Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
Data
from Very-Low-Q Data?
Summary
References
All Topics
Physics
Nuclear and High Energy Physics

Proton Charge Radius from Electron Scattering

Profile image of Atoms ( I S S N : 2 2 1 8 - 2 0 0 4 ) (ESCI & Scopus Indexing)Atoms ( I S S N : 2 2 1 8 - 2 0 0 4 ) (ESCI & Scopus Indexing)

2017, Atoms

https://doi.org/10.3390/ATOMS6010002
visibility

…

description

24 pages

link

1 file

Abstract

The rms-radius R of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor G e (q 2) extrapolated to momentum transfer q 2 = 0, shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies and explore alternative parameterizations. The problem lies in the model dependence of the parameterized G(q) needed for the extrapolation. This shape of G(q < q min) is closely related to the shape of the charge density ρ(r) at large radii r, a quantity that is ignored in most analyses. When using our physics knowledge about this larger density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for R = 0.887 ± 0.012 fm. This value disagrees with the more precise value 0.8409 ± 0.0004 fm determined from the Lamb shift in muonic hydrogen.

Related papers

Radiative corrections to elastic-electron proton scattering and uncertainty in proton charge radius
Andrej Arbuzov

EPJ Web of Conferences

Higher-order QED radiative corrections to elastic electron-proton scattering are discussed. It is shown that they are relevant for high-precision experiments on proton form factor measurements. Analytic result are obtained for next-to-leading second order corrections to the electron line. Light pair corrections are taken into account. The role of the hadronic contribution to vacuum polarization is discussed. Numerical results are given for the conditions of the experiment on proton form factors performed by A1 Collaboration. Preliminary results are also shown for the set-up with reconstruction of momentum transfer from the recoil proton momentum.

View PDFchevron_right
A small proton charge radius from an electron–proton scattering experiment
Latiful Kabir

Nature, 2019

Elastic electron-proton scattering (e−p) and the spectroscopy of hydrogen atoms are the two traditional methods used to determine the proton charge radius (r p). About a decade ago, a new method using muonic hydrogen (µH) atoms 1 found a significant discrepancy with the compilation of all previous results 2 , creating the "proton radius puzzle". Despite intensive worldwide experimental and theoretical efforts, the "puzzle" remains unresolved. In fact, a new discrepancy was reported between the two most recent spectroscopic measurements on ordinary hydrogen 3, 4. Here, we report on the PRad experiment, the first high-precision e − p experiment since the emergence of the "puzzle". For the first time, a magnetic-spectrometerfree method was employed along with a windowless hydrogen gas target, which overcame several limitations of previous e − p experiments and reached unprecedented small angles.

View PDFchevron_right
The proton charge radius and the proton to electron mass ratio equations
EMMANUEL SAUCEDO FLORES

SCIREA, 2020

New expressions in terms of the proton charge radius are derived for the Sommerfeld or finestructure constant, the proton to electron mass ratio and the elementary particles Wirkungsquanta. Through the derivation of these expressions, it was found that a small correction factor was needed to be applied on the currently accepted proton charge radius numeric value so that the calculated α values were matched with good relative standard uncertainties. Quasi-exact matches to the h-value were used to confirm the numerical value of the used proposed proton charge radius.

View PDFchevron_right
High-precision measurement of the proton elastic form factor ratio μpGE/GM at low Q2
Kawtar Hafidi

Physics Letters B, 2011

View PDFchevron_right
Studying the Proton" Radius" Puzzle with\ mu p Elastic Scattering
Edward Brash, B. Dongwi, J. Arrington, Fatiha Benmokhtar, Y. Ilieva, William Briscoe, G. Kumbartzki

2013

The Proton Radius Puzzle is the inconsistency between the proton radius determined from muonic hydrogen and the proton radius determined from atomic hydrogen level transitions and ep elastic scattering. No generally accepted resolution to the Puzzle has been found. Possible solutions generally fall into one of three categories: the two radii are different due to novel beyond-standardmodel physics, the two radii are different due to novel aspects of nucleon structure, and the two radii are the same, but there are underestimated uncertainties or other issues in the ep experiments.

View PDFchevron_right
Model independent extraction of the proton magnetic radius from electron scattering
Zachary Epstein

Physical Review D, 2014

We combine constraints from analyticity with experimental electron-proton scattering data to determine the proton magnetic radius without model-dependent assumptions on the shape of the form factor. We also study the impact of including electron-neutron scattering data, and ππ → NN data. Using representative datasets we find for a cut of Q 2 ≤ 0.5 GeV 2 , r p M = 0.91 +0.03 −0.06 ± 0.02 fm using just proton scattering data; r p M = 0.87 +0.04 −0.05 ± 0.01 fm adding neutron data; and r p M = 0.87 +0.02 −0.02 fm adding ππ data. We also extract the neutron magnetic radius from these data sets obtaining r n M = 0.89 +0.03 −0.03 fm from the combined proton, neutron, and ππ data.

View PDFchevron_right
Towards a Resolution of the Proton Form Factor Problem: New Electron and Positron Scattering Data
Reinhard Schumacher

Physical Review Letters, 2015

View PDFchevron_right
On the proton radius problem
Elena Santopinto, Mauro Giannini

The recent values of the proton charge radius obtained by means of muonic-hydrogen laser spectroscopy are about $4\%$ different from the electron scattering data. It has been suggested that the proton radius is actually measured in different frames and that, starting from a non relativistic quark model calculation, the Lorentz transformation of the form factors accounts properly for the discepancy. We shall show that the relation between the charge radii measured in different frames can be determined on very general grounds by taking into account the Lorentz transformation of the charge density. In this way, the discrepancy between muonic-hydrogen laser spectroscopy and electron scattering data can be removed.

