Precise Determination of the Electric and Magnetic Form Factors of the Proton
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1 Precise Determination of the Electric and Magnetic Michael O. Distler for the A1 MAMI Institut für Kernphysik Johannes Gutenberg-Universität Mainz GDR Nucleon meeting at CEA/SPhN Saclay, France, November 25, 2010
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 The Mainz Microtron MAMI
10 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed
11 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps
12 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.5 GeV,15 MeV steps
13 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.5 GeV,15 MeV steps
14 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.5 GeV,15 MeV steps
15 The Mainz Microtron MAMI MAMI-A: 180 MeV fixed MAMI-B: 855 MeV,15 MeV steps MAMI-C: 1.5 GeV,15 MeV steps
16 The Mainz high-precision p(e,e )p measurement: Three spectrometer facility of the A1 collaboration
17 Design goal: High precision Statistical precision: 20 min beam time for <0.1%
18 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:
19 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
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: 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
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 Luminosity: current density target length third magnetic spectrometer as monitor Overlapping acceptance Where possible: Measure at the same scattering angle with two spectrometers
22 Measured settings and future (high Q 2 ) expansion dσ dω = ( ) dσ dω Mott 1 [ ( εge 2 Q 2) + τgm (Q 2 2)] 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 ]
23 Measured settings and future (high Q 2 ) expansion dσ dω = ( ) dσ dω Mott 1 [ ( εge 2 Q 2) + τgm (Q 2 2)] 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.
24 Background 48 mm 20 mm 10 mm
25 Background 48 mm 20 mm 10 mm Liquid Hydrogen de [MeV]
26 Background 48 mm 20 mm 10 mm Liquid Hydrogen Havar foil de [MeV] de [MeV] de [MeV]
27 Data Simulation matching Simulation: Model for energy loss and small angle scattering Input: momentum-, angular-, vertex resolution data simulated background residue de [MeV]
28 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
29 Description of the radiative tail counts E [MeV] integrated tail exp./sim. [arb. units] E [MeV]
30 Cross sections standard dipole 1000 cross section dσ/dω / µbarn/sr scattering angle
31 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
32 How to extract the form factors? Two methods: 1 Classical Rosenbluth separation
33 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.
34 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?
35 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.
36 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 )
37 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
38 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))
39 Models: Misc Also: Friedrich / Walcher phenomenological ansatz extended Gari-Krümpelmann (VMD), Lomon et al. Arrington type: P N P N+2
40 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
41 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
42 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 ]
43 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, arxiv:
44 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]
45 Conclusion Part I High precision e-p scattering data from MAMI. e-print: arxiv: accepted by PRL 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).
46 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.
47 2S 2P splitting in muonic hydrogen
48 2S 2P splitting in muonic hydrogen
49 Discussion of the Lamb shift / electron scattering discrepancy
50 Discussion of the Lamb shift / electron scattering discrepancy E = (49) r 2 p r 3 p Values are in mev and radii in fm.
51 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
52 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, arxiv:
53 2S 2P splitting in muonic hydrogen
54 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
55 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
56 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
57 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
58 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. M.O.D., J.C. Bernauer, and Th. Walcher, The RMS Charge Radius of the Proton and Zemach Moments, arxiv: Supported by the Deutsche Forschungsgemeinschaft (DFG) with a Sonderforschungsbereich (SFB443).
59 Outlook Jan Bernauer joined the OLYMPUS DESY/Hamburg (Spokesperson: Richard Milner, MIT) OLYMPUS: Determine the effect of two-photon exchange in elastic lepton-proton scattering by precisely measuring the ratio of positron-proton to electron-proton elastic unpolarized cross sections. low Q 2 extension: MAMI
60 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
61 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)
62 Backup
63 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.
64 Discussion of the Lamb shift / electron scattering discrepancy
65 Discussion of the Lamb shift / electron scattering discrepancy
66 Discussion of the Lamb shift / electron scattering discrepancy
67 Discussion of the Lamb shift / electron scattering discrepancy E = (49) r 2 p r 3 p Values are in mev and radii in fm.
68 Data taking periods August 2006 November 2006 May 2007 Duration 10 days 11 days 17 days without setup/calibration 8 days 9 days 11 days Energies 575, 850 MeV 180, 720 MeV 315, 450 MeV Setting changes data taking time 3.3 days 4.3 days 5.3 days Average time per setting 31 min 35 min 38 min Overhead per setting 44 min 40 min 40 min Overhead includes angle changes, momentum changes and down times. Average time for angle only setting changes: 10 min.
