Lamb Shift in Muonic Hydrogen the Proton Radius Puzzle Muonic News Muonic Deuterium and Helium Muonic Hydrogen and Deuterium

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Lamb shift in muonic hydrogen The Proton Radius Puzzle Muonic news Muonic deuterium and helium Muonic hydrogen and deuterium

Randolf Pohl

Max-Planck-Institut fur¨ Quantenoptik Garching 1

7.9 p 2013 electron avg.

scatt. JLab

p 2010 scatt. Mainz

H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] There is the muon g-2 puzzle.

RandolfPohl LeptonMoments,July222014 2 ––––––––––––––––There is the muon g-2 puzzle.

RandolfPohl LeptonMoments,July222014 2 There are TWO muon puzzles.

RandolfPohl LeptonMoments,July222014 2 Two muon puzzles

• Anomalous magnetic moment of the muon ∼ 3.6σ

J. Phys. G 38, 085003 (2011). RandolfPohl LeptonMoments,July222014 3 Two muon puzzles

• Anomalous magnetic moment of the muon ∼ 3.6σ

• Proton radius from muonic hydrogen

RandolfPohl LeptonMoments,July222014 3 Two muon puzzles

• Anomalous magnetic moment of the muon ∼ 3.6σ

• Proton radius from muonic hydrogen ∼ 7.9σ The measured value of the proton rms charge radius from muonic hydrogen µ p is 10 times more accurate, but 4% smaller than the value from both hydrogen spectroscopy and elastic electron proton scattering. 7.9 σ µp 2013 electron avg.

scatt. JLab

µp 2010 scatt. Mainz

H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch RP et al., Nature 466, 213 (2010); Science 339, 417 (2013); ARNPS 63, 175 (2013). RandolfPohl LeptonMoments,July222014 3 Two muon puzzles

• Anomalous magnetic moment of the muon ∼ 3.6σ

• Proton radius from muonic hydrogen ∼ 7.9σ

• These 2 discrepancies may be connected.

rp aµ

Karshenboim, McKeen, Pospelov, arXiv 1401.6156 RandolfPohl LeptonMoments,July222014 3 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

RandolfPohl LeptonMoments,July222014 4 Proton radius vs. time

The proton rms charge radius is not the most accurate quantity in the universe. 0.920 • • electron scattering 0.900 • 2 slope of GE at Q = 0 0.880 • 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states)

0.820 Orsay Sick, 2003

Proton radius (fm) Proton radius Stanford Hydrogen 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 0.780 Mergell VMD year → 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm (ur = 2 %) Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %)

RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time

The proton rms charge radius is not the most accurate quantity in the universe. 0.920 Electron scattering: • 0.900 • electron scattering dG Q2 • 2 2 E ( ) 2 2 hr i = −6h¯ ⇒ slope of GE at Q = 0 p 2 2 slope of GE at Q = 0 0.880 dQ Q =0

• 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states)

0.820 Orsay Sick, 2003

RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time

The proton rms charge radius is not the most accurate quantity in the universe. 0.920 Hydrogen spectroscopy (Lamb shift): • • electron scattering 0.900 • 2 2 L1S(rp)= 8171.636(4)+ 1.5645hrpi MHz slope of GE at Q = 0 0.880 8S 0.860 4S • hydrogen spectr. 3S 3D • 2S-8S 2S-8D 0.840 Lamb shift (S-states) 2S 2P 0.820 R∞ L1S OrsayEnS ≃− 2 +Sick,3 2003

Proton radius (fm) Proton radius Stanford n Hydrogenn 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 2 unknowns 2 transitions 0.780 1S-2S Mergell VMD⇒ → year • Rydberg constant R∞ 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm• Lamb shift (uLr1=S ←2 %)rp Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %) 1S

RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time

The proton rms charge radius is not the most accurate quantity in the universe. 0.920 • • electron scattering 0.900 • 2 our goal slope of GE at Q = 0 0.880 • 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states)

0.820 Orsay Sick, 2003

RandolfPohl LeptonMoments,July222014 5 Atomic physics

Spectrum of atomic hydrogen 8S ... 4S Bohr model quantum mechanics → 3S 3D

n=2 2S 2P

n=1

RandolfPohl LeptonMoments,July222014 6 Atomic physics

Bohr model → quantum mechanics 8S ... 4S planetary orbits wave function → 3S 3D

n=2 2S 2P

n=1

Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics

Wave functions of S and P states: 8S ...

1 4S 2S 3S 3D 2P radial w.f. radial 0.5 2S 2P

0 1 2 3 4 5 6 7 8 r [Zr/a0] S states: max. at r=0 P states: zero at r=0

Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted.

Shift ist proportional to the

size of the proton 1S

Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics

8S ... 4S arb. units 3S 3D

Coulomb potential: V = 1/r 2S 2P

0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0

Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted.

Shift ist proportional to the

size of the proton 1S

Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics

8S ... proton charge 4S arb. units 3S 3D

Coulomb potential: V = 1/r 2S 2P

0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0

Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted.

