The size of the proton

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Max-Planck-Institut für Quantenoptik Garching, Germany Randolf Pohl

1 The size of the proton from the Lamb shift in muonic hydrogen Randolf Pohl The size of the proton from the Lamb shift in muonic hydrogen for the CREMA collaboration Randolf Pohl Max-Planck-Institut für Quantenoptik Garching, Germany Randolf Pohl ACFC, 18 July 2011 p. 1

2 Outline Randolf Pohl ACFC, 18 July 2011 p. 2 The problem: Proton rms charge radius r p from muonic hydrogen µp is 4 % smaller than the values from elastic electron-proton scattering and hydrogen spectroscopy. That s 5σ σ. But the µp result is 10 times more accurate than any other measurement. Introduction: Hydrogen, fundamental constants, QED tests and all that. How large is the proton? Muonic hydrogen: (Finite) size does matter! Experiment: Principle Muon beam Laser system A solution of the proton size puzzle

3 Hydrogen energy levels Randolf Pohl ACFC, 18 July 2011 p. 3 Energy n=3 n=2 n=1 Bohr E = R /n 2 V 1/r

4 Hydrogen energy levels Randolf Pohl ACFC, 18 July 2011 p. 3 Energy n=3 n=2 2P 3/2 2S 1/2, 2P 1/2 n=1 Bohr E = R /n 2 V 1/r Shift: GHz 1S 1/2 Dirac e spin relativity

5 Hydrogen energy levels Randolf Pohl ACFC, 18 July 2011 p. 3 Energy n=3 n=2 2P 3/2 2S 1/2, 2P 1/2 2S 1/2 2P 1/2 n=1 Shift: GHz 1S 1/2 8.2 GHz Bohr Dirac Lamb E = R /n 2 V 1/r e spin relativity QED

6 Hydrogen energy levels Randolf Pohl ACFC, 18 July 2011 p. 3 Energy n=3 n=2 2P 3/2 2S 1/2, 2P 1/2 2S 1/2 2P 1/2 F=1 F=0 n=1 Shift: GHz 1S 1/2 8.2 GHz 1.4 GHz F=1 F=0 Bohr Dirac Lamb hfs-splitting E = R /n 2 V 1/r e spin relativity QED proton-spin H hfs µ p µ e

7 Hydrogen energy levels Randolf Pohl ACFC, 18 July 2011 p. 3 Energy n=3 n=2 2P 3/2 2S 1/2, 2P 1/2 2S 1/2 2P 1/2 F=1 F= MHz n=1 Shift: GHz 1S 1/2 8.2 GHz 1.4 GHz F=1 F=0 1.2 MHz Bohr Dirac Lamb hfs-splitting r p E = R /n 2 V 1/r e spin relativity QED proton-spin H hfs µ p µ e proton size V 1/r

8 The Rydberg constant Randolf Pohl ACFC, 18 July 2011 p. 4 Accuracy of the Rydberg constant fractional uncertainty single measurements least-square adjustments year 2006: R = ± m 1 (u r = ) is the 2 nd most accurately determined fundamental constant.

9 Test of bound-state QED Randolf Pohl ACFC, 18 July 2011 p. 5 1S Lamb shift in hydrogen: L 1S (r p ) = (4) r 2 p ep 1S Lamb shift precision 10-5 δr p / r p = Munich Paris Yale δr p / r p = year MHz slide from 1999 until now accuracy of QED calculations future? QED-test is limited by the uncertainty of the proton rms charge radius.

10 Proton radius vs. time Randolf Pohl ACFC, 18 July 2011 p. 6 The proton rms charge radius is not the most accurate quantity in the universe ±2% electron scattering slope of G E at Q 2 = 0 Proton radius (fm) Orsay, 1962 Stanford, 1963 Saskatoon, 1974 Mainz, 1980 Mainz, free norm. dispersion fit Paris, 1996 Garching, Paris, 1999 Rosenfelder, 2000 Eides, 2001 Sick, 2003 Pachucki Jentschura, 03 CODATA e-p scattering: r p = 0.895(18) fm (u r = 2 %) CODATA: r p = (69) fm (u r = 0.8 %) 2008 year hydrogen spectr. Lamb shift (S-states)

