured value of the proton rms charge radius from muonic hydrogen µ pis 10 times more accurate, but 4% smaller than the value from both hydrogenspectroscopy and elastic electron proton scattering.

[fm]ch

Proton charge radius R0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

H spectroscopy

scatt. Mainz

scatt. JLab

p 2010µ

p 2013µ electron avg.

σ7.9

RP et al., Nature 466, 213 (2010); Science 339, 417 (2013); ARNPS 63, 175 (2013).


Two muon puzzles


•Proton radius from muonic hydrogen ∼ 7.9σ

• These 2 discrepancies may be connected.

rp aµ

Karshenboim, McKeen, Pospelov, arXiv 1401.6156


Outline

Introduction: Proton radius, hydrogen and all that

Muonic hydrogen

The proton radius puzzle

(Electronic) hydrogen

Proton polarizability aka two-photon-exchange

BSM

Muonic deuterium

Muonic helium


Proton radius vs. time

1962

1963

1974

1980

1994

1996

1997

1999

2000

2001

2003

2006

2007

2010

0.780

0.800

0.820

0.840

0.860

0.880

0.900

0.920

OrsayStanfordSaskatoonMainzMergell VMD

Sick, 2003HydrogenCODATA 2006Bonn VMD

year →

Pro

ton

radi

us (

fm)

The proton rms charge radius is not the most accurate quantity in the universe.

e-p scattering: rp = 0.895(18) fm (ur = 2 %)

Hydrogen: rp = 0.8760(78) fm (ur = 0.9 %)

•••

electron scattering

slope of GE at Q2 = 0

•• hydrogen spectr.

Lamb shift (S-states)



1962

1963

1974

1980

1994

1996

1997

1999

2000

2001

2003

2006

2007

2010

0.780

0.800

0.820

0.840

0.860

0.880

0.900

0.920



year →

Pro

ton

radi

us (

fm)



Hydrogen: rp = 0.8760(78) fm (ur = 0.9 %)

•••

electron scattering




Electron scattering:

〈r2p〉=−6h̄2 dGE (Q

2)

dQ2

∣∣∣Q2=0

⇒ slope of GE at Q2 = 0

Vanderhaeghen, Walcher

1008.4225



1962

1963

1974

1980

1994

1996

1997

1999

2000

2001

2003

2006

2007

2010

0.780

0.800

0.820

0.840

0.860

0.880

0.900

0.920



year →

Pro

ton

radi

us (

fm)



Hydrogen: rp = 0.8760(78) fm (ur = 0.9 %)

•••

electron scattering




Hydrogen spectroscopy (Lamb shift):

L1S(rp) = 8171.636(4)+1.5645〈r2p〉 MHz

1S

2S 2P

3S 3D4S8S

1S-2S

2S-8S 2S-8D

EnS ≃−R∞

n2+

L1S

n3

2 unknowns⇒ 2 transitions

• Rydberg constant R∞

• Lamb shift L1S← rp



our goal

1962

1963

1974

1980

1994

1996

1997

1999

2000

2001

2003

2006

2007

2010

0.780

0.800

0.820

0.840

0.860

0.880

0.900

0.920



year →

Pro

ton

radi

us (

fm)

muonic hydrogen goal (1998): ur = 0.1 %

20x improvement(aim: 10x better QED test in H)



Hydrogen: rp = 0.8760(78) fm (ur = 0.9 %)

•••

electron scattering





Atomic physics

Spectrum of atomic hydrogen

Bohr model→ quantum mechanics

n=1

n=2

1S

2S 2P

3S 3D4S8S ...


Atomic physics

Bohr model→ quantum mechanics

planetary orbits→ wave function

n=1

n=2

Orbital pictures from Wikipedia

1S

2S 2P

3S 3D4S8S ...


Atomic and nuclear physics

Wave functions of S and P states:


r [Zr/a0]0 1 2 3 4 5 6 7 8

radi

al w

.f.

0

0.5

12S

2P

S states: max. at r=0

Electron sometimes inside the proton.

S states are shifted.

Shift ist proportional to the

size of the proton

P states: zero at r=0

Electron is not

inside the proton.

1S

2S 2P

3S 3D4S8S ...








size of the proton


Electron is not

inside the proton.

radius [fm]0 0.5 1 1.5 2 2.5

arb.

uni

ts

Coulomb potential: V = 1/r

1S

2S 2P

3S 3D4S8S ...








size of the proton


Electron is not

inside the proton.

radius [fm]0 0.5 1 1.5 2 2.5

arb.

uni

ts


proton charge

1S

2S 2P

3S 3D4S8S ...








size of the proton


Electron is not

inside the proton.

radius [fm]0 0.5 1 1.5 2 2.5

arb.

uni

ts


proton charge

true potential

1S

2S 2P

3S 3D4S8S ...


Muonic hydrogen

Regular hydrogen:

electron e− + proton p

Muonic hydrogen:

muon µ− + proton p

electron


Muonic hydrogen

Regular hydrogen:


Muonic hydrogen:


electron

from Wikipedia✒


Muonic hydrogen

Regular hydrogen:


Muonic hydrogen:


muon mass mµ ≈ 200 ×me

Bohr radius rµ ≈ 1/200 ×re

µ inside the proton: 2003 ≈ 107

muon much is more sensitive to rp

electron

muon


Proton charge radius and muonic hydrogen

2S1/2

2P1/22P3/2

F=0

F=0

F=1

F=2

F=1 F=1

23 meV

8.4 meV

3.7 meVfin. size:

206 meV50 THz6 µm

225 meV55 THz5.5 µm

µp(n=2) levels:Lamb shift in µp [meV]:

∆E = 206.0668(25)−5.2275(10)r2p [meV]

Proton size effect is 2% of the µ p Lamb shift

Measure to 10−5 ⇒ rp to 0.05 %

Experiment:

R. Pohl et al., Nature 466, 213 (2010).

A. Antognini, RP et al., Science 339, 417 (2013).

Theory summary:

A. Antognini, RP et al., Ann. Phys. 331, 127 (2013).


Muonic measurements.