Shift ist proportional to the

size of the proton 1S

Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics

8S ... proton charge 4S arb. units 3S 3D

true potential Coulomb potential: V = 1/r 2S 2P

0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0

Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted.

Shift ist proportional to the

size of the proton 1S

Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Muonic hydrogen

Regular hydrogen: Muonic hydrogen:

electron e− + proton p muon µ− + proton p

electron

RandolfPohl LeptonMoments,July222014 7 Muonic hydrogen

Regular hydrogen: Muonic hydrogen:

electron e− + proton p muon µ− + proton p

electron

✒ from Wikipedia

RandolfPohl LeptonMoments,July222014 7 Muonic hydrogen

Regular hydrogen: Muonic hydrogen:

electron e− + proton p muon µ− + proton p

muon mass mµ ≈ 200 ×me

Bohr radius rµ ≈ 1/200 ×re electron µ inside the proton: 2003 ≈ 107

muon

muon much is more sensitive to rp

RandolfPohl LeptonMoments,July222014 7 Proton charge radius and muonic hydrogen

µp(n=2) levels: 8.4 meV F=2 Lamb shift in µp [meV]: 2P3/2 F=1 2P1/2 F=1 F=0 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] 206 meV 50 THz 6 µm Proton size effect is 2% of the µ p Lamb shift

225 meV Measure to 10−5 ⇒ r to 0.05% p 55 THz 5.5 µm

Experiment: R. Pohl et al., Nature 466, 213 (2010). fin. size: A. Antognini, RP et al., Science 339, 417 (2013). 3.7 meV F=1 2S1/2 Theory summary: 23 meV A. Antognini, RP et al., Ann. Phys. 331, 127 (2013). F=0

RandolfPohl LeptonMoments,July222014 8 Muonic measurements.

RandolfPohl LeptonMoments,July222014 9 Setup

RandolfPohl LeptonMoments,July222014 10 The resonance: discrepancy, sys., stat.

Water-line/laser wavelength: ∆ν water-line to resonance: 300 MHz uncertainty 200 kHz uncertainty

7 CODATA-06 our value ] -4

6 e-p scattering

H2O Statistics: 700 MHz 5 calib. Systematics: 300 MHz

delayed / prompt events [10 3

0 49.75 49.8 49.85 49.9 49.95 laser frequency [THz]

Discrepancy: R. Pohl et al., Nature 466, 213 (2010). 5.0σ ↔ 75 GHz ↔ δν /ν = 1.5 × 10−3 A. Antognini, RP et al.,Science 339, 417 (2013).

RandolfPohl LeptonMoments,July222014 11 The proton radius puzzle.

RandolfPohl LeptonMoments,July222014 12 The proton radius puzzle

The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm muons: 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg.

scatt. JLab

µp 2010 scatt. Mainz

H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] RP, Gilman, Miller, Pachucki, Annu. Rev. Nucl. Part. Sci. 63, 175 (2013). ch RandolfPohl LeptonMoments,July222014 13 The proton radius puzzle

The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm muons: 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg.

scatt. JLab

µp 2010 scatt. Mainz

H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch

RandolfPohl LeptonMoments,July222014 13 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? µp experiment 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)

RandolfPohl LeptonMoments,July222014 14 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)?

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

4 line widths ! Γ = 19GHz 7 CODATA-06 our value ] -4

6 e-p scattering 2 resonances in µp give the same rp H2O 5 calib.

delayed / prompt events [10 3

0 49.75 49.8 49.85 49.9 49.95 laser frequency [THz]

RandolfPohl LeptonMoments,July222014 15 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)?

µp experiment probably not wrong by 100 σ

RandolfPohl LeptonMoments,July222014 15 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] Discrepancy = 0.31 meV Theory uncert. = 0.0025 meV Some contributions to the µp Lamb shift =⇒ 120δ(theory) deviation 1-loop eVP 205 meV proton size 2-loop eVP double-checked by many groups µSE and µVP th discrepancy 5 largest term! 1-loop eVP in 2 Coul. recoil 2-photon exchange hadronic VP Theory summary: proton SE A. Antognini, RP et al. 3-loop eVP Annals of Physics 331, 127 (2013) light-by-light 0.5 1 1.5 2 2.5 3 3.5 4meV