11 Proton radius vs. time Randolf Pohl ACFC, 18 July 2011 p. 6 The proton rms charge radius is not the most accurate quantity in the universe Electron scattering: r 2 ±2% p = dg E(Q 2 ) Q2 6 2 dq 2 =0 slope of G E at Q 2 = 0 electron scattering slope of G E at Q 2 = 0 Proton radius (fm) Orsay, 1962 Stanford, 1963 Saskatoon, 1974 Mainz, 1980 Mainz, free norm. dispersion fit Paris, 1996 Garching, Paris, 1999 Rosenfelder, 2000 Eides, 2001 Sick, 2003 Pachucki Jentschura, 03 CODATA e-p scattering: r p = 0.895(18) fm (u r = 2 %) CODATA: r p = (69) fm (u r = 0.8 %) Vanderhaeghen, Walcher year hydrogen spectr. Lamb shift (S-states)

12 Proton radius vs. time Randolf Pohl ACFC, 18 July 2011 p. 6 Proton radius (fm) The proton rms charge radius is not the most accurate quantity in the universe Hydrogen spectroscopy (Lamb shift): 1962 L 1S (r p ) = (4) r 2 p ±2% 8S 4S 3S 2S-8S 2S 1S-2S S-8D 2P D Orsay, 1962 Stanford, 1963 Saskatoon, 1974 Mainz, 1980 Mainz, free norm. dispersion fit Paris, 1996 Garching, E ns R n 2 + L 1S Paris, 1999 Rosenfelder, 2000 Eides, 2001 Sick, 2003 n 3 Pachucki Jentschura, 03 CODATA Lamb shift L e-p scattering: r p = 0.895(18) fm (u 1S r r = 2 %) p CODATA: 1S r p = (69) fm (u r = 0.8 %) MHz 2 unknowns 2 transitions Rydberg constant R 2008 year electron scattering slope of G E at Q 2 = 0 hydrogen spectr. Lamb shift (S-states)

13 Proton radius vs. time Randolf Pohl ACFC, 18 July 2011 p. 6 Proton radius (fm) The proton rms charge radius is not the most accurate quantity in the universe ±2% Orsay, 1962 Stanford, 1963 Saskatoon, 1974 Mainz, 1980 Mainz, free norm. dispersion fit Paris, 1996 Garching, our goal Paris, 1999 Rosenfelder, 2000 Eides, 2001 Sick, 2003 Pachucki Jentschura, 03 CODATA 2006 e-p scattering: r p = 0.895(18) fm (u r = 2 %) CODATA: r p = (69) fm (u r = 0.8 %) muonic hydrogen goal (1998): u r = 0.1 % electron scattering hydrogen spectr year slope of G E at Q 2 = 0 Lamb shift (S-states) 20x improvement (aim: 10x better QED test in H)

14 Proton charge radius and muonic hydrogen Randolf Pohl ACFC, 18 July 2011 p. 7 muonic hydrogen = µ p Bohr: r orbit Zα m r c n2 E finite size (nl) r 2 p Ψ(r = 0) 2 E finite size (nl) = 2(Zα)4 c n 3 mass m µ = 207 m e m 3 r r 2 p δ l0 Lamb shift in µp: E(2P F=2 3/2 2SF=1 1/2 ) = (49) r 2 p r 3 p [mev] µp(n=2) levels: 2P 3/2 2P 1/2 206 mev 50 THz 6 µm 8.4 mev F=2 F=1 F=1 F=0 finite size contribution is 2% of the µp Lamb shift measure E(2S-2P) to 30 ppm = 1.5 GHz r p to 10 3 Γ 2P = 18.6 GHz (Γ rad. ) fin. size: 3.8 mev 2S 1/2 F=1 23 mev F=0

15 µp Lamb shift experiment: Principle Randolf Pohl ACFC, 18 July 2011 p. 8 prompt (t 0) delayed (t 1 µs) n~14 2 S 1 % 99 % 2 P 2 kev γ 2 S Laser 2 P 2 kev γ 1 S 1 S µ stop in H 2 gas µp atoms formed (n 14) 99%: cascade to µp(1s), emitting prompt K α, K β... 1%: long-lived µp(2s) atoms lifetime τ 2S 1 µs at 1 mbar H 2 R. Pohl et. al., Phys. Rev. Lett. 97, (2006). fire laser (λ 6 µm, E 0.2 ev) induce µp(2s) µp(2p) observe delayed K α x-rays normalize delayed K α prompt K α x-rays

16 µp Lamb shift experiment: Principle Randolf Pohl ACFC, 18 July 2011 p. 8 time spectrum of 2 kev x-rays ( 13 hours of data) events in 25 ns time [us]

17 µp Lamb shift experiment: Principle Randolf Pohl ACFC, 18 July 2011 p. 8 time spectrum of 2 kev x-rays events in 25 ns prompt (t 0) n~14 2 S 1 S 1 % 99 % 2 P 2 kev γ time [us]