Setup


The resonance: discrepancy, sys., stat.

laser frequency [THz]49.75 49.8 49.85 49.9 49.95

]-4

dela

yed

/ pro

mpt

eve

nts

[10

0

1

2

3

4

5

6

7

e-p scattering

CODATA-06 our value

O2Hcalib.

Water-line/laser wavelength:

300 MHz uncertainty

∆ν water-line to resonance:

200 kHz uncertainty

Statistics: 700 MHz

Systematics: 300 MHz

Discrepancy:

5.0σ ↔ 75 GHz ↔ δν/ν = 1.5×10−3R. Pohl et al., Nature 466, 213 (2010).

A. Antognini, RP et al.,Science 339, 417 (2013).


The proton radius puzzle.



[fm]ch


H spectroscopy

scatt. Mainz

scatt. JLab

p 2010µ


σ7.9

The proton rms charge radius measured with

electrons: 0.8770 ± 0.0045 fm

muons: 0.8409 ± 0.0004 fm

RP, Gilman, Miller, Pachucki, Annu. Rev. Nucl. Part. Sci. 63, 175 (2013).



[fm]ch


H spectroscopy

scatt. Mainz

scatt. JLab

p 2010µ


σ7.9


electrons: 0.8770 ± 0.0045 fm

muons: 0.8409 ± 0.0004 fm


What may be wrong?

L̃theo.µ p (rCODATAp ) − L̃

exp.µ p =

75 GHz

0.31 meV

0.15 %

µp experiment wrong?µp theory wrong?

H theory wrong?H experiments wrong? → R∞ wrong?

AND e-p scattering exp. wrong?

Standard Model wrong?!?

RP, R. Gilman, G.A. Miller, K. Pachucki, “Muonic hydrogen and the proton radius puzzle”,

Annu. Rev. Nucl. Part. Sci. 63, 175 (2013) (arXiv 1301.0905)


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)?

That is > 100 δ (µp) ! σtot = 650 MHz, [ 570 MHzstat, 300 MHzsyst ]

4 line widths ! Γ = 19 GHz

2 resonances in µp give the same rp


]-4

dela

yed

/ pro

mpt

eve

nts

[10

0

1

2

3

4

5

6

7

e-p scattering

CODATA-06 our value

O2Hcalib.


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



µp experiment probably not wrong by 100 σ


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp theory wrong?

Discrepancy = 0.31 meVTheory uncert. = 0.0025 meV

=⇒ 120δ (theory) deviation

∆E = 206.0668(25)−5.2275(10)r2p [meV]

Some contributions to the µp Lamb shift

double-checked by many groups

5th largest term!

Theory summary:A. Antognini, RP et al.

Annals of Physics 331, 127 (2013)0.5 1 1.5 2 2.5 3 3.5 4

1-loop eVP

proton size

2-loop eVP

µSE and µVPdiscrepancy

1-loop eVP in 2 Coul.

recoil

2-photon exchange

hadronic VP

proton SE

3-loop eVP

light-by-lightmeV

205 meV


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp theory wrong?



∆E = 206.0668(25)−5.2275(10)r2p [meV]



5th largest term!


Annals of Physics 331, 127 (2013)

10-3

10-2

10-1

1 10 102

1-loop eVP

proton size

2-loop eVP



recoil

2-photon exchange

hadronic VP

proton SE

3-loop eVP

light-by-light

meV


Discussions: Proton polarizability

proton polarizability aka. two-photon exchange

Seems to be the only contribution which might be able to solve theproton size puzzle by changing theory in µp.

Keep in mind:

Discrepancy: 0.31 meV

Polarizability: 0.015(4) meV 20 times smaller!



G.A. Miller et al., PRA 84, 020101(R) (2011)“Toward a resolution of the proton size puzzle”

New off-mass-shell effect ∼ α m4

M3solves puzzle.

R.J. Hill, G. Paz, PRL, 107, 160402 (2011)“Model independent analysis of proton structure for hydrogenic bound states”

forward Compton amplitude’s W1(0,Q2) is now well known

“Crazy” functional behaviour can give any correction.No numbers given.

C.E. Carlson, M. Vanderhaeghen, PRA 84, 020102(R) (2011)“Higher-order proton structure corrections to the Lamb shift in muonic hydrogen”

All off-shell effects are automatically included in standard treatment.

C.E. Carlson, M. Vanderhaeghen, arXiv 1109.3779 (atom-ph)

“Constraining off-shell effects using low-energy Compton scattering”

Off-shell effects are 100 times smaller than needed to explain the puzzle.



M.C. Birse, J.A. McGovern, Eur. Phys. J. A 48, 120 (2012)“Proton polarisability contribution to the Lamb shift in muonic hydrogen

at fourth order in chiral perturbation theory”

Calculate T1(0,Q2) in heavy-baryon chiral pert. theory.