View PDFchevron_right
Form Factor of Proton Predicted Using the Data of ppbar Elastic Scattering at $$\boldsymbol{\sqrt{s}=1.96}$$ eV
Bushra Kanwal

Physics of Atomic Nuclei, 2020

Based on the behavior of elastic scattering of proton and anti-proton at √ s = 1.96 TeV for squared four-momentum transfer 0.26 < −t < 1.2 (GeV/c) 2 , form factor of proton is predicted. Simplest version of Chou-Yang model is employed for extracting this form factor by fitting experimental data of differential cross section from D0 experiment to a single Gaussian. Root mean square (rms) matter radius of proton is calculated using this form factor. It is found to be equal to 0.89 fm. Which is in good agreement with experimental data and theoretically predicted values from other models.

View PDFchevron_right
A unitary and analytic model of nucleon EM structure, the puzzle of JLab proton polarization data and new insight into the proton charge distribution
Cyril Adamuscin

Progress in Particle and Nuclear Physics, 2005

The Unitary and analytic model of nucleon electromagnetic structure, describing all existing nucleon form factor data, is briefly reviewed. Then in the framework of this model the problem of inconsistency of older proton electric form factor data in space-like region (obtained from e − p → e − p process by the Rosenbluth technique) with recent Jefferson Lab data on the ratio G Ep (t)/G M p (t) (measured in precise polarization − → e − p → e −− → p experiment) is suggested to be solved in favour of the latter data which, however, unlike older data cause an existence of the form factor zero, i.e. a difraction minimum in |G Ep (t)| around t = −Q 2 = −13GeV 2 . The new behaviour of G Ep (t) with the zero gives modified proton charge distribution with enlarged value of the mean square charge radius.

View PDFchevron_right

References (121)