18 µp Lamb shift experiment: Principle Randolf Pohl ACFC, 18 July 2011 p. 8 time spectrum of 2 kev x-rays events in 25 ns prompt (t 0) n~14 2 S 1 S 1 % 99 % 2 P 2 kev γ delayed (t 1 µs) 2 S 1 S Laser 2 P 2 kev γ time [us]

19 µp Lamb shift experiment: Principle Randolf Pohl ACFC, 18 July 2011 p. 8 time spectrum of 2 kev x-rays events in 25 ns prompt (t 0) n~14 2 S 1 S 1 % 99 % 2 P 2 kev γ delayed (t 1 µs) 2 S 1 S Laser 2 P 2 kev γ normalize delayed K α prompt K α Resonance ] -4 delayed / prompt events [ time [us] laser frequency [THz]

20 Muon beam line Randolf Pohl ACFC, 18 July 2011 p. 9

21 Muon beam: inside 5 T solenoid Randolf Pohl ACFC, 18 July 2011 p. 10 PM 1 B=5 Tesla Collimator µ PM 2 S 1 10 cm e e ExB HV S 2 Laser pulse Gas Target PM 3

22 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG SHG 23 mj 515 nm 23 mj 1.5 mj TiSa Amp. cw TiSa laser Wave meter FP I / Cs 2 7 mj Verdi 5 W cw TiSa 708 nm 400 mw TiSa Osc. 708 nm, 15 mj Main components: Thin-disk laser fast response to detected µ Frequency doubling TiSa laser: frequency stabilized cw laser injection seeded oscillator multipass amplifier 6 µ m monitoring 20 m H O Ge filter 6 m 2 µ 0.25 mj Raman cell Raman cell 3 Stokes: 708 nm 6 µm λ 6 µm Target cavity µ 6 µ m cavity A. Antognini et. al., Opt. Comm. 253, 362 (2005).

23 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG SHG 23 mj 515 nm 23 mj 1.5 mj cw TiSa laser Wave meter FP I / Cs 2 7 mj Verdi 5 W cw TiSa 708 nm 400 mw 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) TiSa Amp. TiSa Osc. 708 nm, 15 mj Each single µ triggers the laser system 2S lifetime 1 µs short laser delay 6 µ m µ monitoring 20 m H O Ge filter 6 m 2 µ 0.25 mj 6 µ m cavity Raman cell A. Antognini et. al., IEEE J. Quant. Electr. 45, 993 (2009).

24 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj µ Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG 23 mj 515 nm 23 mj 1.5 mj 6 µ m monitoring TiSa Amp. 20 m H O Ge filter SHG 6 m 2 µ 0.25 mj 6 µ m cavity cw TiSa laser Wave meter FP I / Cs 2 7 mj Raman cell Verdi 5 W cw TiSa 708 nm 400 mw TiSa Osc. 708 nm, 15 mj MOPA TiSa laser: Cw frequency stabilized laser - referenced to a stable FP cavity - FP cavity calibrated with I 2, Rb, Cs lines ν FP = N FSR FSR = (6) MHz ν cw TiSa absolutely known to 30 MHz Γ 2P 2S = 18.6 GHz Seeded oscillator ν pulsed TiSa = ν cw TiSa (frequency chirp 100 MHz) Multipass amplifier (2f- configuration) gain=10

25 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG SHG cw TiSa laser Wave meter FP I / Cs 2 Verdi 5 W cw TiSa 708 nm 400 mw Raman cell: 708 nm st 1 Stokes H 2 nd rd 2 Stokes 3 Stokes 6.02 µ m 23 mj 515 nm 23 mj 1.5 mj TiSa Amp. 7 mj TiSa Osc. 708 nm, 15 mj 708 nm 4155 cm µ m v=1 v= µ m 6.02 µ m H 2 6 µ m monitoring H O 6 m 2 µ 0.25 mj 20 m ν 6µm = ν 708nm 3 ω vib Ge filter Raman cell tunable ω vib (p, T) = const µ 6 µ m cavity P. Rabinowitz et. al., IEEE J. QE 22, 797 (1986)

26 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG SHG cw TiSa laser Wave meter FP I / Cs 2 Verdi 5 W cw TiSa 708 nm 400 mw µ Laser pulse 2 mm 190 mm α 25 β 12 3 mm 23 mj 515 nm 23 mj 1.5 mj TiSa Amp. 7 mj TiSa Osc. 708 nm, 15 mj Horiz. plane Vert. plane Design: insensitive to misalignment Transverse illumination Large volume 6 µ m monitoring 20 m H O Ge filter 6 m 2 µ 0.25 mj Raman cell Dielectric coating with R 99.9% (at 6 µm ) Light makes 1000 reflections Light is confined for τ=50 ns µ 6 µ m cavity 0.15 mj saturates the 2S 2P transition

