Proton charge radius. Michael O. Distler for the A1 MAMI

Transcription

1 "2011 JLab Users Group Meeting" - June 6-8, Jefferson Lab, Newport News, VA Proton charge radius Michael O. Distler for the A1 MAMI Institut für Kernphysik Johannes Gutenberg-Universität Mainz

2 Outline 1 Introduction I: The size of the proton from the Lamb shift in muonic hydrogen and electron scattering 2 Introduction II: Electric and magnetic form factors of the Proton 3 The Mainz high-precision p(e,e )p measurement 4 Results Design considerations Covered kinematical region Analysis technique Cross section results Checks: Rosenbluth and model dependence 5 Conclusion and Outlook 6 Discussion of the Lamb shift / electron scattering discrepancy

3 Introduction I: The size of the proton Nature 466, (8 July 2010)

4 Cross section and form factors for elastic e-p scattering The cross section: ) with: ( dσ dω ( dσ dω ) Mott = 1 [ ( εge 2 Q 2) + τgm (Q 2 2)] ε (1 + τ) ( τ = Q2 4mp 2, ε = (1 + τ) tan 2 θ ) 1 e 2 Fourier-transform of G E, G M spatial distribution (Breit frame) re 2 = 6 2 dg E dq 2 Q 2 =0 rm 2 = 6 2 d (G M/µ p ) dq 2 Q 2 =0

5 Overview of different proton charge-radius results Pohl et al. (2010) Bernauer et al. (2010) CODATA 06 (2008) CODATA 02 (2005) Melnikov et al. (2000) Udem et al. (1997) Blunden et al. (2005) Sick et al. (2003) Rosenfelder et al. (2000) Mergell et al. (1996) Wong et al. (1994) Eschrich et al. (2001) McCord et al. (1991) Simon et al. (1980) Borkowski et al. (1975) Akimov et al. (1972) Frerejacque et al. (1966) Hand et al. (1963) <r E > [fm] Filled dots: Results from new measurements. Hollow dots: Reanalysis of existing data.

6 Overview of different proton charge-radius results Pohl et al. (2010) Bernauer et al. (2010) CODATA 06 (2008) CODATA 02 (2005) Melnikov et al. (2000) Udem et al. (1997) Blunden et al. (2005) Sick et al. (2003) Rosenfelder et al. (2000) Mergell et al. (1996) Wong et al. (1994) Eschrich et al. (2001) McCord et al. (1991) Simon et al. (1980) Borkowski et al. (1975) Akimov et al. (1972) Frerejacque et al. (1966) Hand et al. (1963) <r E > [fm] Filled dots: Results from new measurements. Hollow dots: Reanalysis of existing data.

7 Introduction II: Original Motivation G EP /G dipole total smooth Simon et al. Price et al. Berger et al. Hanson et al. polarisation data G MP /(µ p G dipole ) total smooth Hoehler et al. Janssens et al. Berger et al. Bartel et al. Walker et al. Litt et al. Andivahis et al. Sill et al Q / (GeV/c) Q / (GeV/c) G EP -G EP,phaen total-smooth Simon et al. Price et al. Berger et al. Hanson et al. polarisation data G MP -G MP,phaen total - smooth Hoehler et al. Janssens et al. Berger et al. Bartel et al. Walker et al. Litt et al. Andivahis et al. Sill et al Q 2 / (GeV/c) Q 2 / (GeV/c) 2 (see J. Friedrich and Th. Walcher, Eur. Phys. J. A 17 (2003) 607)

8 Introduction II: Original Motivation G EP /G dipole total smooth Simon et al. Price et al. Berger et al. Hanson et al. polarisation data G MP /(µ p G dipole ) total smooth Hoehler et al. Janssens et al. Berger et al. Bartel et al. Walker et al. Litt et al. Andivahis et al. Sill et al. G EP -G EP,phaen Q / (GeV/c) Discrepancy of existing values for proton electric radius: Q / (GeV/c) 0.809(11) fm: standard dipole at HEPL (Hand et al. 1963) total - smooth total-smooth Simon Price et et al. Hoehler et al (12) fm: low Q 2 at Mainz (Simon et al. 1979) Janssens et al. al. Berger et al. Berger et al Hanson et al Bartel et al. Walker et al (09) polarisation data fm: dispersion relation (Mergell et al. 1996) Litt et al. Andivahis et al. Sill et al (14) fm: Hydrogen Lamb shift (Udem et al. 1997) G MP -G MP,phaen Q 2 / (GeV/c) Q 2 / (GeV/c) 2 (see J. Friedrich and Th. Walcher, Eur. Phys. J. A 17 (2003) 607)