  1. Mohr, P.; Taylor, B.; Newell, D. CODATA Recommended Values of the Fundamental Physical Constants: 2010. Rev. Mod. Phys. 2012, 84, 1527.
  2. Arrington, J.; Sick, I. Evaluation of the Proton Charge Radius from Electron-Proton Scattering. J. Phys. Chem. Ref. Data 2015, 44, 031204.
  3. Pohl, R.; Antognini, A.; Nez, F.; Amaro, F.; Biraben, F.; Cardoso, J.M.R.; Covita, D.S.; Dax, A.; Dhawan, S.; Fernandes, L.M.P.; et al. The size of the proton. Nature 2010, 466, 213.
  4. Pohl, R.; Nez, F.; Fernandes, L.M.P.; Amaro, F.D.; Biraben, F.; Cardoso, J.M.R.; Covita, D.S.; Dax, A.; Dhawan, S.; Diepold, M.; et al. Laser spectroscopy of muonic deuterium. Science 2016, 353, 669-673.
  5. Peset, C.; Pineda, A. The Lamb shift in muonic hydrogen and the proton radius from effective field theories. Eur. Phys. J. A 2015, 51, 156.
  6. Beyer, A.; Maisenbacher, L.; Matveev, A.; Pohl, R.; Khabarova, K.; Grinin, A.; Lamour, T.; Yost, D.C.; Hänsch, T.W.; Kolachevsky, N.; et al. The Rydberg constant and proton size from atomic hydrogen. Science 2017, 358, 79-85.
  7. Fleurbaey, H. Frequency metrology of the 1S-3S transition of hydrogen: contribution to the proton charge radius puzzle. Available online: https://tel.archives-ouvertes.fr/tel-01633631 (accessed on 15 November 2017).
  8. Sick, I.; Trautmann, D. On the rms radius of the deuteron. Nucl. Phys. A 1998, 637, 559.
  9. Rosenfelder, R. Coulomb corrections to elastic electron-proton scattering and the proton charge radius. Phys. Lett. B 2000, 479, 381.
  10. Blunden, P.; Melnitchouk, W.; Tjon, J. Two-photon exchange in elastic electron-nucleon scattering. Phys. Rev. C 2005, 72, 034612.
  11. Afanasev, A.; Blunden, P.; Hasell, D.; Raue, B. Two-photon exchange in elastic electron-proton scattering. Prog. Part. Nucl. Phys. 2017, 95, 245-278.
  12. Rimal, D.; Adikaram, D.; Raue, B.A.; Weinstein, L.B.; Arrington, J.; Brooks, W.K.; Ungaro, M.; Adhikari, K.P.; Afanasev, A.V.; Akbar, Z.; et al. Measurement of two-photon exchange effect by comparing elastic e±p cross sections. Phys. Rev. C 2017, 95, 065201.
  13. Rachek, I.A.; Arrington, J.; Dmitriev, V.F.; Gauzshtein, V.V.; Gerasimov, R.E.; Gramolin, A.V.; Holt, R.J.; Kaminskiy, V.V.; Lazarenko, B.A.; Mishnev, S.I.; et al. Measurement of the Two-Photon Exchange Contribution to the Elastic Scattering Cross Sections at the VEPP-3 Storage Ring. Phys. Rev. Lett. 2015, 114, 062005.
  14. Henderson, B.S.; Ice, L.D.; Khaneft, D.; O'Connor, C.; Russell, R.; Schmidt, A.; Bernauer, J.C.; Kohl, M.; Akopov, N.; Alarcon, R.; et al. Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering Determined by the OLYMPUS Experiment. Phys. Rev. Lett. 2017, 118, 092501.
  15. Sick, I. On the rms-radius of the proton. Phys. Lett. B 2003, 576, 62-67.
  16. Licht, A.; Pagnamenta, A. Wave Functions and Form Factors for Relativistic Composite Particles. I. Phys. Rev. D 1970, 2, 1150.
  17. Mitra, A.; Kumari, I. Relativistic form factors for clusters with nonrelativistic wave functions. Phys. Rev. D 1977, 15, 261.
  18. Ji, X. A relativistic skyrmion and its form factors. Phys. Lett. B 1991, 254, 456-461.
  19. Kelly, J. Nucleon charge and magnetization densities from Sachs form factors. Phys. Rev. C 2002, 66, 065203.
  20. Kelly, J. Simple parametrization of nucleon form factors. Phys. Rev. C 2004, 70, 068202.
  21. Bumiller, F.; Croissiaux, M.; Dally, E.; Hofstadter, R. Electromagnetic Form Factors of the Proton. Phys. Rev. 1961, 124, 1623.
  22. Janssens, T.; Hofstadter, R.; Hughes, E.; Yearian, M. Proton form factors from elastic electron-proton scattering. Phys. Rev. 1966, 142, 922.
  23. Borkowski, F.; Peuser, P.; Simon, G.; Walther, V.; Wendling, R. Electromagnetic form factors of the proton at low four-momentum transfer. Nucl. Phys. A 1974, 222, 269-275.
  24. Borkowski, F.; Simon, G.; Walther, V.; Wendling, R. Electromagnetic form factors of the peoton at low four-momentum transfer (II). Nucl. Phys. B 1975, 93, 461-478.
  25. Simon, G.; Schmitt, C.; Borkowski, F.; Walther, V. Absolute electron-proton cross sections at low momentum transfer measured with a high pressure gas target system. Nucl. Phys. A 1980, 333, 381-391.
  26. Simon, G.; Schmitt, C.; Walther, V. Elastic electric and magnetic e-d scattering at low momentum transfer. Nucl. Phys. A 1981, 364, 285-296.
  27. Albrecht, W.; Behrend, H.; Brasse, F.; Flauger, W.; Hultschig, H.; Steffen, K.G. Elastic Electron-Proton Scattering at Momentum Transfers up to 245 F -2 . Phys. Rev. Lett. 1966, 17, 1192.
  28. Bartel, W.; Dudelzak, B.; Krehbiel, H.; McElroz, J.; Meyer-Berkhout, U.; Morrison, R.J.; Nguyen-Ngoc, H.; Schmidt, W.; Weber, G. Small-Angle Electron-Proton Elastic-Scattering Cross Sections for Squared Momentum Transfers Between 10 and 105 F -2 . Phys. Rev. Lett. 1966, 17, 608.
  29. Frerejacque, D.; Benaksas, D.; Drickey, D. Proton Form Factors from Observation of Recoil Protons. Phys. Rev. 1966, 141, 1308.
  30. Albrecht, W.; Behrend, H.-J.; Dorner, H.; Flauger, W.; Hultschig, H. Some Recent Measurements of Proton Form Factors. Phys. Rev. Lett. 1967, 18, 1014.
  31. Bartel, W.; Dudelzak, B.; Krehbiel, H.; McElroy, J.; Meyer-Berkhout, U.; Morrison, R.J.; Nguyen-Ngoc, H.; Schmidt, W.; Weber, G. The charge form factor of the proton at a momentum transfer of 75 F -2 . Phys. Lett. B 1967, 25, 236.
  32. Bartel, W.; Buesser, F.; Dix, W.; Felst, R.; Harms, D.; Krehbiel, H.; Kuhlmann, P.E.; McElroy, j.; Meyer, J.; Weber, G. Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c) 2 . Nucl. Phys. B 1973, 58, 429-475.
