The size of the proton from the Lamb shift in muonic hydrogen from - PowerPoint PPT Presentation

The size of the proton The size of the proton from the Lamb shift in muonic hydrogen from the Lamb shift in muonic hydrogen Randolf Pohl for the CREMA collaboration Randolf Pohl Max-Planck-Institut f¨ ur Quantenoptik Garching, Germany Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 1

Outline The problem: Proton rms charge radius r p from muonic hydrogen µ p is 4 % smaller than the values from elastic electron-proton scattering and hydrogen spectroscopy. That’s 5 σ ... 9.4 σ . But the µ p 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” Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 2

Hydrogen energy levels ✻ Energy n=3 n=2 n=1 Bohr E = R ∞ /n 2 V ∼ 1 /r Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 3

Hydrogen energy levels ✻ Energy n=3 2 P 3 / 2 ❍ ❍ ▲ n=2 ▲ ▲ ▲ 2 S 1 / 2 , 2 P 1 / 2 Shift: -43.5 GHz ▲ n=1 ▲ ▲ 1 S 1 / 2 ▲ Bohr Dirac e − spin E = R ∞ /n 2 V ∼ 1 /r relativity Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 3

Hydrogen energy levels ✻ Energy n=3 2 P 3 / 2 ❍ ❍ ▲ n=2 ▲ 2 S 1 / 2 ▲ ✟ ▲ ✟ 2 S 1 / 2 , 2 P 1 / 2 2 P 1 / 2 Shift: -43.5 GHz 8.2 GHz ▲ n=1 ▲ ▲ � 1 S 1 / 2 ▲ � Bohr Dirac Lamb e − spin E = R ∞ /n 2 QED V ∼ 1 /r relativity Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 3

Hydrogen energy levels ✻ Energy n=3 2 P 3 / 2 ❍ ❍ ▲ n=2 ▲ F=1 2 S 1 / 2 ✥ ✥ ▲ ❵ ❵ ✟ ▲ ✟ F=0 2 S 1 / 2 , 2 P 1 / 2 2 P 1 / 2 Shift: -43.5 GHz 8.2 GHz 1.4 GHz ▲ n=1 F=1 ▲ ✘ ✘ ▲ � ❅ 1 S 1 / 2 ▲ � ❅ F=0 Bohr Dirac Lamb hfs-splitting e − spin E = R ∞ /n 2 QED proton-spin H hfs ∼ � V ∼ 1 /r relativity µ p · � µ e Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 3

Hydrogen energy levels ✻ Energy n=3 2 P 3 / 2 ❍ ❍ ▲ n=2 ▲ 0.15 MHz ✥ F=1 ✥ 2 S 1 / 2 ✥ ✥ ▲ ❵ ✥ ❵ ✥ ✟ ▲ ✟ F=0 2 S 1 / 2 , 2 P 1 / 2 2 P 1 / 2 Shift: -43.5 GHz 8.2 GHz 1.4 GHz 1.2 MHz ▲ n=1 ✦ F=1 ✦ ▲ ✘ ✘ ▲ � ❅ 1 S 1 / 2 ✦ ▲ � ❅ ✦ F=0 r p Bohr Dirac Lamb hfs-splitting e − spin E = R ∞ /n 2 QED proton-spin proton size H hfs ∼ � V ∼ 1 /r relativity µ p · � µ e V ≁ 1 /r Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 3

The Rydberg constant Accuracy of the Rydberg constant -6 10 fractional uncertainty -7 10 -8 10 -9 10 single measurements least-square adjustments -10 10 -11 10 1930 1940 1950 1960 1970 1980 1990 2000 year 2006: R ∞ = 10 973 731 . 568 525 ± 0 . 000 073 m − 1 ( u r = 6 . 6 · 10 − 12 ) is the 2 nd most accurately determined fundamental constant. Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 4

Test of bound-state QED 1S Lamb shift in hydrogen: L 1 S ( r p ) = 8171 . 636(4) + 1 . 5645 � r 2 p � MHz 9 9 9 1 m o r 10 -5 f e d i ep 1S Lamb shift precision l s δ r p / r p = 0.02 until “now” Munich 10 -6 accuracy of Paris QED calculations Yale future? δ r p / r p = 10 -3 10 -7 1990 1992 1994 1996 1998 2000 2002 2004 year QED-test is limited by the uncertainty of the proton rms charge radius. Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 5

Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 • 0.900 • • electron scattering ± 2 % slope of G E at Q 2 = 0 0.880 Proton radius (fm) 0.860 • • hydrogen spectr. 0.840 Lamb shift (S-states) Orsay, 1962 Paris, 1999 0.820 Stanford, 1963 Rosenfelder, 2000 Saskatoon, 1974 Eides, 2001 0.800 Mainz, 1980 Sick, 2003 Mainz, free norm. Pachucki Jentschura, 03 dispersion fit CODATA 2006 0.780 Paris, 1996 Garching, 1997 0.760 year 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 2008 e-p scattering: r p = 0.895(18) fm ( u r = 2 %) CODATA: r p = 0.8768(69) fm ( u r = 0 . 8 %) Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 6