9 Location of Mainz, Germany

10 Location of Mainz, Germany

11 The Mainz Microtron MAMI

12 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed

13 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps

14 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.6 GeV,15 MeV steps

15 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.6 GeV,15 MeV steps

16 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.6 GeV,15 MeV steps

17 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.6 GeV,15 MeV steps

18 The Mainz high-precision p(e,e )p measurement: Three spectrometer facility of the A1 collaboration

19 Design goal: High precision Statistical precision: 20 min beam time for <0.1%

20 Design goal: High precision through redundancy Statistical precision: 20 min beam time for <0.1% Control of luminosity and systematic errors: Measure all quantities in as many ways as possible:

21 Design goal: High precision through redundancy Statistical precision: 20 min beam time for <0.1% Control of luminosity and systematic errors: Measure all quantities in as many ways as possible: Beam current: Foerster probe (usual way) pa-meter measures down to extremely low currents for small θ

22 Design goal: High precision through redundancy Statistical precision: 20 min beam time for <0.1% Control of luminosity and systematic errors: Measure all quantities in as many ways as possible: Beam current: Foerster probe (usual way) pa-meter measures down to extremely low currents for small θ Luminosity: current density target length third magnetic spectrometer as monitor

23 Design goal: High precision through redundancy Statistical precision: 20 min beam time for <0.1% Control of luminosity and systematic errors: Measure all quantities in as many ways as possible: Beam current: Foerster probe (usual way) pa-meter measures down to extremely low currents for small θ Luminosity: current density target length third magnetic spectrometer as monitor Overlapping acceptance Where possible: Measure at the same scattering angle with two spectrometers

24 Measured settings and future (high Q 2 ) expansion dσ dω = «dσ dω Mott 1 h εge 2 Q 2 + τgm Q 2 2 i ε (1 + τ) Q [GeV/c] spectrometer A limit spectrometer B limit ε MAMI min. E= 180 MeV MAMI-C max. E=1.53 GeV MAMI-B max. E= 855 MeV Q 2 [(GeV/c) 2 ]

25 Measured settings and future (high Q 2 ) expansion dσ dω = «dσ dω Mott 1 h εge 2 Q 2 + τgm Q 2 2 i ε (1 + τ) Q [GeV/c] spectrometer A spectrometer B spectrometer C ε Q 2 [(GeV/c) 2 ] 90 GByte on disc 1400 Settings > 10 9 events.

26 Background 48 mm 20 mm 10 mm

27 Background 48 mm 20 mm 10 mm Liquid Hydrogen de [MeV]

28 Background 48 mm 20 mm 10 mm Liquid Hydrogen Havar foil de [MeV] de [MeV] de [MeV]

29 Data Simulation matching Simulation: Model for energy loss and small angle scattering Input: momentum-, angular-, vertex resolution data simulated background residue de [MeV]

30 Feynman graphs of leading and next to leading order for elastic scattering All graphs are taken into account: vacuum polarization (v1): e, (µ, τ) Maximon/Tjon (2000) and Vanderhaeghen et al. (2000) electron vertex correction Coulomb distortion (two photon exchange) real photon emission

31 Comments on Coulomb distortion and TPE Coulomb distortion: Exchange of one hard and multiple soft photons Feshbach (1948), Mo and Tsai (1969). Two-photon exchange (TPE) with and w/o excited intermediate states: Exchange of two hard photons Still not reliable and highly debated Figure shows a recent experimental result from JLab. Meziane, M. et al.: Search for effects beyond the Born approximation in polarization transfer observables in ep elastic scattering, PRL 106, (2011), arxiv:

32 Description of the radiative tail counts E [MeV] integrated tail exp./sim. [arb. units] E [MeV]

33 Cross sections standard dipole 1000 cross section dσ/dω / µbarn/sr scattering angle

34 Cross sections / standard dipole , 855 MeV 1.6 σ exp /σ std. dipole , 720 MeV +0.3, 585 MeV +0.2, 450 MeV +0.1, 315 MeV scattering angle 180 MeV

35 How to extract the form factors? Two methods: 1 Classical Rosenbluth separation

36 How to extract the form factors? Two methods: 1 Classical Rosenbluth separation 2 Super-Rosenbluth separation : Fit of form factor models directly to the measured cross sections Feasible due to fast computers. All data at all Q 2 and ε values contribute to the fit, i.e. full kinematical region used, no projection (to specific Q 2 ) needed. Easy fixing of normalization.