27 The laser system Randolf Pohl ACFC, 18 July 2011 p W Yb:YAG thin disk laser 500 W 43 mj Oscillator 1030 nm Oscillator 1030 nm 200 W 9 mj 9 mj Amplifier SHG Amplifier 500 W 43 mj SHG SHG 23 mj 515 nm 23 mj 1.5 mj cw TiSa laser Wave meter FP I / Cs 2 7 mj Verdi 5 W cw TiSa 708 nm 400 mw 0.7 Water absorption wavenumber (cm -1 ) 0.7 scan region 0.6 TiSa Amp. TiSa Osc. 708 nm, 15 mj µ m µ monitoring 20 m H O Ge filter 6 m 2 µ 0.25 mj 6 µ m cavity Raman cell wavenumber (cm -1 ) Vacuum tube for 6 µm beam transport. Direct frequency calibration at 6 µm.

28 6 µm wavelength calibration Randolf Pohl ACFC, 18 July 2011 p. 12 water-air dat water1662reverse-newcell dat water1695-air dat Intensity [ u.a.] Pos= 127 (57) MHz Width= 6799(228) MHz Pos= -47 (10) MHz Width= 1894(40) MHz Pos= 240 (78) MHz Width= 5453(227) MHz x 10 2 Frequency [ MHz ] Frequency [ MHz ] Frequency [ MHz ] 6 µm light calibration: H 2 O vapor absoprtion measurement in air / cell H 2 O absorption lines known to a few MHz (HITRAN) δν 300 MHz uncertainty (6 ppm of E 2S 2P ) due to our calibration accuracy over the whole wavelength range λ = µm Laser frequency detuning is measured in number of Fabry-Perot cavity fringes grid spacing of our measurement: FSR(FP) = (6) MHz all measured resonances are within ±70 FP fringes of a H 2 O line

29 Target, cavity and detectors Randolf Pohl ACFC, 18 July 2011 p. 13 Muons Laser pulse

30 Target, cavity and detectors Randolf Pohl ACFC, 18 July 2011 p. 13 Play movie: The Search Muons Laser pulse

31 There are surprises in physics. Randolf Pohl ACFC, 18 July 2011 p. 14

32 The resonance: discrepancy, sys., stat. Randolf Pohl ACFC, 18 July 2011 p. 15 Water-line/laser wavelength: 300 MHz uncertainty ν water-line to resonance: 200 khz uncertainty ] -4 delayed / prompt events [ e-p scattering CODATA-06 H 2 O calib. our value Systematics: 300 MHz Statistics: 700 MHz laser frequency [THz] Discrepancy: 5.0 σ 75 GHz δν/ν = R. Pohl et al., Nature 466, 213 (2010).

33 The resonance: discrepancy, sys., stat. Randolf Pohl ACFC, 18 July 2011 p. 15 Water-line/laser wavelength: 300 MHz uncertainty ν water-line to resonance: 200 khz uncertainty ] -4 delayed / prompt events [ events measured 6 on resonance e-p scattering where 155 bgr events are expected fit Lorentz + flat bgr χ 2 /dof = 28.1/28 width agrees with expectation bgr agrees with laser OFF data χ 2 /dof = 283/31 for flat line 16σ CODATA-06 H 2 O calib. our value Systematics: 300 MHz Statistics: 700 MHz laser frequency [THz] Discrepancy: 5.0 σ 75 GHz δν/ν = R. Pohl et al., Nature 466, 213 (2010).

34 The time spectra Randolf Pohl ACFC, 18 July 2011 p. 16 events in 25 ns events Laser ON resonance events Laser OFF resonance time [µs]

35 Uncertainty budget and sensitivity Randolf Pohl ACFC, 18 July 2011 p. 17 Statistics Center position uncertainty ( 4% of Γ) Systematics Laser frequency (H 2 0 calibration) AC and DC stark shift Zeeman shift (5 Tesla) Doppler shift Collisional shift Total uncertainty of the line determination 700 MHz 300 MHz < 1 MHz < 30 MHz < 1 MHz 2 MHz 760 MHz Theory: proton polarizability Discrepancy with CODATA prediction 1200 MHz MHz Systematic effects are small since they scale like 1/m Finite size effect scales like m 3

36 Proton radius Randolf Pohl ACFC, 18 July 2011 p. 18 ν(2s1/2 F=1 2P3/2 F=2 L exp. = (32) mev ) = (76) GHz. L th. = (49) r 2 p r 3 p mev r p = (67) fm (u r = ) r p= (36)(56) fm u exp = u theo = r p is 4% smaller CODATA 2006: r p = ( ± ) fm Hydrogen: r p = (0.876 ± 0.008) fm e-p scattering: r p = (0.895 ± 0.018) fm (Sick 2005) 5.0σ from CODATA σ from H 3.1σ from e-p scatt. R. Pohl et al., Nature 466, 213 (2010).