RandolfPohl LeptonMoments,July222014 16 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] Discrepancy = 0.31 meV Theory uncert. = 0.0025 meV Some contributions to the µp Lamb shift =⇒ 120δ(theory) deviation 1-loop eVP proton size 2-loop eVP double-checked by many groups µSE and µVP th discrepancy 5 largest term! 1-loop eVP in 2 Coul. recoil 2-photon exchange hadronic VP Theory summary: proton SE A. Antognini, RP et al. 3-loop eVP Annals of Physics 331, 127 (2013) light-by-light -3 -2 -1 2 10 10 10 1 10 10 meV RandolfPohl LeptonMoments,July222014 16 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] Discrepancy = 0.31 meV Theory uncert. = 0.0025 meV Some contributions to the µp Lamb shift =⇒ 120δ(theory) deviation 1-loop eVP proton size 2-loop eVP double-checked by many groups µSE and µVP th discrepancy 5 largest term! 1-loop eVP in 2 Coul. recoil 2-photon exchange hadronic VP Theory summary: proton SE A. Antognini, RP et al. 3-loop eVP Annals of Physics 331, 127 (2013) light-by-light -3 -2 -1 2 10 10 10 1 10 10 meV RandolfPohl LeptonMoments,July222014 16 Discussions: Proton polarizability

proton polarizability aka. two-photon exchange

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

Keep in mind: Discrepancy: 0.31meV Polarizability: 0.015(4) meV 20 times smaller!

RandolfPohl LeptonMoments,July222014 17 Discussions: Proton polarizability

G.A. Miller et al., PRA 84, 020101(R) (2011) “Toward a resolution of the proton size puzzle” 4 New off-mass-shell effect m solves puzzle. ∼ α M3 R.J. Hill, G. Paz, PRL, 107, 160402 (2011) “Model independent analysis of proton structure for hydrogenic bound states” 2 forward Compton amplitude’s W1(0,Q ) 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.

RandolfPohl LeptonMoments,July222014 17 Discussions: Proton polarizability

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” 2 Calculate T1(0,Q ) 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 responsible 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 rp problem is urgently needed in light of the new signiﬁcant investments made in the continuation of the experimental g − 2 program.” RandolfPohl LeptonMoments,July222014 17 Discussions: Proton polarizability

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 !]

RandolfPohl LeptonMoments,July222014 17 What may be wrong?

Standard Model wrong?!?

RandolfPohl LeptonMoments,July222014 18 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)µ IF coupling to e, n is suppressed relative to coupling to µ, p prediction for µHe+, µ+µ−

RandolfPohl LeptonMoments,July222014 19 Discussions: New Physics

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.”

RandolfPohl LeptonMoments,July222014 19 Discussions: New Physics

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 interactions. [...] 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.

RandolfPohl LeptonMoments,July222014 19 rp and aµ

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 −9 −7 5 × 10 < |∆(aµ )| < 10 (for Λhad = mπ ...mp). J. Phys. G 38, 085003 (2011). −9 This is much larger than the (g − 2)µ discrepancy of ∼ 1 × 10 .

after Pospelov Karshenboim, McKeen, Pospelov, arXiv 1401.6156 RandolfPohl LeptonMoments,July222014 20 rp and aµ

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 −9 −7 5 × 10 < |∆(aµ )| < 10 (for Λhad = mπ ...mp). J. Phys. G 38, 085003 (2011). −9 This is much larger than the (g − 2)µ discrepancy of ∼ 1 × 10 .

Maybe one can invert the argument:

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

after Pospelov Karshenboim, McKeen, Pospelov, arXiv 1401.6156 RandolfPohl LeptonMoments,July222014 20 What may be wrong?

Standard Model wrong?

RandolfPohl LeptonMoments,July222014 21 What may be wrong?

Standard Model wrong?

RandolfPohl LeptonMoments,July222014 21 Hydrogen spectroscopy

2 Lamb shift : L1S(rp) = 8171.636(4)+ 1.5645hrpi MHz L L ≃ 1S nS n3 8S 4S 3S 3D

2S 2P

RandolfPohl LeptonMoments,July222014 22 Hydrogen spectroscopy

2 Lamb shift : L1S(rp) = 8171.636(4)+ 1.5645hrpi MHz L L ≃ 1S nS n3 8S 4S

3S 3D F=2 2P3/2 F=1

2S 2P classical Lamb shift: 2S-2P 2S-2P Lamb, Retherford 1946

Lundeen, Pipkin 1986 9910 MHz = µ Hagley, Pipkin 1994 40 eV Hessels et al., 201x

2S F=1 1058 MHz = 1/2 F=0 4 µeV F=1 2P1/2 F=0 1S

RandolfPohl LeptonMoments,July222014 22 Hydrogen spectroscopy

2 Lamb shift : L1S(rp) = 8171.636(4)+ 1.5645hrpi MHz L L ≃ 1S nS n3 8S 4S 3S 3D 2S-4P 2S-8D

2S 2P

R L E ≃− ∞ + 1S nS n2 n3 1S-2S 2 unknowns ⇒ 2 transitions

• Rydberg constant R∞

• Lamb shift L1S ← rp

RandolfPohl LeptonMoments,July222014 22 Hydrogen spectroscopy

2S1/2 - 2P1/2

2S1/2 - 2P3/2

1S-2S + 2S- 4S1/2

1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2

1S-2S + 2S- 6S1/2

1S-2S + 2S- 6D5/2

1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2

1S-2S + 2S- 8D5/2

1S-2S + 2S-12D3/2

1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 23 Hydrogen spectroscopy

2S1/2 - 2P1/2

2S1/2 - 2P3/2

1S-2S + 2S- 4S1/2

1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2

1S-2S + 2S- 6S1/2

1S-2S + 2S- 6D5/2

1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2

1S-2S + 2S- 8D5/2

1S-2S + 2S-12D3/2 µp : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 23 Hydrogen spectroscopy