Proton polarizability is not responsible for the radius puzzle.

Gorchtein, Llanes-Estrada, Szczepaniak, PRA 87, 052501 (2013)“µ-H Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy

sum rule”

Sum rule + virtual photoabsorption data.

“We conclude that nucleon structure-dependent uncertainty by itself is un-likely to resolve the large discrepancy...”

Karshenboim, McKeen, Pospelov, arXiv 1401.6156 [hep-ph]“Constraints on muon-specific dark forces”

“These estimates show that if indeed large muon-proton interactions are re-

sponsible for the rp discrepancy, one can no longer insist that theoretical

calculations of the muon g−2 are under control. Thus, a resolution of the rpproblem is urgently needed in light of the new significant investments made

in the continuation of the experimental g−2 program.”Randolf Pohl Lepton Moments, July 22 2014 17


Proton off-shell effects can in principle shift the µp value.

Evil subtraction function.

Evidence is growing, that this effect can NOT solve the puzzle.

Clarification needed [(g−2)µ !]


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %




Standard Model wrong?!?


Discussions: New Physics

Jaeckel, Roy, PRD 82, 125020 (2010)“Spectroscopy as a test of Coulomb’s law - A probe of the hidden sector”

hidden photons, minicharged particles→ deviations from Coulomb’s law.

µp transition can NOT be explained this. (contradicts Lamb shift in H)

U.D. Jentschura, Ann. Phys. 326, 516 (2011)“Lamb shift in muonic hydrogen – II. Analysis of the discrepancy of theory and

experiment”

no millicharged particles, no unstable neutral vector boson.

Barger, Chiang, Keung, Marfatia, PRL 106, 153001 (2011)“Proton size anomaly”

decay of ϒ, J/ψ , π0, η , neutron scattering, muon g-2, µ24Mg, µ28Si

⇒ It’s NOT a new flavor-conserving spin-0, 1 or 2 particle

Tucker-Smith, Yavin, PRD 83, 101702 (2011)“Muonic hydrogen and MeV forces”

MeV force carrier can explain discrepancies for rp and (g-2)µIF coupling to e, n is suppressed relative to coupling to µ , p

prediction for µHe+, µ+µ−



Batell, McKeen, Pospelov, PRL 107, 011803 (2011)“New Parity-violating muonic forces and the proton charge radius”

10...100 MeV heavy photon (“light Higgs”) can explain rp and (g-2)µ

prediction for µHe+, enhanced PNC in muonic systems

Barger, Chiang, Keung, Marfatia, PRL 108, 081802 (2011)

“Constraint on Parity-violating muonic forces”

No missing mass events observed in leptonic Kaon decay.⇒ contraints on light Higgs.

Pospelov (private comm.)

Lack of missing mass events in leptonic Kaon decays no problem.

Light Higgs is short-lived (decays inside the detector).

C.E. Carlson, B.C. Rislow, PRD 86, 035013 (2012)“New physics and the proton radius problem”

“New physics with fine-tuned couplings may be entertained as a possible

explanation for the Lamb shift discrepancy.”



Wang, Ni, Mod. Phys. Lett. A 28, 1350094 (2013)“Proton puzzle and large extra dimensions” (arXiv 1303.4885)

“Extra gravitational force between the proton and the muon at very short

range provides an energy shift which accounts for the discrepancy...”

Li, Chen, arXiv 1303.5146“Can large extra dimensions solve the proton radius puzzle?”

“We find that such effect could be produced by four or more large extra

dimensions which are allowed by the current constraints from low energy

physics.”

R. Onofrio, Eur. Phys. Lett. 104, 20002 (2013)“Proton radius puzzle and quantum gravity at the Fermi scale” (1312.3469)

“We show how the proton radius puzzle ... may be solved by means of ...

an effective Yukawian gravitational potential related to charged weak inter-

actions. [...] Muonic hydrogen plays a crucial role to test possible scenarios

for a gravitoweak unification, with weak interactions seen as manifestations

of quantum gravity effects at the Fermi scale.


rp and aµ

after PospelovKarshenboim, McKeen, Pospelov, arXiv 1401.6156

Both the rp and the aµ discrepancy could originate

from the same new proton structure effect (two-photon-

exchange) or “New light Physics” (m≈ MeV)

rp aµ

Fixing rp could give rise to

5×10−9 < |∆(aµ)|< 10−7 (for Λhad = mπ . . .mp).

This is much larger than the (g−2)µ discrepancy of ∼ 1×10−9.

J. Phys. G 38, 085003 (2011).


rp and aµ

after PospelovKarshenboim, McKeen, Pospelov, arXiv 1401.6156

Both the rp and the aµ discrepancy could originate

from the same new proton structure effect (two-photon-

exchange) or “New light Physics” (m≈ MeV)

rp aµ

Fixing rp could give rise to

5×10−9 < |∆(aµ)|< 10−7 (for Λhad = mπ . . .mp).

This is much larger than the (g−2)µ discrepancy of ∼ 1×10−9.

J. Phys. G 38, 085003 (2011).

Maybe one can invert the argument:

aµ “not so wrong” =⇒ rp is not due to proton TPE or this kind of BSM


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %




Standard Model wrong?