  33. Ganichot, D.; Grossetête, B.; Isabelle, D. Backward electron-deuteron scattering below 280 MeV. Nucl. Phys. A 1972, 178, 545-562.
  34. Kirk, P.; Breidenbach, M.; Friedman, J.; Hartmann, G.; Kendall, H.; Buschhorn, G.; Coward, D.H.; DeStaebler, H.; Early, R.A.; Litt, J.; et al. Elastic Electron-Proton Scattering at Large Four-Momentum Transfer. Phys. Rev. D 1973, 8, 63.
  35. Murphy, J.; Shin, Y.; Skopik, D. Proton form factor from 0.15 to 0.79 fm -2 . Phys. Rev. C 1974, 9, 2125.
  36. Berger, C.; Burkert, V.; Knop, G.; Langenbeck, B.; Rith, K. Electromagnetic form factors of the proton at squared four-momentum transfers between 10 and 50 fm -2 . Phys. Lett. B 1971, 35, 87-89.
  37. Bartel, W.; Buesser, F.W.; Dix, W.R.; Felst, R.; Harms, D.; Krehbiel, H.; Kuhlmann, P.E.; McElroy, J.; Weber, G. Electromagnetic proton form factors at squared four-momentum transfers between 1 and 3(GeV/c) 2 . Phys. Rev. Lett. 1970, 33, 245-248.
  38. Borkowski, F.; Simon, G.; Walther, V.; Wendling, R. On the determination of the proton RMS-radius from electron scattering data. Z. Physik A 1975, 275, 29.
  39. Bernauer, J.; Achenbach, P.; Gayoso, C.A.; Böhm, R.; Bosnar, D.; Debenjak, L.; Distler, M.O.; Doria, L.; Esser, A.; Fonvieille, H.; et al. High-Precision Determination of the Electric and Magnetic Form Factors of the Proton. Phys. Rev. Lett. 2010, 105, 242001.
  40. Amroun, A. Mesure Des Facteurs De Forme Electromagnetiques Des Noyaux Helium-3 Et Tritium Par Diffusion D'electrons. Ph.D. Thesis, Université de Bordeaux, Bordeaux, France, 1989
  41. Dudelzak, B.; Sauvage, G.; Lehmann, P. Measurements of the form factors of the proton at momentum transfers q 2 2 fermi -2 . Nuov. Cim. 1963, 28, 18-24.
  42. Qattan, I.; Arrington, J.; Segel, R.; Zheng, X.; Aniol, K.; Baker, O.K.; Beams, R.; Brash, E.J.; Calarco, J.; Camsonne, A.; et al. Precision Rosenbluth Measurement of the Proton Elastic Form Factors. Phys. Rev. Lett. 2005, 94, 142301.
  43. Christy, M.E.; Ahmidouch, A.; Armstrong, C.S.; Arrington, J.; Asaturyan, R.; Avery, S.; Baker, O.; Beck, D.; Blok, H.P.; Bochna, C.W.; et al. Measurements of electron-proton elastic cross sections for 0.
  44. < Q 2 < 5.5 (GeV/c) 2 . Phys. Rev. C 2004, 70, 015206.
  45. Dutta, D.; Van Westrum, D.; Abbott, D.; Ahmidouch, A.; Amatuoni, T.A.; Armstrong, C.; Arrington, J.; Assamagan, K.A.; Bailey, K.; Baker, O.K.; et al. Quasielastic (e,e p) reaction on 12 C, 56 Fe, and 197 Au. Phys. Rev. C 2003, 68, 064603.
  46. Niculescu, I.; Armstrong, C.; Arrington, J.; Assamagan, K.; Baker, O.; Beck, D.H.; Bochna, C.W.; Carlini, R.D.; Cha, J.; Cothran, C.; et al. Evidence for valencelike quark-hadron duality. Phys. Rev. Lett. 2000, 85, 1182.
  47. Rock, S.; Arnold, R.; Bosted, P.; Chertok, B.; Mecking, B.; Schmidt, I.; Szalata, Z.M.; York, R.C.; Zdarko, R. Measurement of elastic electron-neutron scattering and inelastic electron-deuteron scattering cross sections at high momentum transfer. Phys. Rev. D 1992, 46, 24.
  48. Stein, S.; Atwood, W.; Bloom, E.; Cottrell, R.; DeStaebler, H.; Jordan, C.L.; Piel, H.G.; Prescott, C.Y.; Siemann, R.; Taylor, R.E.; et al. Electron scattering at 4 • with energies of 4.5-20 GeV. Phys. Rev. D 1975, 12, 1884.
  49. Goitein, M.; Budnitz, R.; Carroll, L.; Chen, J.; Dunning, J.; Hanson, K.; Imrie, D.C.; Mistretta, C.; Wilson, R. Elastic Electron-Proton Scattering Cross Sections Measured by a Coincidence Technique. Phys. Rev. D 1970, 1, 2449.
  50. Bosted, P.; Katramatou, A.; Arnold, R.; Benton, D.; Clogher, L.; DeChambrier, G.; Lambert, J.; Lung, A.; Petratos, G.G.; Rahbar, A.; et al. Measurements of the deuteron and proton magnetic form factors at large momentum transfers. Phys. Rev. C 1990, 42, 38.
  51. Bosted, P.E.; Andivahis, L.; Lung, A.; Stuart, L.M.; Alster, J.; Arnold, R.G.; Chang, C.C.; Dietrich, F.S.; Dodge, W.; Gearhart, R.; et al. Measurements of the electric and magnetic form factors of the proton from Q 2 = 1.75 to 8.83 (GeV/c) 2 . Phys. Rev. Lett. 1992, 68, 3841-3844.
  52. Sill, A. Jailbar optical studies of the SLAC 8-GeV/c spectrometer. Available online: http://inspirehep.net/ record/243145/ (accessed on 10 November 2017).
  53. Price, L.E.; Dunning, J.R.; Goitein, M.; Hanson, K.; Kirk, T.; Wilson, R. Backward-angle electron-proton elastic scattering and proton electromagnetic form factors. Phys. Rev. D 1971, 4, 45.
  54. Litt, J.; Buschhorn, G.; Coward, D.; Destaebler, H.; Mo, L.; Taylor, R.E.; Barish, B.C.; Loken, S.C.; Pine, J.; Friedman, J.I.; et al. Measurement of the ratio of the proton form factors, G E /G M , at high momentum transfers and the question of scaling. Phys. Lett. B 1970, 31, 40-44.
  55. Walker, R.; Filippone, B.; Jourdan, J.; Milner, R.; McKeown, R.; Potterveld, D.; Arnold, R.; Benton, D.; Bosted, P.; Clogher, L.; et al. Measurement of the proton elastic form factors for Q 2 = 1-3 (Gev/c) 2 . Phys. Lett. B 1989, 224, 353-358.
  56. Walker, R.; Filippone, B.; Jourdan, J.; Milner, R.; McKeown, R.; Potterveld, D.; Andivahis, L.; Arnold, R.; Benton, D.; Bosted, P.; et al. Measurements of the proton elastic form factors for 1 ≤ Q 2 ≤ 3 (GeV/c) 2 at SLAC. Phys. Rev. D 1994, 49, 5671.
  57. Andivahis, L.; Bosted, P.E.; Lung, A.; Stuart, L.M.; Alster, J.; Arnold, R.G.; Chang, C.C.; Dietrich, F.S.; Dodge, W.; Gearhart, R.; et al. Measurements of the electric and magnetic form factors of the proton from Q 2 = 1.75 to 8.83 (GeVc) 2 . Phys. Rev. D 1994, 50, 5491.