2S1/2 - 2P1/2

2S1/2 - 2P3/2

1S-2S + 2S- 4S1/2

1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2

1S-2S + 2S- 6S1/2

1S-2S + 2S- 6D5/2

1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2

1S-2S + 2S- 8D5/2 H = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D3/2 avg µp : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 23 Hydrogen spectroscopy

2S1/2 - 2P1/2

2S1/2 - 2P3/2

1S-2S + 2S- 4S1/2

1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2

1S-2S + 2S- 6S1/2

1S-2S + 2S- 6D5/2

1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2

1S-2S + 2S- 8D5/2 H = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D3/2 avg µp : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 23 Hydrogen spectroscopy

New measurements of the Rydberg constant are 2S1/2 - 2P1/2 urgently needed to resolve the puzzle µp vs. H 2S1/2 - 2P1/2 • Flowers @ NPL: 2S − nS,D : n > 4 2S1/2 - 2P3/2 [Flowers et al., IEEE Trans. Instr. Meas. 56, 331 (2007)] 1S-2S + 2S- 4S1/2 • Tan @ NIST: Ne9+ 1S-2S + 2S- 4D5/2 [Tan et al., Phys. Scr. T144, 014009 (2011)] 1S-2S + 2S- 4P1/2 • Udem, RP et al. @ MPQ: 2S − 4P 1S-2S + 2S- 4P3/2 [Beyer, RP et al., Ann.d.Phys. 525, 671 (2013)] 1S-2S + 2S- 6S 1/2 • Hessels @ York: 2S − 2P 1S-2S + 2S- 6D 5/2 [Hessels et al., Bull. APS 57(5), Q1.138 (2012)] 1S-2S + 2S- 8S 1/2 • Pachucki: He 1S-2S + 2S- 8D 3/2 • Udem @ MPQ, Eikema @ Amsterdam: He+ 1S-2S + 2S- 8D5/2 [Herrmann et al., PRA 79, 052505 (2009)] H = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D3/2 avg µp : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 23 Hydrogen spectroscopy

2S1/2 - 2P1/2

2S1/2 - 2P3/2

1S-2S + 2S- 4S1/2

1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2 Projected accuracy Garching 2S-4P

1S-2S + 2S- 6S1/2

1S-2S + 2S- 6D5/2

1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2

1S-2S + 2S- 8D5/2 H = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D3/2 avg µp : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

RandolfPohl LeptonMoments,July222014 24 Muonic deuterium

RandolfPohl LeptonMoments,July222014 25 muonic deuterium

2P3/2 2P1/2

F=3/2 2S1/2 F=1/2

RandolfPohl LeptonMoments,July222014 26 muonic deuterium

F=5/2 2P3/2 2P 2P3/2 F=1/2 1/2 F=3/2

F=3/2 2P1/2 ✲ F=1/2

F=3/2

2S1/2

F=3/2 2S1/2 F=1/2 F=1/2

RandolfPohl LeptonMoments,July222014 26 Muonic DEUTERIUM

] 2.5 resonances in muonic deuterium -4

8 • µd[2S1/2(F=3/2) → 2P3/2(F=5/2) ]

6 20 ppm (stat., online)

d[2S (F=1/2) 2P (F=3/2) ] 4 • µ 1/2 → 3/2 45 ppm (stat., online)

2 delayed / prompt events [10 delayed / • µd[2S1/2(F=1/2) → 2P3/2(F=1/2) ]

0 70 ppm (stat., online) 780 800 820 840 860 880 F=5/2 ν - 50.0 THz (GHz) only 5σ signiﬁcant 2P3/2 F=1/2 8 F=3/2 identiﬁes F=3/2 line

] 7

-4 F=3/2 2P1/2 6 F=1/2

3 F=3/2

2 2S1/2 delayed / prompt events [10 delayed / 1

0 -40 -20 0 20 40 60 80 100 120 140 160 F=1/2 ν - 52.0 THz (GHz) RandolfPohl LeptonMoments,July222014 27 Deuteron charge radius

2 2 2 H/D isotope shift: rd − rp = 3.82007(65) fm C.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

µH + iso H/D(1S-2S) CODATA-2010

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 Deuteron charge radius [fm] RandolfPohl LeptonMoments,July222014 28 Deuteron charge radius

2 2 2 H/D isotope shift: rd − rp = 3.82007(65) fm C.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! µd Borie+Pachucki+Ji+Friar µd Borie+Ji µd Borie+Pachucki PRELIMINARY µd Martynenko µH + iso H/D(1S-2S) CODATA-2010

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 Deuteron charge radius [fm] RandolfPohl LeptonMoments,July222014 28 Deuteron charge radius

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

µd Borie+Pachucki+Ji+Friar µd Borie+Ji µd Borie+Pachucki PRELIMINARY µd Martynenko µH + iso H/D(1S-2S) CODATA-2010

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 Deuteron charge radius [fm] RandolfPohl LeptonMoments,July222014 28 Proton-deuteron isotope shift

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

2 2 2 rd − rp: H/D isotope shift 3.82007 ± 0.00065 fm muonic Lamb shift 3.8221 ± 0.0052 fm2 PRELIMINARY! scattering 3.764 ± 0.045 fm2 The muonic error is conservative (nucl. structure terms).