37 Proton radius Randolf Pohl ACFC, 18 July 2011 p. 18 ν(2s1/2 F=1 2P3/2 F=2 L exp. = (32) mev ) = (76) GHz. L th. = (49) r 2 p r 3 p mev r p = (67) fm (u r = ) r p= (36)(56) fm u exp = u theo = CODATA 2006: r p = ( ± ) fm Hydrogen: r p = (0.876 ± 0.008) fm e-p scattering: r p = (0.894 ± 0.008) fm (Sick 2011) r p = (0.879 ± 0.008) fm (Mainz 2010) r p = (0.875 ± 0.010) fm (JLab Hall A 2011) r p is 4% smaller 5.0σ from CODATA σ from H 8.4σ from scatt.

38 What s wrong?? Randolf Pohl ACFC, 18 July 2011 p. 19

39 What is wrong? Randolf Pohl ACFC, 18 July 2011 p. 20 µp experiment: discrepancy 75 GHz 100σ 4 Γ nat two independent wavelength calibrations one very significant line, no satellite fitted width = natural width another transition in µp confirms our r p µp theory: discrepancy 0.31 mev 60σ 0.15% of the total Lamb shift 4th largest term several independent calculations H theory: L 1S off by 100 khz 25σ most terms only calculated by 2 groups + methods convergence?

40 What is wrong? Randolf Pohl ACFC, 18 July 2011 p. 20 µp experiment: discrepancy 75 GHz 100σ ok 4 Γ nat two independent wavelength calibrations one very significant line, no satellite fitted width = natural width another transition in µp confirms our r p µp theory: discrepancy 0.31 mev 60σ 0.15% of the total Lamb shift 4th largest term several independent calculations H theory: L 1S off by 100 khz 25σ most terms only calculated by 2 groups + methods convergence?

41 What is wrong? Randolf Pohl ACFC, 18 July 2011 p. 20 µp experiment: discrepancy 75 GHz 100σ ok 4 Γ nat two independent wavelength calibrations one very significant line, no satellite fitted width = natural width another transition in µp confirms our r p µp theory: discrepancy 0.31 mev 60σ ok H theory: 0.15% of the total Lamb shift 4th largest term several independent calculations L 1S off by 100 khz 25σ most terms only calculated by 2 groups + methods convergence?

42 What is wrong? Randolf Pohl ACFC, 18 July 2011 p. 20 µp experiment: discrepancy 75 GHz 100σ ok 4 Γ nat two independent wavelength calibrations one very significant line, no satellite fitted width = natural width another transition in µp confirms our r p µp theory: discrepancy 0.31 mev 60σ ok H theory: likely ok 0.15% of the total Lamb shift 4th largest term several independent calculations L 1S off by 100 khz 25σ most terms only calculated by 2 groups + methods convergence?

43 What is wrong? Randolf Pohl ACFC, 18 July 2011 p. 20 µp experiment: discrepancy 75 GHz 100σ ok 4 Γ nat two independent wavelength calibrations one very significant line, no satellite fitted width = natural width another transition in µp confirms our r p µp theory: discrepancy 0.31 mev 60σ 0.15% of the total Lamb shift ok 4th largest term several independent calculations H theory: likely ok Are H spectroscopy and e-p scattering really obviously correct? L 1S off by 100 khz 25σ most terms only calculated by 2 groups + methods convergence?

44 Hydrogen spectroscopy Randolf Pohl ACFC, 18 July 2011 p. 21 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/ proton charge radius (fm)

45 Hydrogen spectroscopy Randolf Pohl ACFC, 18 July 2011 p. 21 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 µp : fm proton charge radius (fm)

46 Hydrogen spectroscopy Randolf Pohl ACFC, 18 July 2011 p. 21 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 H avg = fm µp : fm proton charge radius (fm)

47 Hydrogen spectroscopy Randolf Pohl ACFC, 18 July 2011 p. 21 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 H avg = fm µp : fm proton charge radius (fm)