37 How to extract the form factors? Two methods: 1 Classical Rosenbluth separation 2 Super-Rosenbluth separation : Fit of form factor models directly to the measured cross sections Feasible due to fast computers. All data at all Q 2 and ε values contribute to the fit, i.e. full kinematical region used, no projection (to specific Q 2 ) needed. Easy fixing of normalization. Model dependence?

38 How to extract the form factors? Two methods: 1 Classical Rosenbluth separation 2 Super-Rosenbluth separation : Fit of form factor models directly to the measured cross sections Feasible due to fast computers. All data at all Q 2 and ε values contribute to the fit, i.e. full kinematical region used, no projection (to specific Q 2 ) needed. Easy fixing of normalization. Model dependence? For radii extraction: Needs a fit anyway! Classical Rosenbluth: Extracted G E and G M highly correlated! = Error propagation very involved.

39 Models: Dipols Dipole (different b for G E and G M ): ) G D (Q 2, b = ( Q2 b ) 2 Double Dipole (as in Friedrich/Walcher phenomenological fit [Eur. Phys. J. A 17 (2003) 607]): G DD ( Q 2, a, b 1, b 2 ) = ag D ( Q 2, b 1 ) + (1 a) G D ( Q 2, b 2 )

40 Models: Polynomial Polynomial G P ( Q 2, a 1,..., a n ) = 1 + Polynomial + standard Dipole n a i Q 2 i i=1 ( ) ) G PAD Q 2, a 1,..., a n = G D (Q 2, Polynomial standard Dipole ( ( ) ) G PMD Q 2, a 1,..., a n = G D (Q 2, n a i Q 2 i i=1 ) n a i Q 2 i i=1

41 Models: Splines Uniform cubic splines ) spline (Q 2, a 1,..., a n Spline: Knots λ i ( ) G Spline Q 2, a 1,..., a n = 1 + Q 2 spline (Q 2) Spline standard Dipole ( ) ) ( G SMD Q 2, a 1,..., a n = G D (Q 2, Q 2 spline (Q 2))

42 Models: Misc Also: Friedrich / Walcher phenomenological ansatz extended Gari-Krümpelmann (VMD), Lomon et al. Arrington type: P N P N+2

43 Cross sections / standard dipole , 855 MeV 1.6 σ exp /σ std. dipole , 720 MeV +0.3, 585 MeV +0.2, 450 MeV +0.1, 315 MeV scattering angle 180 MeV

44 Cross sections + spline fit , 855 MeV 1.6 σ exp /σ std. dipole , 720 MeV +0.3, 585 MeV +0.2, 450 MeV +0.1, 315 MeV scattering angle 180 MeV

45 Cross sections: 180 MeV σ exp /σ std. dipole Polynomial Poly. + dip. Poly. dip. Inv. poly. Spline Spline dip. Friedrich-Walcher Double Dipole Extended G.K Q 2 [(GeV/c) 2 ]

46 Form factor results G E /G std. dipole Christy et al. Simon et al. Price et al. Berger et al. Hanson et al. Borkowski et al. Janssens et al. Murphy et al G M /(µ p G std. dipole ) Christy et al. Price et al. Berger et al. Hanson et al. Borkowski et al. Janssens et al. Bosted et al. Bartel et al G E /G std. dipole Arrington et al. Friedrich/Walcher Simon et al. Price et al. Borkowski et al. Janssens et al. Murphy et al µ p G E /G M Arrington w/o TPE Jones et al Arrington w/ TPE Crawford et al. Pospischil et al. Dieterich et al. 0.8 Gayou et al. Milbrath et al. Ron et al. Punjabi et al Q 2 / (GeV/c) Jan C. Bernauer et al., High-precision determination of the electric and magnetic form factors of the proton, PRL 105, (2010), arxiv:

47 Form factor results: G E /G M ratio Bernauer et al. Zhan et al. Arrington w/o TPE (2007) Arrington w/ TPE (2007) Friedrich/Walcher (2003) µ p G E /G M Q 2 / (GeV/c) 2 Jan C. Bernauer et al., PRL 105, (2010), arxiv: X. Zhan et al., arxiv: J. Arrington et al., Phys. Rev. C76 (2007) , arxiv:

48 Comparison: Rosenbluth vs. Spline fit G E /G std. dipole Q 2 [(GeV/c) 2 ] Spline fit Rosenbluth

49 The electric rms radius - extracted by different models Spline 3 Ord. 8 par. Spline 3 Ord. 9 par. Spline 3 Ord. 10 par. Spline 3 Ord. 11 par. Spline 4 Ord. 8 par. Spline 4 Ord. 9 par. Spline 4 Ord. 10 par. Spline 4 Ord. 11 par. Spline 5 Ord. 8 par. Spline 5 Ord. 9 par. Spline 5 Ord. 10 par. Spline 5 Ord. 11 par. Spline dipole 7 par. Spline dipole 8 par. Spline dipole 9 par. Spline dipole 10 par. Spline dipole 11 par. Inv. Poly. 6 par. Inv. Poly. 7 par. Inv. Poly. 8 par. Inv. Poly. 9 par. Poly. 9 par. Poly. 10 par. Poly. 11 par. Poly. 12 par. Poly. + dipole 9 par. Poly. + dipole 10 par. Poly. + dipole 11 par. Poly. + dipole 12 par. Poly. dipole 7 par. Poly. dipole 8 par. Poly. dipole 9 par. Poly. dipole 10 par. Friedrich-Walcher <r E > [fm]

50 Conclusion Part I High precision e-p scattering data from MAMI. PRL 105, (2010), arxiv: Q 2 range from to 1 (GeV/c) 2. Consistent data set. Super-Rosenbluth fit to determine form factors and radii. The charge and magnetic rms radii are determined as r e = ± stat. ± syst. ± model ± group fm, r m = ± stat. ± syst. ± model ± group fm. Supported by the Deutsche Forschungsgemeinschaft (DFG) with a Sonderforschungsbereich (SFB443).

51 Discussion of the Lamb shift / electron scattering discrepancy Muonic hydrogen (Lamb Shift) r p = (67) fm R. Pohl et al., Nature 466, (2010)

52 Discussion of the Lamb shift / electron scattering discrepancy Muonic hydrogen (Lamb Shift) r p = (67) fm R. Pohl et al., Nature 466, (2010) Mainz form factor measurement r p = 0.879(8) fm J.C. Bernauer et al., Phys. Rev. Lett. 105, (2010).

53 Discussion of the Lamb shift / electron scattering discrepancy Muonic hydrogen (Lamb Shift) r p = (67) fm R. Pohl et al., Nature 466, (2010) Mainz form factor measurement r p = 0.879(8) fm J.C. Bernauer et al., Phys. Rev. Lett. 105, (2010). Analysis of previous ep scattering data r p = 0.895(18) fm I. Sick, Phys. Lett. B (2003).

54 Discussion of the Lamb shift / electron scattering discrepancy Muonic hydrogen (Lamb Shift) r p = (67) fm R. Pohl et al., Nature 466, (2010) Mainz form factor measurement r p = 0.879(8) fm J.C. Bernauer et al., Phys. Rev. Lett. 105, (2010). Analysis of previous ep scattering data r p = 0.895(18) fm I. Sick, Phys. Lett. B (2003). Electronic hydrogen - (CODATA) (Hyperfine structure and Lamb shift) r p = (69) fm P.J. Mohr et al., Rev. Mod. Phys (2008).

55 Discussion of the Lamb shift / electron scattering discrepancy Muonic hydrogen (Lamb Shift) r p = (67) fm R. Pohl et al., Nature 466, (2010) Mainz form factor measurement r p = 0.879(8) fm J.C. Bernauer et al., Phys. Rev. Lett. 105, (2010). Analysis of previous ep scattering data r p = 0.895(18) fm I. Sick, Phys. Lett. B (2003). Electronic hydrogen - (CODATA) (Hyperfine structure and Lamb shift) r p = (69) fm P.J. Mohr et al., Rev. Mod. Phys (2008). Discrepancy is between myonic and electronic measurements

56 Possible explanations of the discrepancy Exotic particles e.g. V. Barger et al., arxiv: and references. Contributions to the Lamb shift in µp C.E. Carlson und M. Vanderhaeghen, arxiv: U.D. Jentschura, Annals Phys. 326, (2011) E. Borie, arxiv: Higher moments of the charge distribution and Zemach radii M.O.D., J.C. Bernauer, and Th. Walcher, Phys. Lett. B696, (2011)

57 Speculation about the discrepancy Reminder: The muon g-2 experiment has a 2 3σ discrepancy. Hadronic corrections may provide an explanation. The main contribution to the Lamb shift in...