PRELIMINARY µd/µp (2S-2P)

electronic H/D (1S-2S) scattering

3.72 3.74 3.76 3.78 3.8 3.82 2 2 2 Rd - Rp [fm ] RandolfPohl LeptonMoments,July222014 29 Muonic helium ions.

RandolfPohl LeptonMoments,July222014 30 Lamb shift in muonic helium

RandolfPohl LeptonMoments,July222014 31 Lamb shift in muonic helium

146 meV 145 meV 8.4 meV F=1 F=2 2P3/2 2P3/2 2P3/2 F=1 F=2 2P F=1 2P 1/2 2P 2P F=0 F=0 4 1/2 3 2P F=1 µp µ He µ He 1/2 206 meV 812 nm 50 THz 6 µm 898 nm

F=0 167 meV 2S fin. size: 1/2 F=1 3.8 meV 2S1/2 F=1 fin. size effect fin. size effect 2S1/2 23 meV 290 meV 397 meV F=0

RandolfPohl LeptonMoments,July222014 31 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) 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]

RandolfPohl LeptonMoments,July222014 31 Lamb shift in muonic helium

4He beam time: Oct.-Dec. 2013 3He beam time: May-Aug. 2014

RandolfPohl LeptonMoments,July222014 31 1st resonance in muonic He-4 4 µ He(2S1/2 → 2P3/2) at ∼ 813 nm wavelength

10›3

1.2

1 Events / Prompt

0.8 Preliminary

0.6

0.4

0.2

0 ›3 ›2 ›1 0 1 2 3 4 Frequency [THz]

RandolfPohl LeptonMoments,July222014 32 1st resonance in muonic He-4 4 µ He(2S1/2 → 2P3/2) at ∼ 813 nm wavelength

10›3

1.2 Theory + Sick

1 Events / Prompt

0.8 Preliminary

0.6

0.4

0.2

0 ›3 ›2 ›1 0 1 2 3 4 Frequency [THz] Sick, PRD 77, 040302(R) (2008) Borie, Ann. Phys. 327, 733 (2012)

RandolfPohl LeptonMoments,July222014 32 1st resonance in muonic He-4 4 µ He(2S1/2 → 2P3/2) at ∼ 813 nm wavelength

10›3

1.2 Zavattini

1 Events / Prompt

0.8 Preliminary

0.6

0.4

0.2

0 ›3 ›2 ›1 0 1 2 3 4 Frequency [THz] Carboni et al, Nucl. Phys. A273, 381 (1977)

RandolfPohl LeptonMoments,July222014 32 1st resonance in muonic He-4 4 µ He(2S1/2 → 2P3/2) at ∼ 813 nm wavelength

10›3

1.2 Pospelov

1 Events / Prompt

0.8 Preliminary

0.6

0.4

0.2

0 ›3 ›2 ›1 0 1 2 3 4 Frequency [THz] Batell, McKeen, Pospelov, PRL 107, 011803 (2011)

RandolfPohl LeptonMoments,July222014 32 2nd resonance in muonic He-4 4 µ He(2S1/2 → 2P1/2) at ∼ 899 nm wavelength

›3 0.6 10

0.5 PRELIMINARY 0.4

0.3

0.2

0.1

0 ›0.6 ›0.4 ›0.2 0 0.2 0.4 0.6

RandolfPohl LeptonMoments,July222014 33 1st resonance in muonic He-3 3 F=1 F=2 µ He(2S1/2 → 2P3/2 ) at ∼ 864 nm wavelength

›3 0.6 10

0.5 PRELIMINARY 0.4

0.3

0.2

0.1

0 ›0.8 ›0.6 ›0.4 ›0.2 0 0.2 0.4 0.6 0.8 1 1.2

RandolfPohl LeptonMoments,July222014 34 Summary Muonic hydrogen gives:

Proton charge radius: rp= 0.84087(39) fm Proton Zemach radius: RZ = 1.082(37) fm Rydberg constant: radius QED 15 R∞ = 3.2898419602495 (10) (25) × 10 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 ...