  58. Drickey, D.; Hand, L. Precise Neutron and Proton Form Factors at Low Momentum Transfers. Phys. Rev. Lett. 1962, 9, 521.
  59. Punjabi, V.; Perdrisat, C.F.; Aniol, K.A.; Baker, F.T.; Berthot, J.; Bertin, P.Y.; Bertozzi, W.; Besson, A.; Bimbot, L.; Boeglin, W.U.; et al. Proton elastic form factor ratios to Q 2 = 3.5 GeV 2 by polarization transfer. Phys. Rev. C 2005, 71, 055202.
  60. Gayou, O.; Wijesooriya, K.; Afanasev, A.; Amarian, M.; Aniol, K.; Becher, S.; Benslama, K.; Bimbot, L.; Bosted, P.; Brash, E.; et al. Measurements of the elastic electromagnetic form factor ratio µp G Ep /G Mp via polarization transfer. Phys. Rev. C 2001, 64, 038202.
  61. Gayou, O.; Aniol, K.A.; Averett, T.; Benmokhtar, F.; Bertozzi, W.; Bimbot, L.; Brash, E.J.; Calarco, J.R.; Cavata, C.; Chai, Z.; et al. Measurement of G Ep /G Mp in -→ e p → -→ p to Q 2 = 5.6 GeV 2 . Phys. Rev. Lett. 2002, 88, 092301.
  62. Zhan, X.; Allada, K.; Armstrong, D.; Arrington, J.; Bertozzi, W.; Boeglin, W.; Chen, J.P.; Chirapatpimol, K.; Choi, S.; Chudakov, E.; et al. High-precision measurement of the proton elastic form factor ratio µpG E /G M at low Q 2 . Phys. Lett. B 2011, 705, 59-64.
  63. Botterill, D.; Braben, D.; Montgomery, H.; Norton, P.; Matone, G.; Del Guerra, A.; Giazotto, A.; Giorgi, M.A.; Orsitto, F.; Stefaninia, A. Elastic electron-proton scattering between 0.05 and 0.30 (GeV/c) 2 . Phys. Lett. B 1973, 46, 125-128.
  64. Bernauer, J. Measurement of the elastic electron-proton cross section and separation of the electric and magnetic form factor in the Q 2 range from 0.004 to 1 (GeV/c) 2 . Available online: http://wwwa1.kph.uni- mainz.de/A1/publications/doctor/bernauer.pdf (accessed on 12 November 2017).
  65. Lee, G.; Arrington, J.; Hill, R. Extraction of the proton radius from electron-proton scattering data. Phys. Rev. D 2015, 92, 013013.
  66. Sick, I. Problems with proton radii. Prog. Part. Nucl. Phys. 2012, 67, 473-478.
  67. Mo, L.; Tsai, Y. Radiative Corrections to Elastic and Inelastic ep and up Scattering. Rev. Mod. Phys. 1969, 41, 205.
  68. Maximon, L.; Tjon, J. Radiative corrections to electron-proton scattering. Phys. Rev. C 2000, 62, 054320.
  69. Strauch, S.; Dieterich, S.; Aniol, K.A.; Annand, J.R.M.; Baker, O.K.; Bertozzi, W.; Boswell, M.; Brash, E.J.; Chai, Z.; Chen, J.P.; et al. Polarization Transfer in the 4 He ( -→ e , e' -→ p ) 3 H Reaction up to Q 2 = 2.6 (GeV/c) 2 . Phys. Rev. Lett. 2003, 91, 052301.
  70. Milbrath, B.; McIntyre, J.; Armstrong, C.; Barkhuff, D.; Bertozzi, W.; Chen, J.P.; Dale, D.; Dodson, G.; Dow, K.A.; Epstein, M.B.; et al. Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron. Phys. Rev. Lett. 1998, 80, 452.
  71. Pospischil, T.; Bartsch, P.; Baumann, D.; Bermuth, J.; Böhm, J.B.R.; Bohinc, K.; Derber, S.; Ding, M.; Distler, M.; Drechsel, D.; et al. Measurement of the Recoil Polarization in the p ( -→ e , e' -→ p ) π 0 Reaction at the ∆ (1232) Resonance. Phys Rev. Lett. 2001, 86, 2959.
  72. Crawford, C.B.; Sindile, A.; Akdogan, T.; Alarcon, R.; Bertozzi, W.; Booth, E.; Botto, T.; Calarco, J.; Clasie, B.; DeGrush, A.; et al. Measurement of the Proton's Electric to Magnetic Form Factor Ratio from -→ H ( -→ e ,e'p).
  73. Phys. Rev. Lett. 2007, 98, 052301.
  74. Ron, G.; Glister, J.; Lee, B.; Allada, K.; Armstrong, W.; Arrington, J.; Beck, A.; Benmokhtar, F.; Berman, B.L.; Boeglin, W.; et al. Measurements of the Proton Elastic-Form-Factor Ratio mu pG p E/G p M at Low Momentum Transfer. Phys. Rev. Lett. 2007, 99, 202002.
  75. MacLachlan, G.; Aghalaryan, A.; Ahmidouch, A.; Anderson, B.D.; Asaturyan, R.; Baker, O.; Baldwin, A.R.; Barkhuff, D.; Breuer, H.; Carlini, R.; et al. The ratio of proton electromagnetic form factors via recoil polarimetry at Q 2 = 1.13 (GeV/c) 2 . Nucl. Phys. A 2006, 764, 261-273.
  76. Jones, M.K.; Aniol, K.A.; Baker, F.T.; Berthot, J.; Bertin, P.Y.; Bertozzi, W.; Besson, A.; Bimbot, L.; Boeglin, W.U.; Brash, E.J.; et al. G Ep /G Mp Ratio by Polarization Transfer in -→ e p→ -→ e . Phys. Rev. Lett. 2000, 84, 1398.
  77. Jones, M.K.; Aghalaryan, A.; Ahmidouch, A.; Asaturyan, R.; Bloch, F.; Boeglin, W.; Bosted, P.; Carasco, C.; Carlini, R.; Cha, J.; et al. Proton G E /G M from beam-target asymmetry. Phys. Rev. C 2006, 74, 035201.
  78. Puckett, A.J.R.; Brash, E.J.; Jones, M.K.; Luo, W.; Meziane, M.; Pentchev, L.; Perdrisat, C.F.; Punjabi, V.; Wesselmann, F.R.; Abdellah, A.; et al. Recoil Polarization Measurements of the Proton Electromagnetic Form Factor Ratio to Q 2 = 8.5 GeV 2 . Phy. Rev. Lett. 2010, 104, 242301.
  79. Puckett, A.J.R.; Brash, E.J.; Gayou, O.; Jones, M.K.; Pentchev, L.; Perdrisat, C.F.; Punjabi, V.; Aniol, K.A.; Averett, T.; Benmokhtar, F.; et al. Final analysis of proton form factor ratio data at Q 2 = 4.0, 4.8, and 5.6 GeV 2 . Phys. Rev. C 2012, 85, 045203.
  80. Dieterich, S.; Bartsch, P.; Baumann, D.; Böhm, J.B.R.; Bohinc, K.; Böhm, R.; Bosnar, D.; Derber, S.; Ding, M.; Distler, M.; et al. Polarization transfer in the 4 He (e→, e'p→) 3 H reaction Phys. Lett. B 2001, 500, 47-52.
  81. Paolone, M.; Malace, S.P.; Strauch, S.; Albayrak, I.; Arrington, J.; Berman, B.L.; Brash, E.J.; Briscoe, B.; Camsonne, A.; Chen, J.P.; et al. Polarization Transfer in the 4 He( -→ e ,e' -→ p )3H Reaction at Q 2 = 0.8 and 1.3 (GeV/c) 2 . Phys. Rev. Lett. 2010, 105, 072001.
  82. Friar, J.; Sick, I. Zemach moments for hydrogen and deuterium. Phys. Lett. B 2004, 579, 285-289.