48 Hydrogen spectroscopy Randolf Pohl ACFC, 18 July 2011 p. 21 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 New measurements of the Rydberg constant are urgently needed to resolve the puzzle µp vs. H NPL: 2S ns, D : n > 4 [Flowers et al., IEEE Trans. Instr. Meas. 56, 331 (2007)] NIST: Ne 9+ [Tan et al., Phys. Scr. T144, (2011)] MPQ: 2S 4P 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 H avg = fm µp : fm proton charge radius (fm)

49 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 22 Rosenbluth cross section Sachs form factor r p dσ dσ dω = Ros. dω Mott εg E 2 + τg M 2 ε(1 + τ) ε = 1 + 2(1 + τ)tan 2 θ 2 PhD thesis J.C. Bernauer 1 ; τ = Q2 4m 2 p G E and G M are the Fourier transforms of the charge and magnetization distributions G E (0) = 1 (charge), and G M (0) = µ p (magnetic moment) r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0

50 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder 2000 Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011)

51 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el µp fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder 2000 Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011)

52 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el µp H fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder 2000 Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011)

53 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el µp H JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) r mag Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011) fm

54 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el µp H = 4% JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) 3.4σ = 11%! r mag Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011) fm

55 Electron scattering Randolf Pohl ACFC, 18 July 2011 p. 23 r el µp H JLab Hall A 2011 MAMI A Borisyuk 2010 Belushkin et al Sick 2011 Blunden, Sick 2005 Rosenfelder fm Rosenfelder, Phys Lett B 479, 381 (2000) Blunden, Sick, PRC 72, (2005) Sick, Few Body Syst. (2011) Belushkin et al., PRC 75, (2007) H r mag Borisyuk, Nucl Phys A 843, 59 (2010) MAMI A1 Bernauer et al., PRL 105, (2010) JLab Hall A Zhan et al., (nucl-ex) (2011) r mag (H) Volotka et al., Eur Phys J D33, 23 (2005) fm

56 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 24 Rosenbluth cross section Sachs form factor r p dσ dσ dω = Ros. dω Mott εg E 2 + τg M 2 ε(1 + τ) ε = 1 + 2(1 + τ)tan 2 θ 2 PhD thesis J.C. Bernauer 1 ; τ = Q2 4m 2 p G E and G M are the Fourier transforms of the charge and magnetization distributions G E (0) = 1 (charge), and G M (0) = µ p (magnetic moment) r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0 extrapolation to Q 2 0 required Q 2 [ (GeV/c) 2 ] = ( (µp) > (e-p scatt.)

57 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 24 Extrapolation non-trivial - Presence of bump/dip structure at lower Q 2? - Model assumption of the functional behavior of the form factor? - Normalization problems. Fitting with G E (Q 2 = 0) = 1 uncertainty underestimated. r p from new scattering data with 1% accuracy. Is that realistic?

58 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 24 Extrapolation non-trivial - Presence of bump/dip structure at lower Q 2? - Model assumption of the functional behavior of the form factor? - Normalization problems. Fitting with G E (Q 2 = 0) = 1 uncertainty underestimated. New Mainz data: G E /G dipole vs. Q 2 world s most accurate data at low Q 2 Vanderhaeghen and Walcher, r p = (0.879 ± stat ± syst ± model ) fm Bernauer et al., PRL 105, (2010)

59 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 24 Bernauer et al., PRL 105, (2010) r p = (0.879 ± stat ± syst ± model ) fm Bernauer, PhD thesis (2010) Fig (top): The dependence of the extracted electric radius of the different flexible models on the number of parameters. µp ±0.005 fm

60 r p from electron scattering Randolf Pohl ACFC, 18 July 2011 p. 24 Bernauer et al., PRL 105, (2010) r p = (0.879 ± stat ± syst ± model ) fm Bernauer, PhD thesis (2010) Fig (top): The dependence of the extracted electric radius of the different flexible of χ 2 models on the Fig. 8.3: Dependence red on the number of parameters N p ofnumber the formof factor parameters. parametrizations... µp

61 Mainz scattering data at lowest Q 2 Randolf Pohl ACFC, 18 July 2011 p. 25 r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 New Mainz data: G E /G dipole vs. Q 2 rms charge radius = slope of G E at Q 2 = 0 Vanderhaeghen and Walcher, extrapolation to Q 2 0 required

62 Mainz scattering data at lowest Q 2 Randolf Pohl ACFC, 18 July 2011 p. 25 r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0 1 Lower half of 180MeV data extrapolation to Q 2 0 required G E µp Bernauer et al PhD thesis J. Bernauer Q 2 (GeV 2 /c 2 ) r p (fm)