RandolfPohl LeptonMoments,July222014 35 RandolfPohl LeptonMoments,July222014 36 CREMA collaboration

Charge Radius Experiment with Muonic Atoms

M. Diepold, B. Franke, J. Götzfried, T.W. Hänsch, J. Krauth, F. Mul- MPQ, Garching, Germany hauser, T. Nebel, R. Pohl A. Antognini, K. Kirch, F. Kottmann, B. Naar, K. Schuhmann, ETH Zürich, Switzerland D. Taqqu M. Hildebrandt, A. Knecht, A. Dax PSI, Switzerland F. Biraben, P. Indelicato, E.-O. Le Bigot, S. Galtier, L. Julien, F. Nez, Labor. Kastler Brossel, Paris, France C. Szabo-Foster F.D. Amaro, J.M.R. Cardoso, L.M.P. Fernandes, A.L. Gouvea, Uni Coimbra, Portugal J.A.M. Lopez, C.M.B. Monteiro, J.M.F. dos Santos 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

RandolfPohl LeptonMoments,July222014 37 Backup slides.

RandolfPohl LeptonMoments,July222014 38 The proton radius puzzle

The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm muons: 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg.

dispersion 2012 scatt. JLab

µp 2010 scatt. Mainz dispersion 2007 H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Belushkin, Hammer, Meissner PRC 75, 035202 (2007). Proton charge radius R [fm] Lorenz, Hammer, Meissner EPJ A 48, 151 (2012). ch RandolfPohl LeptonMoments,July222014 39 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)?

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

4 line widths ! Γ = 19GHz 7 CODATA-06 our value ] -4

6 e-p scattering 2 resonances in µp give the same rp H2O 5 calib.

delayed / prompt events [10 3

0 49.75 49.8 49.85 49.9 49.95 laser frequency [THz]

RandolfPohl LeptonMoments,July222014 40 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)? Wrong transition?

FS, HFS huge. signal [a.u.] µ H Next transition: ∼ 1 THz away.

46 47 48 49 50 51 52 53 54 frequency [THz] RandolfPohl LeptonMoments,July222014 40 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)? Wrong transition? Systematic error?

Laser frequency (H20 calibration) 300 MHz

intrinsic H2O uncertainty 2 MHz ACandDCstarkshift <1MHz Zeemanshift(5Tesla) <30MHz Dopplershift <1MHz Collisionalshift 2MHz ————– 300 MHz µp atom is small and not easily perturbed by external ﬁelds.

RandolfPohl LeptonMoments,July222014 40 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 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).

RandolfPohl LeptonMoments,July222014 40 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 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

RandolfPohl LeptonMoments,July222014 40 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp experiment wrong?

Frequency mistake by 75 GHz (⇔ 0.15%)? Wrong transition? Systematic error? Molecular effects? Gas imputities?

µp experiment probably not wrong by 100 σ

RandolfPohl LeptonMoments,July222014 40 What may be wrong?

RandolfPohl LeptonMoments,July222014 41 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] Discrepancy = 0.31 meV Theory uncert. = 0.0025 meV Some contributions to the µp Lamb shift =⇒ 120δ(theory) deviation 1-loop eVP proton size 2-loop eVP double-checked by many groups µSE and µVP th discrepancy 5 largest term! 1-loop eVP in 2 Coul. recoil 2-photon exchange hadronic VP Theory summary: proton SE A. Antognini, RP et al. 3-loop eVP Annals of Physics 331, 127 (2013) light-by-light -3 -2 -1 2 10 10 10 1 10 10 meV RandolfPohl LeptonMoments,July222014 41 What may be wrong?

75 GHz theo. CODATA exp.  Lµ p (rp ) − Lµ p =  0.31 meV e e 0.15 %  µp theory wrong? 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] Discrepancy = 0.31 meV Theory uncert. = 0.0025 meV =⇒ 120δ(theory) deviation

µp theory probably not wrong by 100 σ

RandolfPohl LeptonMoments,July222014 41 Discussions: 3rd Zemach moment

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

3 3 3 3 A large third Zemach moment hr i = d r1 d r2 ρ(r1)ρ(r2)|r1 − r2| p (2) R 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. 3 3 hrpi(2) (DeRujula) = 36.6 ± 6.9 fm 3 3 hrpi(2) (Sick) = 2.71 ± 0.13 fm

PLB 696, 343 Distler et al: “The RMS radius of the proton and Zemach moments” (1011.1861) 3 3 hrpi(2) (Mainz 2010) = 2.85 ± 0.08 fm

RandolfPohl LeptonMoments,July222014 42 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 (F1(0), F2(0)) −11.243 Recoil corrections (Zα)4, (Zα)5, (Zα)6 −0.355 Radiative-recoil corrections −0.040 4 2 Nuclear structure contribution of order (Zα) : -105.322 rHe −297.615 (1.420) 5 3 Nuclear structure contribution of order (Zα) : 1.529 rHe 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