69 Form factor results G E /G std. dip [13] [2] Christy et al. Simon et al. Price et al. Berger et al. Hanson et al. Borkowski et al. [15] Janssens et al. Murphy et al. [16] G E /G std. dipole G E /G std. dipole [13] [2] Simon et al. Price et al. Borkowski et al. [15] Janssens et al. Murphy et al. [16] [13] [2] Christy et al. Simon et al. Price et al. Berger et al. Hanson et al. Borkowski et al. [15] Janssens et al. Murphy et al. [16] G M /(µ p G std. dipole ) µ p G E /G M [13] [2] Christy et al. Price et al. Berger et al. Hanson et al. Borkowski et al. [15] Janssens et al. Bosted et al. Bartel et al [13] w/o TPE Gayou et al. [13] w/ TPE Milbrath et al. Pospischil et al. 0.8 [2] Punjabi et al. Dieterich et al. Crawford et al. Jones et al. Ron et al. [17] Q 2 / (GeV/c) 2 M /(µ p G std. dipole ) [13] [2] Christy et al. Price et al. Berger et al. Hanson et al. Borkowski et al. [15] Janssens et al. Bosted et al. Bartel et al.
70 Backup Polynomial Poly. + Dip. Poly. Dip. Inv. Poly. Spline Spline Dip. Friedrich/Walcher σ exp /σ std. dipole PRELIMINARY Central angle of spectrometer
71 Cross sections: 315 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 ]
72 Cross sections: 450 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 ]
73 Cross sections: 585 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 ]
74 Cross sections: 720 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 ]
75 Cross sections: 855 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 ]
76 Rosenbluth separation Q 2 = 0.15 (GeV/c) ε (1+τ) σ exp /σ Mott ε
77 ... more...
78 ... and more...
79 ... and even more
80 Comparison: Rosenbluth vs. Spline fit G E /G std. dipole Q 2 [(GeV/c) 2 ] Spline fit Rosenbluth
81 Model dependence of radius extraction Check extraction of radii with Monte-Carlo data: Monte-Carlo data from given parametrization (known radii!) Error distribution of this simulated data according to errors from real data Fit with different models Assumption: ±5% normalization error (per spectrometer/energy)
82 Model dependence: Charge Radius Analysis of simulated pseudo data Input Analysis Dipole Dbl-D. Poly. P.+D. P. D. Spline S. D. F./W. Std. dipole 811 0±1 0±1 0±3 0±3 0±4 0±5 0±7 0±1 Arrington ±1 3±3 3±3 2±3 1±4 4±5 1±6 2±3 Arr. 03 (P) ±1 10±1 1±3 1±3 0±4 1±5 0±6 2±6 Arr. 03 (R) 868 9±1 0±2 0±3 0±3 0±4 3±5 0±6 1±3 FW 860 4±1 31±14 1±3 1±3 1±4 0±5 0±6 0±3
83 Spline fit + error band G E /G std. dipole Q 2 [(GeV/c) 2 ] Spline fit stat. errors exp. syst. errors theo. syst. errors Simon et al. Price et al. Berger et al. Hanson et al. Borkowski et al. Janssens et al. Murphy et al.
84 Spline fit + error band µ p G M /G std. dipole Q 2 [(GeV/c) 2 ] Spline fit stat. errors exp. syst. errors theo. syst. errors Price et al. Berger et al. Hanson et al. Borkowski et al. Janssens et al.
85 The cryogenic target system 11.5 mm 49.5 mm Electronbeam liquid hydrogen 10 µm Havar Target cell Ventilator Heat exchanger "Basel-Loop" Scattering chamber
86 Model dependence: Magnetic Radius Analysis of simulated pseudo data Input Analysis Dipole Dbl-D. Poly. P.+D. P. D. Spline S. D. F./W. Std. dipole 811 0±1 0±1 1±7 0±7 0±10 2±14 1±18 0±1 Arrington ±1 4±4 5±6 4±6 1±9 2±13 0±17 10±4 Arr. 03 (P) ±1 12±3 1±7 0±7 0±9 2±13 0±19 5±5 Arr. 03 (R) ±1 2±4 4±6 3±6 0±9 3±13 0±17 8±4 FW 805 4±1 49±2 0±7 1±7 1±10 1±13 1±18 1±4
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