  83. Friar, J.; Sick, I. Muonic hydrogen and the third Zemach moment. Phys. Rev. A 2005, 72, 040502.
  84. Horbatsch, M.; Hessels, E. Evaluation of the strength of electron-proton scattering data for determining the proton charge radius. Phys. Rev. C 2016, 93, 015204.
  85. Higinbotham, D.; Kabir, A.; Lin, V.; Meekins, D.; Norum, B.; Sawatzky, B. Proton radius from electron scattering data. Phys. Rev. C 2016, 93, 055207.
  86. Griffioen, K.; Carlson, C.; Maddox, S. Consistency of electron scattering data with a small proton radius. Phys. Rev. C 2016, 93, 065207.
  87. Lorenz, I.; Meissner, U.G. Reduction of the proton radius discrepancy by 3σ. Phys. Lett. B 2014, 737, 57-59.
  88. Sick, I.; Trautmann, D. Proton root-mean-square radii and electron scattering. Phys. Rev. C 2014, 89, 012201(R).
  89. Sick, I. Importance of Tail of Proton Density. Few-Body Syst. 2014, 55, 903.
  90. Sick, I.; Trautmann, D. Reexamination of proton rms radii from low-q power expansions. Phys. Rev. C 2017, 95, 012501.
  91. Gasparian, A.; Pedroni, R.; Ahmed, A.; Khandaker, M.; Punjabi, V.; Salgado, v.; Akushevich, I.; Gao, H.; Huang, M.; Laskaris, G.; et al. High precision measurement of the proton charge radius. Available online: https://pdfs.semanticscholar.org/06d6/1cc255edb67eb9adccf3605dd313eaff5504.pdf (accessed on 26 November 2017).
  92. Bernauer, J.; Distler, M.; Friedrich, J.; Walcher, T.; Achenbach, P.; Ayerbe Gayoso, C.; Böhm, R.; Bosnar, D.; Debenjak, L.; Doria, L.; et al. Electric and magnetic form factors of the proton. Phys. Rev. C. 2014, 90, 015206.
  93. Arrington, J.; Melnitchouk, W.; Tjon, J. Global analysis of proton elastic form factor data with two-photon exchange corrections. Phys. Rev. C 2007, 76, 035205.
  94. Kraus, E.; Mesick, K.; White, A.; Gilman, R.; Strauch, S. Polynomial fits and the proton radius puzzle. Phys. Rev. C 2014, 90, 045206.
  95. Hill, R.; Paz, G. Model-independent extraction of the proton charge radius from electron scattering. Phys. Rev. D 2010, 82, 113005.
  96. Borisyuk, D. Proton charge and magnetic rms radii from the elastic ep scattering data. Nucl. Phys. A 2010, 843, 59-67.
  97. Friar, J. Relativistic corrections to electron scattering by 2 He, 3 He, and 4 He. Ann. Phys. 1973, 81, 332-363.
  98. Anni, R.; Có, G.; Pellegrino, P. Nuclear charge density distributions from elastic electron scattering data. Nucl. Phys. A 1995, 584, 35-39.
  99. Graczyk, K.; Juszczak, C. Proton radius from Bayesian inference. Phys. Rev. C 2014, 90, 054334.
  100. Sick, I. Model-independent nuclear charge densities from elastic electron scattering. Nucl. Phys. A 1974, 218, 509-541.
  101. Iachello, F.; Jackson, A.; Lande, A. Semi-phenomenological fits to nucleon electromagnetic form factors. Phys. Lett. B 1973, 43, 191-196.
  102. Blatnik, S.; Zovko, N. Nucleon form factors in the extended VDM supplemented with asymptotic constraints. Acta Phys. Austriaca 1974, 39, 62.
  103. Gari, M.; Krümpelmann, W. The electric neutron form factor and the strange quark content of the nucleon. Phys. Lett. B 1992, 274, 159-162.
  104. Lomon, E. Extended Gari-Krümpelmann model fits to nucleon electromagnetic form factors. Phys. Rev. C 2001, 64, 035204.
  105. Bijker, R.; Iachello, F. Reanalysis of the nucleon spacelike and timelike electromagnetic form factors in a two-component model. Phys. Rev. C 2004, 69, 068201.
  106. Bernauer, J.; Distler, M. Avoiding common pitfalls and misconceptions in extractions of the proton radius. arXiv 2016, arXiv:1606.02159.
  107. Lorenz, I.; Hammer, H.W.; Meissner, U.G. The size of the proton: Closing in on the radius puzzle. Eur. Phys. J. A 2012, 48, 151.
  108. Graczyk, K.; Plonski, P.; Sulei, R. Neural network parameterizations of electromagnetic nucleon form-factors. arXiv 2010, arXiv:1006.0342.
  109. Gari, M.; Krümpelmann, W. Semiphenomenological synthesis of meson and quark dynamics and the E.M. structure of the nucleon. Z. Phys. 1985, 322, 689.
  110. Mergell, P.; Meissner, U.G.; Drechsel, D. Dispersion-theoretical analysis of the nucleon electromagnetic form factors. Nucl. Phys. A 1996, 596, 367-396.
  111. Hammer, H.W.; Drechsel, D.; Meissner, U.G. On the pion cloud of the nucleon. Phys. Lett. B 2004, 586, 291-296.
  112. Lorenz, I.; Meissner, U.G.; Hammer, H.W.; Dong, Y. Theoretical constraints and systematic effects in the determination of the proton form factors. Phys. Rev. D 2015, 91, 014023.
  113. Höhler, G.; Pietarinen, E.; Sabba-Stefanescu, I.; Borkowski, F.; Simon, G.; Walther, V.H.; Wendling, R.D. Analysis of electromagnetic nucleon form factors. Nucl. Phys. B 1976, 114, 505-534.
  114. Höhler, G.; Pietarinen, E. Electromagnetic radii of nucleon and pion. Phys. Lett. B 1975, 53, 471-475.
  115. Höhler, G. Landolt-Boernstein; Springer: Berlin, Germany, 1983; Volume 9.
  116. Adamuscin, C.; Dubnicka, S.; Dubnickova, A. New value of the proton charge root mean square radius. Prog. Part. Nucl. Phys. 2012, 67, 479-485.
  117. Alarcon, J.; Weiss, C. Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors. arXiv 2017, arXiv:1710.06430v1.
  118. Horbatsch, M.; Hessels, E.; Pineda, A. Proton radius from electron-proton scattering and chiral perturbation theory. Phys. Rev. C 2017, 95, 035203.
  119. Sick, I. Precise root-mean-square radius of 4 He. Phys. Rev. C 2008, 77, 041302.
  120. Sick, I. Precise nuclear radii from electron scattering. Phys. Lett. B 1982, 116, 212-214.
  121. Lorenz, I. Private communication, 2012.