Hydrogen spectroscopy

Lamb shift : L1S(rp) = 8171.636(4)+1.5645〈r2p〉MHz

LnS ≃L1S

n3

1S

2S 2P

3S 3D4S8S




LnS ≃L1S

n3

1S

2S 2P

3S 3D4S8S

2S-2Pclassical Lamb shift: 2S-2P

Lamb, Retherford 1946

Lundeen, Pipkin 1986

Hagley, Pipkin 1994

Hessels et al., 201x

2S1/2

2P1/2

2P3/2

F=0

F=0

F=1

F=1

F=1

F=2

1058 MHz =4 µeV

9910 MHz =40 µeV




LnS ≃L1S

n3

1S

2S 2P

3S 3D4S8S

1S-2S

2S-4P 2S-8D

EnS ≃−R∞

n2+

L1S

n3

2 unknowns⇒ 2 transitions

• Rydberg constant R∞

• Lamb shift L1S← rp



2S1/2 - 2P1/22S1/2 - 2P1/22S1/2 - 2P3/2

1S-2S + 2S-4S1/21S-2S + 2S-4D5/21S-2S + 2S-4P1/21S-2S + 2S-4P3/21S-2S + 2S-6S1/21S-2S + 2S-6D5/21S-2S + 2S-8S1/21S-2S + 2S-8D3/21S-2S + 2S-8D5/21S-2S + 2S-12D3/21S-2S + 2S-12D5/21S-2S +1S - 3S1/2

proton charge radius (fm) 0.8 0.85 0.9 0.95 1



0.8 0.85 0.9 0.95 1

2S1/2 - 2P1/22S1/2 - 2P1/22S1/2 - 2P3/2


µp : 0.84087 +- 0.00039 fm

proton charge radius (fm)



0.8 0.85 0.9 0.95 1

2S1/2 - 2P1/22S1/2 - 2P1/22S1/2 - 2P3/2


Havg = 0.8779 +- 0.0094 fm

µp : 0.84087 +- 0.00039 fm




0.8 0.85 0.9 0.95 1

2S1/2 - 2P1/22S1/2 - 2P1/22S1/2 - 2P3/2


Havg = 0.8779 +- 0.0094 fm

µp : 0.84087 +- 0.00039 fm


New measurements of the Rydberg constant areurgently needed to resolve the puzzle µp vs. H

• Flowers @ NPL: 2S−nS,D : n > 4[Flowers et al., IEEE Trans. Instr. Meas. 56, 331 (2007)]

• Tan @ NIST: Ne9+

[Tan et al., Phys. Scr. T144, 014009 (2011)]

• Udem, RP et al. @ MPQ: 2S−4P[Beyer, RP et al., Ann.d.Phys. 525, 671 (2013)]

• Hessels @ York: 2S−2P[Hessels et al., Bull. APS 57(5), Q1.138 (2012)]

• Pachucki: He

• Udem @ MPQ, Eikema @ Amsterdam: He+

[Herrmann et al., PRA 79, 052505 (2009)]



0.8 0.85 0.9 0.95 1

2S1/2 - 2P1/22S1/2 - 2P1/22S1/2 - 2P3/2


Havg = 0.8779 +- 0.0094 fm

µp : 0.84087 +- 0.00039 fm


Projected accuracy Garching 2S-4P


Muonic deuterium


muonic deuterium

2S1/2

2P1/22P3/2

F=1/2 F=3/2


muonic deuterium

2S1/2

2P1/22P3/2

F=1/2 F=3/2

✲

2S1/2

2P1/2

2P3/2

F=1/2

F=3/2

F=1/2

F=3/2

F=5/2 F=1/2 F=3/2


Muonic DEUTERIUM

- 50.0 THz (GHz)ν780 800 820 840 860 880

0

2

4

6

8

10

]-4

del

ayed

/ pr

ompt

eve

nts

[10

- 52.0 THz (GHz)ν-40 -20 0 20 40 60 80 100 120 140 160

0

1

2

3

4

5

6

7

8

]-4

del

ayed

/ pr

ompt

eve

nts

[10

2S1/2

2P1/2

2P3/2

F=1/2

F=3/2

F=1/2

F=3/2

F=5/2 F=1/2 F=3/2

2.5 resonances in muonic deuterium

• µd [ 2S1/2(F=3/2)→ 2P3/2(F=5/2) ]20 ppm (stat., online)



only 5σ significant

identifies F=3/2 line


Deuteron charge radius

H/D isotope shift: r2d− r2p = 3.82007(65) fm

2C.G. Parthey, RP et al., PRL 104, 233001 (2010)

CODATA 2010 rd = 2.1424(21) fm

rp= 0.84087(39) fm from µH gives rd = 2.1277( 2) fm

Deuteron charge radius [fm]

2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145

H + iso H/D(1S-2S)µCODATA-2010

CODATA D + e-d

e-d scatt.

n-p scatt.



H/D isotope shift: r2d− r2p = 3.82007(65) fm

2C.G. Parthey, RP et al., PRL 104, 233001 (2010)

CODATA 2010 rd = 2.1424(21) fm

rp= 0.84087(39) fm from µH gives rd = 2.1277( 2) fm

Lamb shift in muonic DEUTERIUM rd = 2.1282(12) fm PRELIMINARY!


2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145

PRELIMINARY

d Borie+Pachucki+Ji+Friarµd Borie+Jiµ

d Borie+Pachuckiµd Martynenkoµ


CODATA D + e-d

e-d scatt.

n-p scatt.




2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145

PRELIMINARY

d Borie+Pachucki+Ji+Friarµd Borie+Jiµ

d Borie+Pachuckiµd Martynenkoµ


CODATA D + e-d

e-d scatt.

n-p scatt.