RandolfPohl LeptonMoments,July222014 43 Contributions to the µ4He+ Lamb shift

RandolfPohl LeptonMoments,July222014 43 meV ] 3 He r 6% 529 . n) 50 ppm meV = 1 r + u 2 size . He r ﬁn ) 10 times better than before) Sick, PRC 77, 041302 (2008) 322 ∼ . ( 1370 ( 105 pol ) − ) 150 ( accuracy 150 th = 1.681(4) fm [ 4 )( ) − He r 10 10 10 ( ( for × 740 390 3 Ji, Nevo Dinur, Bacca, Barnea, PRL 111, 143402 (2013) . . = r u 1669 1379 with = He ) = r GHz) 2 / 1 20 S 2 ⇔ − 2 / 20 Lamb shift, He nuclear radius 1 / Determine P Γ 2 ( + ⇔ E He nuclear polarizability has recetly been calculated with We have measured the 1st transition frequency to (better tha −→ ( ∆ He

µ RandolfPohl LeptonMoments,July222014 44 Old µHe+ resonances

2S→2P3/2 2S→2P1/2

Carboni et al, Nucl. Phys. A273, 381 (1977) Carboni et al, Phys. Lett. 73B, 229 (1978)

RandolfPohl LeptonMoments,July222014 45 , PLB 136, 232 (1984) et al. von Arb Dittus, PhD thesis ETH Zurich (1985) , PRA 46, 2363 (1992) (2S) lifetime + et al. He laser exp.: Hauser

µ RandolfPohl LeptonMoments,July222014 46 APD WFD trace

x-ray

decay electron

WFD bins (4ns)

RandolfPohl LeptonMoments,July222014 47 APD energy spectrum

Lα

Kα (∆E/E = 17% FWHM)

decay electrons

PRELIMINARY

RandolfPohl LeptonMoments,July222014 48 PRELIMINARY x-ray time spectrum

α He K

µ RandolfPohl LeptonMoments,July222014 49 PRELIMINARY x-ray time spectrum

α He K

µ RandolfPohl LeptonMoments,July222014 49 2S – 4P setup atomic beam CEM collimator axis

cryostat

nozzle

486 nm CEM ✁ metal shields HR 2S-4P interaction point A. Beyer, RP et al., Ann. d. Phys. 525, 671 (2013) RandolfPohl LeptonMoments,July222014 50 Retroreﬂector for 2S – 4P

Two exactly counter-propagating wave fronts of same intensity cancel 1st order Doppler shift.

AFR in vacuum H(2S)

PZTs monitor power SM HR fiber1

BS 2D tilt intensity 2S – 4P resonance at stabilization stabilization 88 ± 0.5 ◦ and 90 ± 0.08 ◦ PD1 PD2 ISO

BD SM EOM AOM fiber2 486 nm laser system PBS frequency scan

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

RandolfPohl LeptonMoments,July222014 51 The laser system

Yb:YAG thin−disk laser Main components: cw TiSa laser Oscillator Oscillator 200 W 1030 nm 1030 nm 200 W Wave Verdi meter 9 mJ 9 mJ 5 W • Thin-disk laser Amplifier Amplifier cw TiSa fast response to detected µ− 500 W 500 W FP 43 mJ 708 nm 43 mJ • Frequency doubling SHG 400 mW SHG I2 / Cs SHG • TiSa laser: 7 mJ frequency stabilized cw laser 23 mJ 515 nm 23 mJ 1.5 mJ injection seeded oscillator TiSa Osc. multipass ampliﬁer TiSa Amp. 708 nm, 15 mJ

• Raman cell µ 6 m monitoring H 2 O 6 µ m 0.25 mJ 3 Stokes: 708 nm → 6 µm 20 m λ calibration @ 6 µm Raman cell Ge−filter • Target cavity

µ− 6 µ m cavity A. Antognini, RP et. al., Opt. Comm. 253, 362 (2005).

RandolfPohl LeptonMoments,July222014 52 The laser system

Yb:YAG thin−disk laser cw TiSa laser Oscillator Oscillator 200 W 1030 nm 1030 nm 200 W Wave Verdi Thin-disk laser meter 9 mJ 9 mJ 5 W • Large pulse energy: 85 (160) mJ Amplifier Amplifier cw TiSa 500 W 500 W • Short trigger-to-pulse delay: . 400 ns FP 708 nm 43 mJ 43 mJ SHG 400 mW • Random trigger SHG I2 / Cs SHG • Pulse-to-pulse delays down to 2 ms (rep. rate & 500 Hz) 7 mJ 23 mJ 515 nm 23 mJ 1.5 mJ

TiSa Osc. • Each single µ− triggers the laser system TiSa Amp. 708 nm, 15 mJ • 2S lifetime ≈ 1 µs → short laser delay

µ 6 m monitoring H 2 O 6 µ m 0.25 mJ 20 m Raman cell Ge−filter A. Antognini, RP et. al., µ− 6 µ m cavity IEEE J. Quant. Electr. 45, 993 (2009).