Related papers

Evaluation of the proton charge radius from e-p scattering
John Larry Arrington

2015

In light of the proton radius puzzle, the discrepancy between measurements of the proton charge radius from muonic hydrogen and those from electronic hydrogen and electron-proton scattering measurements, we reexamine the charge radius extractions from electron scattering measurements. We provide a recommended value for the proton RMS charge radius, $r_E = 0.879 \pm 0.011$ fm, based on a global examination of elastic e-p scattering data. The uncertainties include contributions to account for tension between different data sets and inconsistencies between radii using different extraction procedures.

View PDFchevron_right
Coulomb corrections to elastic electron–proton scattering and the proton charge radius
Roland Rosenfelder

Physics Letters B, 2000

Recent values of the proton charge radius derived from the Lamb shift in electronic hydrogen tend to be larger than those from electron scattering. Therefore low-momentum-transfer scattering data from different groups and laboratories have been reanalyzed with Coulomb and recoil corrections included. This was done by calculating at each scattering angle and scattering energy the corresponding correction obtained from a partial wave program which includes recoil approximately. Corrections due to magnetic scattering were also made before the rms-radius was determined by a fit which allows free normalization for each experiment. It is shown that an analysis of electron scattering data including Coulomb corrections lowers the χ 2 of the fit and increases the proton radius by about (0.008 − 0.013) fm depending on the fit strategy. A value of r p = 0.880 (15) fm is obtained which is in good agreement with the one extracted from Lamb shift measurements.