µH and µD are consistent!WIP: deuteron polarizability (theory) complete? double-counting?

WIP: shift from QM-interference


Proton-deuteron isotope shift

In other words: The muonic isotope shift agrees with the electronic one!

r2d− r2p: H/D isotope shift 3.82007±0.00065 fm2

muonic Lamb shift 3.8221 ±0.0052 fm2 PRELIMINARY!

scattering 3.764 ±0.045 fm2

The muonic error is conservative (nucl. structure terms).

]2 [fm2p - R2dR

3.72 3.74 3.76 3.78 3.8 3.82

PRELIMINARY

electronic H/D (1S-2S)

p (2S-2P)µd/µ

scattering


Muonic helium ions.


Lamb shift in muonic helium

CREMA collaboration: Charge Radius Experiment with Muonic Atoms

Experiment R10-01 at PSI

Goal: Measure ∆E(2S-2P) in µ 4He, µ 3He

⇒ alpha particle and helion charge radius to 3×10−4

(± 0.0005 fm)







(± 0.0005 fm)

2S1/2

2P1/22P3/2

F=0

F=0

F=1

F=2

F=1 F=1

23 meV

8.4 meV

3.8 meVfin. size:

206 meV50 THz6 µm

2S1/2

2P2P1/2

2P3/2

146 meV

fin. size effect

290 meV

812 nm

898 nm

2S1/2

2P1/2

2P3/22P

F=0

F=1

F=0 F=1

F=2 F=1

167 meV

145 meV

fin. size effect397 meV

µp µ 4He µ 3He







(± 0.0005 fm)

aims:

help to solve the proton size puzzle

absolute charge radii of helion, alpha

low-energy effective nuclear models: 1H, 2D, 3He, 4He

QED test with He+(1S-2S) [Udem @ MPQ, Eikema @ Amsterdam]







(± 0.0005 fm)

aims:

help to solve the proton size puzzle

absolute charge radii of helion, alpha

low-energy effective nuclear models: 1H, 2D, 3He, 4He

QED test with He+(1S-2S) [Udem @ MPQ, Eikema @ Amsterdam]

4He beam time: Oct.-Dec. 2013

3He beam time: May-Aug. 2014


1st resonance in muonic He-4

µ4He(2S1/2→ 2P3/2) at ∼ 813 nm wavelength

Frequency [THz]›3 ›2 ›1 0 1 2 3 4

Eve

nts

/ Pro

mpt

0

0.2

0.4

0.6

0.8

1

1.2

›310´

Prelim

inary




Frequency [THz]›3 ›2 ›1 0 1 2 3 4

Eve

nts

/ Pro

mpt

0

0.2

0.4

0.6

0.8

1

1.2

›310´

Theory + Sick

Prelim

inary

Sick, PRD 77, 040302(R) (2008) Borie, Ann. Phys. 327, 733 (2012)




Frequency [THz]›3 ›2 ›1 0 1 2 3 4

Eve

nts

/ Pro

mpt

0

0.2

0.4

0.6

0.8

1

1.2

›310´

Zavattini

Prelim

inary

Carboni et al, Nucl. Phys. A273, 381 (1977)




Frequency [THz]›3 ›2 ›1 0 1 2 3 4

Eve

nts

/ Pro

mpt

0

0.2

0.4

0.6

0.8

1

1.2

›310´

Pospelov

Prelim

inary

Batell, McKeen, Pospelov, PRL 107, 011803 (2011)


2nd resonance in muonic He-4


›0.6 ›0.4 ›0.2 0 0.2 0.4 0.60

0.1

0.2

0.3

0.4

0.5

0.6›310´

PRELIMINARY



µ3He(2SF=11/2 → 2PF=23/2 ) at ∼ 864 nm wavelength

›0.8 ›0.6 ›0.4 ›0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6›310´

PRELIMINARY


SummaryMuonic hydrogen gives:

Proton charge radius: rp= 0.84087 (39) fm

Proton Zemach radius: RZ = 1.082 (37) fm

Rydberg constant:

R∞ = 3.2898419602495 (10)radius (25)QED ×1015 Hz/c

Deuteron charge radius: rd = 2.12771 (22) fm from µH + H/D(1S-2S)

The “Proton radius puzzle”

muonic deuterium: rd = 2.1289(12) fm from µD (PRELIMINARY!)

Lamb shift in muD⇒ deuteron charge radius, isotope shift.2S-HFS is missing a large (polarizability) term!

muonic helium-4: charge radius 10x more accurate.muonic helium-3: to come

Proton radius puzzle deepened! New data needed:

Muonic T, He, Li, Be, ..

Hydrogen/Deuterium/Tritium

Positronium

...