RandolfPohl LeptonMoments,July222014 52 The laser system

Yb:YAG thin−disk laser MOPA TiSa laser: cw TiSa laser Oscillator Oscillator 200 W 1030 nm 1030 nm 200 W Wave Verdi cw laser, frequency stabilized meter 9 mJ 9 mJ 5 W - referenced to a stable FP cavity 500 W Amplifier Amplifier 500 W cw TiSa FP 708 nm 43 mJ 43 mJ - FP cavity calibrated with I2, Rb, Cs lines SHG 400 mW SHG I2 / Cs νFP = N · FSR SHG FSR = 1497.344(6) MHz cw 7 mJ νTiSa absolutely known to 30 MHz 23 mJ 515 nm 23 mJ 1.5 mJ Γ2P−2S = 18.6 GHz TiSa Osc. TiSa Amp. 708 nm, 15 mJ Seeded oscillator pulsed cw µ → ν = ν 6 m monitoring H 2 O 6 µ m TiSa TiSa 0.25 mJ (frequency chirp 200 MHz) 20 m ≤ Raman cell Ge−filter Multipass ampliﬁer (2f- conﬁguration) gain=10 µ− 6 µ m cavity

RandolfPohl LeptonMoments,July222014 52 The laser system

Yb:YAG thin−disk laser Raman cell: cw TiSa laser Oscillator Oscillator 200 W 1030 nm 1030 nm 200 W Wave Verdi µ meter 708 nm 6.02 m 9 mJ 9 mJ 5 W H2

500 W Amplifier Amplifier 500 W cw TiSa FP 708 nm 43 mJ 43 mJ st nd rd SHG 400 mW 1 Stokes 2 Stokes 3 Stokes SHG I2 / Cs SHG 708 nm 7 mJ µ 23 mJ 515 nm 23 mJ 1.5 mJ 1.00 m 1.72 µ m 6.02 µ m −1 v=1 TiSa Osc. H v=0 2

TiSa Amp. 708 nm, 15 mJ 4155 cm

µ 6 m monitoring H 2 O 6 µ m 0.25 mJ 6µm 708nm 20 m ν = ν − 3 · h¯ωvib Raman cell Ge−filter tunable ωvib(p,T)= const

µ− 6 µ m cavity P. Rabinowitz et. al., IEEE J. QE 22, 797 (1986)

RandolfPohl LeptonMoments,July222014 52 The laser system

Yb:YAG thin−disk laser cw TiSa laser 12 Oscillator Oscillator 190 mm 200 W 1030 nm 1030 nm 200 W Wave Verdi µ− meter 9 mJ 9 mJ 5 W 25 Amplifier Amplifier cw TiSa 500 W 500 W FP α 43 mJ 708 nm 43 mJ Laser pulse SHG 400 mW SHG I2 / Cs 2 mm SHG 3 mm

Horiz. plane Vert. plane 7 mJ 23 mJ 515 nm 23 mJ 1.5 mJ Design: insensitive to misalignment TiSa Osc. Transverse illumination TiSa Amp. 708 nm, 15 mJ Large volume

µ 6 m monitoring H 2 O 6 µ m 0.25 mJ Dielectric coating with R ≥ 99.9% (at 6 µm ) 20 m → Light makes 1000 reﬂections Raman cell Ge−filter → Light is conﬁned for τ=50 ns → 0.15 mJ saturates the 2S − 2P transition µ− 6 µ m cavity

J. Vogelsang, RP et. al., Opt. Expr. 22, 13050 (2014) RandolfPohl LeptonMoments,July222014 52 The laser system

Yb:YAG thin−disk laser Water absorption cw TiSa laser 0.7 Oscillator Oscillator 0.6 200 W 1030 nm 1030 nm 200 W Wave Verdi meter 0.5 9 mJ 9 mJ 5 W 0.4 500 W Amplifier Amplifier 500 W cw TiSa FP 708 nm 0.3 43 mJ 43 mJ SHG 400 mW 0.2 SHG I2 / Cs 0.1 SHG 0 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 wavenumber (cm-1) 7 mJ 0.7 23 mJ 515 nm 23 mJ 1.5 mJ scan region 0.6 TiSa Osc. 0.5 TiSa Amp. 708 nm, 15 mJ 0.4 0.3

0.2 µ 6 m monitoring H 2 O 6 µ m 0.25 mJ 0.1 20 m 0 1630 1640 1650 1660 1670 1680 1690 1700 -1 Raman cell wavenumber (cm ) Ge−filter • Vacuum tube for 6 µm beam transport. µ− 6 µ m cavity • Direct frequency calibration at 6 µm.

RandolfPohl LeptonMoments,July222014 52 Muon beam line

RandolfPohl LeptonMoments,July222014 53 Muon beam line

RandolfPohl LeptonMoments,July222014 54 Muon beam: inside 5 T solenoid

PM 1 H2 Target e− µ S2 Multipass cavity S 1 − PM 3 PM2 e ExB 10 cm Laser pulse

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

S1: 5 foils, ∆U=2kV − 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

RandolfPohl LeptonMoments,July222014 55 Target, cavity and detectors

Muons

Laser pulse

RandolfPohl LeptonMoments,July222014 56