View PDFchevron_right
Robust extraction of the proton charge radius from electron-proton scattering data
Weizhi Xiong

Physical Review C, 2018

Background: To extract the proton charge radius from electron scattering data, requires determining the slope of the charge form factor at Q 2 of zero. As experimental data cannot reach that limit, numerous methods for making the extraction have been proposed. Purpose: In this study, we seek to find functional forms that will allow for a robust extraction of the proton radius from a wide variety of functional forms. The primary motivation of this study is to have confidence in the extraction of upcoming low Q 2 experimental data. Method: We create a general framework for studying various form-factor functions along with various fitting functions. The input form factors are used to generate pseudo-data with fluctuations mimicking the binning and random uncertainty of a set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fitting functions that are robust for proton radius extractions in an objective fashion. Results: For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of z can extract the input radius regardless of the input charge form factor function that is used. Conclusions: We have created a framework to determine which functional forms allow for a robust extraction of the radius from pseudo-data generated from a wide variety of trial functions. By taking into account both bias and variance, the optimal functions for extracting the proton radius can be determined.

View PDFchevron_right
Reduction of the proton radius discrepancy by 3σ
Ulf-g Meissner

Physics Letters B, 2014

We show that in previous analyses of electron-proton scattering, the uncertainties in the proton charge radius extraction are underestimated. Using a fit function based on a conformal mapping, we can describe the scattering data with high precision and extract a radius value in agreement with the one obtained from muonic hydrogen.

View PDFchevron_right
Extraction of the Proton Charge Radius from Experiments
Marek Nowakowski

Makara Journal of Science, 2016

Static properties of hadrons such as their radii and other moments of the electric and magnetic distributions can only be extracted using theoretical methods and not directly measured from experiments. As a result, discrepancies between the extracted values from different precision measurements can exist. The proton charge radius, r p , which is either extracted from electron proton elastic scattering data or from hydrogen atom spectroscopy seems to be no exception. The value r p = 0.84087(39) fm extracted from muonic hydrogen spectroscopy is about 4% smaller than that obtained from electron proton scattering or standard hydrogen spectroscopy. The resolution of this so called proton radius puzzle has been attempted in many different ways over the past six years. The present article reviews these attempts with a focus on the methods of extracting the radius.

View PDFchevron_right

Related topics

  • Electron scattering

    • Cited by

    São Paulo potential version 2 (SPP2) and Brazilian nuclear potential (BNP)
    Brett Vern Carlson

    Computer Physics Communications, 2021

    View PDFchevron_right
    Robust extraction of the proton charge radius from electron-proton scattering data
    Weizhi Xiong

    Physical Review C, 2018

    Background: To extract the proton charge radius from electron scattering data, requires determining the slope of the charge form factor at Q 2 of zero. As experimental data cannot reach that limit, numerous methods for making the extraction have been proposed. Purpose: In this study, we seek to find functional forms that will allow for a robust extraction of the proton radius from a wide variety of functional forms. The primary motivation of this study is to have confidence in the extraction of upcoming low Q 2 experimental data. Method: We create a general framework for studying various form-factor functions along with various fitting functions. The input form factors are used to generate pseudo-data with fluctuations mimicking the binning and random uncertainty of a set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fitting functions that are robust for proton radius extractions in an objective fashion. Results: For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of z can extract the input radius regardless of the input charge form factor function that is used. Conclusions: We have created a framework to determine which functional forms allow for a robust extraction of the radius from pseudo-data generated from a wide variety of trial functions. By taking into account both bias and variance, the optimal functions for extracting the proton radius can be determined.

    View PDFchevron_right
    Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory
    Pulak Talukdar

    Physical Review D, 2021

    A unified treatment of both chiral and radiative corrections to the low-energy elastic leptonproton scattering processes is presented in Heavy Baryon Chiral Perturbations Theory. The proton hadronic chiral corrections include the next-to-next-to leading order corrections whereas the radiative corrections include the next-to-leading order terms in our novel power counting scheme. We find that the net fractional well-defined chiral corrections with respect to the leading order Born cross section can be as large as 10% (20%) for electron (muon) scattering process for MUon proton Scattering Experiment (MUSE) kinematics. We show via our model-independent treatment of the low-energy lepton-proton kinematics, that the largest theoretical uncertainty is due to the recent different published values of the proton's rms radius while, e.g., the next higher order hadronic chiral terms are expected to give rather nominal errors. For the radiative corrections we demonstrate a systematic order by order cancellation of all infrared singularities and present our finite ultraviolet regularization results. We find that the radiative corrections for muon-proton scattering is of the order of 2%, whereas for electron scattering the radiative corrections could be as large as 25%. We attribute such a contrasting result partially to the fact that in muon scattering the leading radiative order correction goes through zero in some intermediate low-momentum transfer region, leaving the sub-leading radiative chiral order effects to play a dominant role in this particular kinematic region. For the low-energy MUSE experiment, the often neglected lepton mass as well as the Pauli form factor contributions of the relativistic leptons are incorporated in all our computations.

    View PDFchevron_right
    580 California St., Suite 400
    San Francisco, CA, 94104
    © 2025 Academia. All rights reserved