CREMA collaboration

Charge Radius Experiment with Muonic Atoms

M. Diepold, B. Franke, J. Götzfried, T.W. Hänsch, J. Krauth, F. Mul-

hauser, T. Nebel, R. Pohl

MPQ, Garching, Germany

A. Antognini, K. Kirch, F. Kottmann, B. Naar, K. Schuhmann,

D. Taqqu

ETH Zürich, Switzerland

M. Hildebrandt, A. Knecht, A. Dax PSI, Switzerland

F. Biraben, P. Indelicato, E.-O. Le Bigot, S. Galtier, L. Julien, F. Nez,

C. Szabo-Foster

Labor. Kastler Brossel, Paris, France

F.D. Amaro, J.M.R. Cardoso, L.M.P. Fernandes, A.L. Gouvea,

J.A.M. Lopez, C.M.B. Monteiro, J.M.F. dos Santos

Uni Coimbra, Portugal

D.S. Covita, J.F.C.A. Veloso Uni Aveiro, Portugal

M. Abdou Ahmed, T. Graf, A. Voss, B. Weichelt IFSW, Uni Stuttgart, Germany

T.-L. Chen, C.-Y. Kao, Y.-W. Liu Nat. Tsing Hua Uni, Hsinchu, Taiwan

P. Amaro, J.P. Santos Uni Lisbon, Portugal

L. Ludhova, P.E. Knowles, L.A. Schaller Uni Fribourg, Switzerland

A. Giesen Dausinger & Giesen GmbH, Stuttgart, Germany

P. Rabinowitz Uni Princeton, USA


Backup slides.



[fm]ch


H spectroscopy

scatt. Mainz

scatt. JLab

dispersion 2007

dispersion 2012

p 2010µ


σ7.9


electrons: 0.8770 ± 0.0045 fm

muons: 0.8409 ± 0.0004 fm

Belushkin, Hammer, Meissner PRC 75, 035202 (2007).

Lorenz, Hammer, Meissner EPJ A 48, 151 (2012).


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



That is > 100 δ (µp) ! σtot = 650 MHz, [ 570 MHzstat, 300 MHzsyst ]

4 line widths ! Γ = 19 GHz

2 resonances in µp give the same rp


]-4

dela

yed

/ pro

mpt

eve

nts

[10

0

1

2

3

4

5

6

7

e-p scattering

CODATA-06 our value

O2Hcalib.


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



Wrong transition?

FS, HFS huge.

Next transition:∼ 1 THz away.

frequency [THz]46 47 48 49 50 51 52 53 54

sign

al [a

.u.]

Hµ


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



Wrong transition?

Systematic error?

Laser frequency (H20 calibration) 300 MHz

intrinsic H2O uncertainty 2 MHz

AC and DC stark shift < 1 MHz

Zeeman shift (5 Tesla) < 30 MHz

Doppler shift < 1 MHz

Collisional shift 2 MHz————–300 MHz

µp atom is small and not easily perturbed by external fields.


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



Wrong transition?

Systematic error?

Molecular effects?

p µ e molecular ion? U.D. Jentschura, Annals of Physics 326, 516 (2011).

Does not exist! J.-P. Karr, L. Hilico, PRL 109, 103401 (2012).

Experimentally:

- only 1 line observed (> 80% population)

- expected width

- ppµ ion short-lived R. Pohl et al., PRL 97, 193402 (2006).


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



Wrong transition?

Systematic error?

Molecular effects?

Gas imputities? M. Diepold, RP et al., PRA 88, 042520 (2013).

Target gas contained 0.55(5) % air (leak).

Back-of-the-envelope calculation:

collision rate λ ≈ 6 ·103s−1

2S lifetime τ(2S) = 1 µs

⇒ Less than 1% of all µp(2S) atoms see any N2


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %



Wrong transition?

Systematic error?

Molecular effects?

Gas imputities?

µp experiment probably not wrong by 100 σ


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp theory wrong?



∆E = 206.0668(25)−5.2275(10)r2p [meV]



5th largest term!


Annals of Physics 331, 127 (2013)0.5 1 1.5 2 2.5 3 3.5 4

1-loop eVP

proton size

2-loop eVP



recoil

2-photon exchange

hadronic VP

proton SE

3-loop eVP

light-by-lightmeV

205 meV


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp theory wrong?



∆E = 206.0668(25)−5.2275(10)r2p [meV]



5th largest term!


Annals of Physics 331, 127 (2013)

10-3

10-2

10-1

1 10 102

1-loop eVP

proton size

2-loop eVP



recoil

2-photon exchange

hadronic VP

proton SE

3-loop eVP

light-by-light

meV


What may be wrong?


exp.µ p =

75 GHz

0.31 meV

0.15 %

µp theory wrong?



∆E = 206.0668(25)−5.2275(10)r2p [meV]

µp theory probably not wrong by 100 σ


Discussions: 3rd Zemach moment

PLB 693, 555 De Rujula: “QED is not endangered by the proton’s size” (1008.3861)

A large third Zemach moment 〈r3p〉(2) =∫

d3r1 d3r2 ρ(r1)ρ(r2) |r1− r2|

3

of the proton can explain all three measurements: µp, H, e-p

ρ(r) is not a simple Dipole, but has “core” and “tail”

PRC 83, 012201 Cloet, Miller: “Third Zemach moment of the proton” (1008.4345)

Such a large third Zemach moment is impossible.