63 Mainz scattering data at lowest Q 2 Randolf Pohl ACFC, 18 July 2011 p. 25 r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0 G E Fitting a straight line straight line fit P0 = P1 = / GeV 2 Rp = fm extrapolation to Q 2 0 required µp Bernauer et al straight line r p (fm) Q 2 (GeV 2 /c 2 )

64 Mainz scattering data at lowest Q 2 Randolf Pohl ACFC, 18 July 2011 p. 25 r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0 1 Polynomial, G E (0) = 1 extrapolation to Q 2 0 required G E µp Bernauer et al parabola with fixed normalization P0 = P1 = / GeV 2 P2 = / GeV 4 Rp = fm Q 2 (GeV 2 /c 2 ) straight line polynomial + fixed norm r p (fm)

65 Mainz scattering data at lowest Q 2 Randolf Pohl ACFC, 18 July 2011 p. 25 r 2 p = 6 2 dg E(Q 2 ) dq 2 Q2 =0 rms charge radius = slope of G E at Q 2 = 0 G E Extrapolation is subtle straight line fit P0 = P1 = / GeV 2 Rp = fm extrapolation to Q 2 0 required µp Bernauer et al parabola with fixed normalization P0 = P1 = / GeV 2 P2 = / GeV 4 Rp = fm straight line polynomial + fixed norm r p (fm) Q 2 (GeV 2 /c 2 )

66 Proton radius 2011 Randolf Pohl ACFC, 18 July 2011 p r p = (36) exp (56) theo fm Proton radius (fm) Orsay, 1962 Stanford, 1963 Saskatoon, 1974 Mainz, 1980 Sick, 2003 Hydrogen our result CODATA 2006 Pohl, 2010 MAMI, 2010 JLab, 2011 Sick, 2011 CODATA 2010 year R. Pohl et al., Nature 466, 213 (2010).

67 Rydberg constant 2011 Randolf Pohl ACFC, 18 July 2011 p. 27 R = (16) m 1 [1.5 parts in 10 Accuracy of the Rydberg constant 12 ] fractional uncertainty single measurements least-square adjustments muonic hydrogen + H(1S-2S) year R. Pohl et al., Nature 466, 213 (2010).

68 Yeah! Randolf Pohl ACFC, 18 July 2011 p. 28

69 More measurements Randolf Pohl ACFC, 18 July 2011 p. 29

70 2nd line in muonic hydrogen Randolf Pohl ACFC, 18 July 2011 p. 30 signal Prediction (with new r p ) 357 events 106 bgr. (still preliminary) 2P 3/2 2P 1/2 8.4 mev F=2 F=1 F=1 F= mev 55 THz 5.5 µm laser frequency (a.u.) 2S 1/2 F=1 23 mev F=0 σ position = 1.1 GHz 25 ppm (Γ = 18.6 GHz) Position fits perfectly with theory using new r p Extract HFS and r Zemach

71 Muonic DEUTERIUM Randolf Pohl ACFC, 18 July 2011 p. 31 delayed / prompt events x10 PRELIMINARY 2.5 resonances in muonic deuterium µd [ 2S 1/2 (F=3/2) 2P 3/2 (F=5/2) ] 20 ppm (stat., online) µd [ 2S 1/2 (F=1/2) 2P 3/2 (F=3/2) ] 45 ppm (stat., online) delayed / prompt events laser frequency (FP fringes) PRELIMINARY µd [ 2S 1/2 (F=1/2) 2P 3/2 (F=1/2) ] 70 ppm (stat., online) only 5σ significant identifies F=3/2 line 2P 3/2 2P 1/2 F=5/2 F=1/2 F=3/2 F=3/2 F=1/2 3 F=3/2 2 2S 1/ laser frequency (FP fringes) F=1/2

72 Summary Randolf Pohl ACFC, 18 July 2011 p. 32 muonic hydrogen 2S 1/2 (F=1) 2P 3/2 (F=2) to 15 ppm (stat.+syst.) r p to (experimental precision ) 10 r p = ± fm is 5σ away from CODATA σ The proton is 4% smaller, and the Rydberg constant R is sigma off muonic hydrogen 2S 1/2 (F=0) 2P 3/2 (F=1) to 18 ppm (to be published) exactly at the position deduced with our new r p 2S hyperfine splitting to 220 ppm Zemach radius to a few % (radius of the magnetic moment distribution) muonic deuterium 2S 1/2 (F=3/2) 2P 3/2 (F=5/2) to 20 ppm (stat., online) Theory: missing QED and nuclear structure corrections deuteron charge radius and polarizability muonic deuterium 2S 1/2 (F=1/2) 2P 3/2 (F=3/2 and F=1/2) HFS, check calculations in µd

µp Lamb shift collaboration in 2009 Randolf Pohl ACFC, 18 July 2011 p. 33 F. KOTTMANN ETH Zürich, Switzerland A. ANTOGNINI, T.W. HÄNSCH, T. NEBEL, MPQ, Garching, Germany R. POHL D.