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 p � = − 6 � 2 dG E ( Q 2 ) ± 2 % ˛ ⇒ slope of G E at Q 2 = 0 � r 2 slope of G E at Q 2 = 0 ˛ 0.880 dQ 2 ˛ Q 2 =0 Proton radius (fm) 0.860 • • hydrogen spectr. 0.840 Lamb shift (S-states) Orsay, 1962 Paris, 1999 0.820 Stanford, 1963 Rosenfelder, 2000 Saskatoon, 1974 Eides, 2001 0.800 Mainz, 1980 Sick, 2003 Mainz, free norm. Pachucki Jentschura, 03 dispersion fit CODATA 2006 0.780 Paris, 1996 Garching, 1997 0.760 year 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 2008 e-p scattering: r p = 0.895(18) fm ( u r = 2 %) CODATA: r p = 0.8768(69) fm ( u r = 0 . 8 %) Vanderhaeghen, Walcher 1008.4225 Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 6

Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 Hydrogen spectroscopy (Lamb shift): • 0.900 • • electron scattering L 1 S ( r p ) = 8171 . 636(4) + 1 . 5645 � r 2 p � MHz ± 2 % slope of G E at Q 2 = 0 0.880 8S Proton radius (fm) 0.860 4S • 3S 3D • hydrogen spectr. 2S-8D 2S-8S 0.840 Lamb shift (S-states) 2S 2P Orsay, 1962 Paris, 1999 0.820 Stanford, 1963 Rosenfelder, 2000 E nS ≃ − R ∞ n 2 + L 1 S Saskatoon, 1974 Eides, 2001 0.800 n 3 Mainz, 1980 Sick, 2003 Mainz, free norm. Pachucki Jentschura, 03 dispersion fit CODATA 2006 0.780 2 unknowns ⇒ 2 transitions Paris, 1996 1S-2S Garching, 1997 0.760 • Rydberg constant R ∞ year 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 2008 • Lamb shift L 1 S ← r p e-p scattering: r p = 0.895(18) fm ( u r = 2 %) CODATA: r p = 0.8768(69) fm ( u r = 0 . 8 %) 1S Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 6

Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 ✛✘ • 0.900 • • electron scattering ± 2 % our goal slope of G E at Q 2 = 0 ✚✙ 0.880 Proton radius (fm) 0.860 • • hydrogen spectr. 0.840 Lamb shift (S-states) Orsay, 1962 Paris, 1999 0.820 Stanford, 1963 Rosenfelder, 2000 Saskatoon, 1974 Eides, 2001 0.800 Mainz, 1980 Sick, 2003 Mainz, free norm. Pachucki Jentschura, 03 dispersion fit CODATA 2006 0.780 Paris, 1996 Garching, 1997 0.760 year 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 2008 2010 e-p scattering: r p = 0.895(18) fm ( u r = 2 %) 20x improvement CODATA: r p = 0.8768(69) fm ( u r = 0 . 8 %) (aim: 10x better QED test in H) muonic hydrogen goal (1998): u r = 0 . 1 % Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 6

Proton charge radius and muonic hydrogen muonic hydrogen = µ − p mass m µ = 207 m e 8.4 meV � F=2 2P 3/2 ⇒ Bohr: � r orbit � ∼ Zα m r cn 2 F=1 2P 1/2 µ p (n=2) levels: F=1 F=0 ∆ E finite size ( nl ) ∼ r 2 p | Ψ( r = 0) | 2 206 meV 50 THz ⇒ ∆ E finite size ( nl ) = 2( Zα ) 4 c 4 m 3 r r 2 p δ l 0 6 µ m 3 � 2 n 3 Lamb shift in µ p : ∆ E (2 P F=2 3 / 2 − 2 S F=1 1 / 2 ) = 209 . 9779(49) − 5 . 2262 r 2 p + 0 . 0347 r 3 p [meV] finite size contribution is 2% of the µp Lamb shift measure ∆ E(2S-2P) to 30 ppm = 1.5 GHz fin. size: 3.8 meV F=1 ⇒ r p to 10 − 3 2S 1/2 23 meV F=0 Γ 2 P = 18 . 6 GHz ( Γ rad . ) Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 7

µ p Lamb shift experiment: Principle “delayed” ( t ∼ 1 µ s) “prompt” ( t ∼ 0 ) n~14 2 P Laser 1 % 99 % 2 S 2 P 2 S 2 keV γ 2 keV γ 1 S 1 S µ − stop in H 2 gas fire laser ( λ ≈ 6 µ m, ∆ E ≈ 0 . 2 eV) ⇒ µ p ∗ atoms formed ( n ∼ 14 ) ⇒ induce µ p( 2S ) → µ p( 2P ) 99%: cascade to µ p( 1S ), emitting prompt K α , K β ... ⇒ observe delayed K α x-rays 1%: long-lived µ p( 2S ) atoms ⇒ normalize delayed K α x-rays lifetime τ 2 S ≈ 1 µ s at 1 mbar H 2 prompt K α R. Pohl et. al. , Phys. Rev. Lett. 97, 193402 (2006). Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 8

µ p Lamb shift experiment: Principle time spectrum of 2 keV x-rays ( ∼ 13 hours of data) events in 25 ns 4 10 3 10 2 10 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 8

µ p Lamb shift experiment: Principle “prompt” ( t ∼ 0 ) time spectrum of 2 keV x-rays n~14 events in 25 ns 1 % 99 % 2 P 2 S 4 10 2 keV γ 1 S 3 10 2 10 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 8

µ p Lamb shift experiment: Principle “prompt” ( t ∼ 0 ) “delayed” ( t ∼ 1 µ s) time spectrum of 2 keV x-rays n~14 2 P Laser events in 25 ns 1 % 99 % 2 S 2 P 2 S 4 10 2 keV γ 2 keV γ 1 S 1 S 3 10 2 10 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl HADRON M¨ unchen, 13. June 2011 p. 8