〈r3p〉(2) (De Rujula) = 36.6 ± 6.9 fm3

〈r3p〉(2) (Sick) = 2.71± 0.13 fm3

PLB 696, 343 Distler et al: “The RMS radius of the proton and Zemach moments”(1011.1861)

〈r3p〉(2) (Mainz 2010) = 2.85± 0.08 fm3


Contributions to the µ4He+ Lamb shift

Contributions ∆E (meV)

One-photon VP contribution, α(Zα)2 1665.782

Two-loop VP contributions in first and second order PT, α2(Zα)2 15.188

Wichmann-Kroll correction 0.135

Three-loop VP in first and second order PT α3(Zα)2 0.138

Relativistic VP effects −0.203

Hadronic VP 0.223

µ self-energy, µ VP, µ form factor corrections (F ′1(0), F2(0)) −11.243

Recoil corrections (Zα)4, (Zα)5, (Zα)6 −0.355

Radiative-recoil corrections −0.040

Nuclear structure contribution of order (Zα)4: -105.322 rHe2 −297.615 (1.420)

Nuclear structure contribution of order (Zα)5: 1.529 rHe3 7.261 (0.035)

Nuclear structure and one- two-loop VP+ higher order nucl. structure −2.357

Nuclear polarizability contribution: Borie, Rinker, PRA 14, 18 (1978) 3.100 (0.600)

Total splitting 1380.014 meV


Contributions to the µ4He+ Lamb shift

Contributions ∆E (meV)

One-photon VP contribution, α(Zα)2 1665.782

Two-loop VP contributions in first and second order PT, α2(Zα)2 15.188

Wichmann-Kroll correction 0.135

Three-loop VP in first and second order PT α3(Zα)2 0.138

Relativistic VP effects −0.203

Hadronic VP 0.223

µ self-energy, µ VP, µ form factor corrections (F ′1(0), F2(0)) −11.243

Recoil corrections (Zα)4, (Zα)5, (Zα)6 −0.355

Radiative-recoil corrections −0.040

Nuclear structure contribution of order (Zα)4: -105.322 rHe2 −297.615 (1.420)

Nuclear structure contribution of order (Zα)5: 1.529 rHe3 7.261 (0.035)

Nuclear structure and one- two-loop VP+ higher order nucl. structure −2.357

Nuclear polarizability contribution: Borie, Rinker, PRA 14, 18 (1978) 3.100 (0.600)−−−−−−−−

Ji, Nevo Dinur, Bacca, Barnea, PRL 111, 143402 (2013) 2.470 (0.148)

Total splitting 1379.384 meV


µHe+ Lamb shift, He nuclear radius

∆E(2P1/2−2S1/2) = 1669.740(10)(150)−105.322rHe2 +1.529rHe

3 meV

= 1379.390(10)th(150)pol(1370)fin. size meV

for rHe = 1.681(4) fm [Sick, PRC 77, 041302 (2008)]

He nuclear polarizability has recetly been calculated with ur = 6%

Ji, Nevo Dinur, Bacca, Barnea, PRL 111, 143402 (2013)

We have measured the 1st transition frequency to (better than) 50 ppm

(⇔ Γ/20⇔ 20 GHz)

−→ Determine rHe with ur = 3×10−4 accuracy (∼ 10 times better than before)


Old µHe+ resonances

2S→2P3/2

Carboni et al, Nucl. Phys. A273, 381 (1977)

2S→2P1/2

Carboni et al, Phys. Lett. 73B, 229 (1978)


µHe+(2S) lifetime

Hauser et al., PRA 46, 2363 (1992)

laser exp.: Dittus, PhD thesis ETH Zurich (1985)

von Arb et al., PLB 136, 232 (1984)


APD WFD trace

x-ray

decay electron

WFD bins (4ns)


APD energy spectrum

Lα

Kα (∆E/E = 17% FWHM)

decay electrons

PRELIMINARYRandolf Pohl Lepton Moments, July 22 2014 48

µHe Kα x-ray time spectrum

PRELIMINARYRandolf Pohl Lepton Moments, July 22 2014 49

2S – 4P setupCEM collimator

cryostat

nozzle

CEMHR

�✁metal shields

2S-4P

interaction point

atomic beam

axis

486 nm

A. Beyer, RP et al., Ann. d. Phys. 525, 671 (2013)


Retroreflector for 2S – 4P

Two exactly counter-propagating wave fronts of same intensity

cancel 1st order Doppler shift.

HR

H(2S)

SMfiber1

SMfiber2AOM

BS

PBS

EOM

AFR in vacuum

2D tiltstabilization

intensitystabilization

486 nmlaser system

BD

frequency scan

ISO

PZTspow

ermon

itor

PD1 PD2

2S – 4P resonance at

88±0.5 ◦ and 90±0.08 ◦

A. Beyer, RP et al., Ann. d. Phys. 525, 671 (2013)


The laser system

cw TiSa laserYb:YAG thin−disk laser

9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

Main components:

• Thin-disk laser

fast response to detected µ−

• Frequency doubling

• TiSa laser:

frequency stabilized cw laser

injection seeded oscillator

multipass amplifier

• Raman cell

3 Stokes: 708 nm→ 6 µm

λ calibration @ 6 µm

• Target cavity

A. Antognini, RP et. al., Opt. Comm. 253, 362 (2005).


The laser system


9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

Thin-disk laser

• Large pulse energy: 85 (160) mJ

• Short trigger-to-pulse delay: . 400 ns

• Random trigger

• Pulse-to-pulse delays down to 2 ms

(rep. rate & 500 Hz)

• Each single µ− triggers the laser system

• 2S lifetime ≈ 1 µs→ short laser delay

A. Antognini, RP et. al.,

IEEE J. Quant. Electr. 45, 993 (2009).