73 µp Lamb shift collaboration in 2009 Randolf Pohl ACFC, 18 July 2011 p. 33 F. KOTTMANN ETH Zürich, Switzerland A. ANTOGNINI, T.W. HÄNSCH, T. NEBEL, MPQ, Garching, Germany R. POHL D. TAQQU PSI, Switzerland E.-O. Le BIGOT, F. BIRABEN, P. INDELICATO, L. JULIEN, F. NEZ F.D. AMARO, J.M.R. CARDOSO, D.S. COVITA, L.M.P. FERNANDES, J.A.M. LOPEZ, C.M.B. MONTEIRO, J.M.F. DOS SANTOS, J.F.C.A. VELOSO Laboratoire Kastler Brossel, Paris, France Department of Physics, Coimbra, Portugal A. GIESEN, K. SCHUHMANN Dausinger + Giesen, Stuttgart, Germany T. GRAF Institut für Strahlwerkzeuge, Stuttgart, Germany C.-Y. KAO, Y.-W. LIU National Tsing Hua University, Hsinchu, Taiwan P. RABINOWITZ Department of Chemistry, Princeton, USA A. DAX, P. KNOWLES, L. LUDHOVA, former members, spent holidays at run 2009 F. MULHAUSER, L. SCHALLER

74 Outlook: Lamb shift in muonic helium Randolf Pohl ACFC, 18 July 2011 p. 34 CREMA collaboration: Charge Radius Experiment with Muonic Atoms Exp. R10-01 approved at PSI in Feb Goal: Measure E(2S-2P) in µ 4 He, µ 3 He alpha particle and helion charge radius to ( fm)

75 Outlook: Lamb shift in muonic helium Randolf Pohl ACFC, 18 July 2011 p. 34 CREMA collaboration: Charge Radius Experiment with Muonic Atoms Exp. R10-01 approved at PSI in Feb Goal: Measure E(2S-2P) in µ 4 He, µ 3 He alpha particle and helion charge radius to ( fm) 2P 3/2 2P 1/2 206 mev 50 THz 6 µm 8.4 mev F=2 F=1 F=1 F=0 2P 146 mev µp µ 4 He µ 3 He 812 nm 898 nm 2P 3/2 2P 1/2 2P 2P 3/2 2P 1/2 145 mev F=1 F=2 F=0 F=1 fin. size: 3.8 mev 2S 1/2 F=1 23 mev F=0 2S 1/2 fin. size effect 290 mev 2S 1/2 F=0 F=1 167 mev fin. size effect 397 mev

76 Outlook: Lamb shift in muonic helium Randolf Pohl ACFC, 18 July 2011 p. 34 CREMA collaboration: Charge Radius Experiment with Muonic Atoms Exp. R10-01 approved at PSI in Feb Goal: Measure E(2S-2P) in µ 4 He, µ 3 He alpha particle and helion charge radius to ( fm) aims: help to solve the proton size puzzle absolute charge radii of helion, alpha low-energy effective nuclear models: 1 H, 2 D, 3 He, 4 He QED test with He + (1S-2S) MPQ, Amsterdam]

77 Outlook: Lamb shift in muonic helium Randolf Pohl ACFC, 18 July 2011 p. 34 CREMA collaboration: Charge Radius Experiment with Muonic Atoms Exp. R10-01 approved at PSI in Feb Goal: Measure E(2S-2P) in µ 4 He, µ 3 He alpha particle and helion charge radius to ( fm) aims: help to solve the proton size puzzle absolute charge radii of helion, alpha low-energy effective nuclear models: 1 H, 2 D, 3 He, 4 He QED test with He + (1S-2S) MPQ, Amsterdam] identical muon beam similar laser, no Raman cell ( more pulse energy) similar, maybe better x-ray detectors (8.2 kev) event rate: events per hour (not 6 per hour, µp) line with 300 GHz (1 nm!)

78 Randolf Pohl ACFC, 18 July 2011 p. 35

News from the Proton Radius Puzzle muonic deuterium

News from the Proton Radius Puzzle muonic deuterium Muonic news Muonic hydrogen and deuterium Randolf Pohl Randolf Pohl Max-Planck-Institut für Quantenoptik Garching, Germany 1 Outline The problem: Proton