58 Speculation about the discrepancy Reminder: The muon g-2 experiment has a 2 3σ discrepancy. Hadronic corrections may provide an explanation. The main contribution to the Lamb shift in... electronic hydrogen muonic hydrogen vertex and self-energy MHz vacuum polarization MHz mev anom. magn. moment MHz + higher order theoretical value (14) MHz mev experimental value (20) MHz : mev

59 Conclusion Part II High precision form factors from MAMI provide constraints for the charge distribution of the proton. Standard dipole approximation is not sufficient for correction of the muonic hydrogen Lamb shift. The proton size discrepancy is between the Lamb shift of muonic hydrogen and every electronic determination. Explanation for the discrepancy? Outlook: Low- and high Q 2 MAMI Lamb shift measurements on D, 3,4 PSI Form factor and polarizability of D, 3,4 MAMI

60 Backup

61 Discussion of the Lamb shift / electron scattering discrepancy The following tables are taken from the QED supplement published in Nature 466, (8 July 2010). All known radius-independent contributions and all relevant radius-dependent contributions to the Lamb shift in µp from different authors are listed.

62 2S 2P splitting in muonic hydrogen

63 2S 2P splitting in muonic hydrogen

64 Discussion of the Lamb shift / electron scattering discrepancy

65 Discussion of the Lamb shift / electron scattering discrepancy E = (49) r 2 p r 3 p Values are in mev and radii in fm.

66 Discussion of the Lamb shift / electron scattering discrepancy Zemach-Moments: A. C. Zemach, Proton Structure and the Hyperfine Shift in Hydrogen, Phys. Rev. 104, 1771 (1956). < r 3 > (2) = 0 dq ( ) q 4 GE 2 (q2 ) 1 + q 2 < r 2 > p /3 < r 3 > (2) = 2.27 fm 3 r p = (67) fm

67 Discussion of the Lamb shift / electron scattering discrepancy Zemach-Moments: A. C. Zemach, Proton Structure and the Hyperfine Shift in Hydrogen, Phys. Rev. 104, 1771 (1956). < r 3 > (2) = 0 dq ( ) q 4 GE 2 (q2 ) 1 + q 2 < r 2 > p /3 < r 3 > (2) = 2.27 fm 3 r p = (67) fm < r 3 > (2) = 2.85(8) fm 3 r p = (67) fm M.O.D., J.C. Bernauer, and Th. Walcher, The RMS Charge Radius of the Proton and Zemach Moments, in Press doi: /j.physletb , arxiv:

68 2S 2P splitting in muonic hydrogen

69 De Rújula s toy model A. De Rújula, QED is not endangered by the proton s size, Phys. Lett. B693, 555 (2010). Sum of single pole and dipole [ ] ρ Proton (r) = 1 M 4 e Mr cos 2 (θ) + m5 e mr sin 2 (θ) D 4πr 8π D M 2 cos 2 (θ) + m 2 sin 2 (θ) using M = GeV/c 2, m = GeV/c 2, and sin 2 (θ) = 0.3 and ρ (2) (r) = d 3 r 2 ρ charge ( r r 2 ) ρ charge (r 2 ) we get the third Zemach moment: r 3 (2) = d 3 r r 3 ρ (2) (r) = 36.2 fm 3

70 De Rújula s toy model... We put r 3 (2) = 36.2 fm 3 in the Lamb shift formular: L 5th [ r 2, r 3 (2) ] = ( (49) r 2 fm r ) 3 (2) fm 3 mev and get r p = fm

71 De Rújula s toy model... We put r 3 (2) = 36.2 fm 3 in the Lamb shift formular: L 5th [ r 2, r 3 (2) ] = ( (49) r 2 fm r ) 3 (2) fm 3 mev and get r p = fm problem solved

72 De Rújula s toy model is excluded by experiment charge distribution form factor 4 Π r 2 Ρ r fm G E,p Q De Rújula s toy model standard dipole Bernauer-Arrington fit assembly

73 Outlook: Initial state radiation e e e e dσ/(de dω ) LAB (dω γ ) CM [µb/(gev sr 2 )] e e γ* p p γ* γ* p p p p e e γ* p p o 90 o 0 o 90 o 180 o ϑ γγ

74 Outlook: Initial state radiation Reconstructed Q 2 (E,θ ) [GeV 2 /c 2 ] Q 2 at Vertex (Simulation) [GeV 2 /c 2 ] Events / (µa h)