The laser system


9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

MOPA TiSa laser:

cw laser, frequency stabilized

- referenced to a stable FP cavity

- FP cavity calibrated with I2, Rb, Cs lines

νFP = N ·FSR

FSR = 1497.344(6) MHz

νcwTiSa absolutely known to 30 MHz

Γ2P−2S = 18.6 GHz

Seeded oscillator

→ νpulsedTiSa = ν

cwTiSa

(frequency chirp ≤ 200 MHz)

Multipass amplifier (2f- configuration)

gain=10


The laser system


9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

Raman cell:

µ6.02 m

µ6.02 mH2

4155

cm−

1

v=0

v=1

H 2

708 nm

2 Stokes 3 Stokesrdnd

1 Stokes st

µ1.00 m1.72 m µ

708 nm

ν6µm = ν708nm−3 · h̄ωvib

ωvib(p,T ) = consttunable

P. Rabinowitz et. al., IEEE J. QE 22, 797 (1986)


The laser system


9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

α

190 mm

2 mm

25 µ

3 mm

12

Horiz. plane Vert. plane

−

Laser pulseb

Design: insensitive to misalignment

Transverse illumination

Large volume

Dielectric coating with R≥ 99.9% (at 6 µm )

→ Light makes 1000 reflections

→ Light is confined for τ=50 ns

→ 0.15 mJ saturates the 2S−2P transition

J. Vogelsang, RP et. al., Opt. Expr. 22, 13050 (2014)


The laser system


9 mJ 9 mJ

Oscillator200 W

500 W43 mJ

Wavemeter

Raman cell

7 mJ

µ

Verdi

Amplifier

5 W

FP

1030 nmOscillator

Amplifier

1030 nm 200 W

500 W

I / Cs2SHG

23 mJ515 nm23 mJ 1.5 mJ

µ6 m cavity

cw TiSa708 nm400 mW

43 mJ

SHG

SHG

H O20.25 mJ

6 m6 m

TiSa Amp.TiSa Osc.

708 nm, 15 mJ

20 m

µµ

−

Ge−filter

monitoring

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

wavenumber (cm-1)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1630 1640 1650 1660 1670 1680 1690 1700

scan region

wavenumber (cm-1)

Water absorption

• Vacuum tube for 6 µm beam transport.

• Direct frequency calibration at 6 µm.


Muon beam line


Muon beam: inside 5 T solenoid

PM PM

PM

−

−2

H Target

µ-3

2

Laser pulse

e

10 cm

2

1

1

ExBe

SS Multipass cavity

S1,S2 Stacks of Carbon foils (4 µg/cm2) ⇒ detection and cooling of keV muons

S1: 5 foils, ∆U=2 kV

S2: 2 foils: e− go upstream or downstream

e− are detected in plastic scintillators + PMTs

~E×~B drift region separates e− from µ−

muon TOF


Target, cavity and detectors

Muons

Laser pulse


Two muon puzzlesTwo muon puzzlesTwo muon puzzlesTwo muon puzzles

OutlineProton radius vs. timeProton radius vs. timeProton radius vs. timeProton radius vs. time

untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics} untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics} untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics} untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics} untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics} untilSlide *{2}{ Atomic physics} �romSlide *{3}{Atomic and nuclear physics}

Muonic hydrogenMuonic hydrogenMuonic hydrogen

mbox {}hspace {-5mm}Proton charge radius and muonic hydrogenSetupThe resonance: discrepancy, sys., stat. The proton radius puzzleThe proton radius puzzle

What may be wrong?What may be wrong?What may be wrong?


Discussions: Proton polarizabilityDiscussions: Proton polarizabilityDiscussions: Proton polarizabilityDiscussions: Proton polarizability

What may be wrong?Discussions: New PhysicsDiscussions: New PhysicsDiscussions: New Physics

p and $a_mu $p and $a_mu $

What may be wrong?What may be wrong?

Hydrogen spectroscopyHydrogen spectroscopyHydrogen spectroscopy

Hydrogen spectroscopyHydrogen spectroscopyHydrogen spectroscopyHydrogen spectroscopyHydrogen spectroscopy

Hydrogen spectroscopyMuonic DEUTERIUMDeuteron charge radiusDeuteron charge radiusDeuteron charge radius

Proton-deuteron isotope shiftLamb shift in muonic {color {BurntOrange} helium}Lamb shift in muonic {color {BurntOrange} helium}Lamb shift in muonic {color {BurntOrange} helium}Lamb shift in muonic {color {BurntOrange} helium}

1st resonance in muonic He-41st resonance in muonic He-41st resonance in muonic He-41st resonance in muonic He-4

2nd resonance in muonic He-41st resonance in muonic He-3SummaryCREMA collaborationThe proton radius puzzleWhat may be wrong?What may be wrong?What may be wrong?What may be wrong?What may be wrong?What may be wrong?


Discussions: 3rd Zemach momentContributions to the �oldmuHef {} Lamb shiftContributions to the �oldmuHef {} Lamb shift

�oldmuHe {} Lamb shift, He nuclear radiusOld �oldmuHe {} resonances�oldmuHe {}(2S)lifetimeAPD WFD traceAPD energy spectrum$mu $He K$_alpha $ x-ray time spectrum$mu $He K$_alpha $ x-ray time spectrum

2S -- 4P setupRetroreflector for 2S -- 4PThe laser system The laser system The laser system The laser system The laser system The laser system

Muon beam lineMuon beam lineMuon beam: inside 5,T solenoidTarget, cavity and detectors

Lamb shift in muonic hydrogen - Boston Universityg2pc1.bu.edu/lept14/talks/Pohl_LM14_V3.pdf ·...

Documents

Transcript of Lamb shift in muonic hydrogen - Boston Universityg2pc1.bu.edu/lept14/talks/Pohl_LM14_V3.pdf ·...