Parametrization and applications of the low- Q 2 nucleon vector form factors

Borah, Kaushik; Hill, Richard J.; Lee, Gabriel; Tomalak, Oleksandr

doi:10.1103/PhysRevD.102.074012

Title: Parametrization and applications of the low- $Q^{2}$ nucleon vector form factors

Journal Article · Tue Oct 20 00:00:00 EDT 2020 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.102.074012· OSTI ID:1678812

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We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $$\lesssim$$ few GeV$^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross section differs by 3-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $$[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$$ fm and $$[r_Z^p, r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$$ fm; the Friar radius of nucleons, $$[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$$ fm$^3$; the electric curvatures, $$[\langle r^4 \rangle^p_E, \langle r^4 \rangle^n_E ] = [1.08(28)(5), -0.33(24)(3)]$$ fm$^4$; and bounds on the magnetic curvatures, $$[ \langle r^4 \rangle^p_M, \langle r^4 \rangle^n_M ] = [ -2.0(1.7)(0.8), -2.3(2.1)(1.1)]$$ fm$^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Samsung Science & Technology Foundation; National Science Foundation (NSF); Universities Research Association

Grant/Contract Number:: SC0019095; AC02-07CH11359; PHY-1719877

OSTI ID:: 1678812

Alternate ID(s):: OSTI ID: 1616307

Report Number(s):: arXiv:2003.13640; FERMILAB-PUB-20-124-T; PRVDAQ; 074012

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 102 Journal Issue: 7; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (144)

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting Carlson, Carl E.; Nazaryan, Vahagn; Griffioen, Keith Physical Review A, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevA.78.022517	journal	August 2008
Two-Photon Exchange and Elastic Electron-Proton Scattering Blunden, P. G.; Melnitchouk, W.; Tjon, J. A. Physical Review Letters, Vol. 91, Issue 14 https://doi.org/10.1103/PhysRevLett.91.142304	journal	October 2003
Proton Structure and the Hyperfine Shift in Hydrogen Zemach, A. C. Physical Review, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRev.104.1771	journal	December 1956
Proton structure effects in muonic hydrogen Pachucki, Krzysztof Physical Review A, Vol. 60, Issue 5 https://doi.org/10.1103/PhysRevA.60.3593	journal	November 1999
The Rydberg constant and proton size from atomic hydrogen Beyer, Axel; Maisenbacher, Lothar; Matveev, Arthur Science, Vol. 358, Issue 6359 https://doi.org/10.1126/science.aah6677	journal	October 2017
Electromagnetic form factors of the proton at squared four-momentum transfers between 10 and 50 fm−2 Berger, Ch.; Burkert, V.; Knop, G. Physics Letters B, Vol. 35, Issue 1 https://doi.org/10.1016/0370-2693(71)90448-5	journal	April 1971
Radiative corrections to high-energy neutrino scattering De Rújula, A.; Petronzio, R.; Savoy-Navarro, A. Nuclear Physics B, Vol. 154, Issue 3 https://doi.org/10.1016/0550-3213(79)90039-7	journal	August 1979
The proton radius: from a puzzle to precision Hammer, Hans-Werner; Meißner, Ulf-G. Science Bulletin, Vol. 65, Issue 4 https://doi.org/10.1016/j.scib.2019.12.012	journal	February 2020
Publisher's Note: Proton elastic form factor ratios to $Q^{2} = 3.5 {GeV}^{2}$ by polarization transfer [Phys. Rev. C 71, 055202 (2005)] Punjabi, V.; Perdrisat, C. F.; Aniol, K. A. Physical Review C, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevC.71.069902	journal	June 2005
Measurements of elastic electron-proton scattering at large momentum transfer Sill, A. F.; Arnold, R. G.; Bosted, P. E. Physical Review D, Vol. 48, Issue 1 https://doi.org/10.1103/PhysRevD.48.29	journal	July 1993
Proton $G_{E} / G_{M}$ from beam-target asymmetry Jones, M. K.; Aghalaryan, A.; Ahmidouch, A. Physical Review C, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevC.74.035201	journal	September 2006
Dispersion analysis of the nucleon form factors including meson continua Belushkin, M. A.; Hammer, H. -W.; Meißner, Ulf-G. Physical Review C, Vol. 75, Issue 3 https://doi.org/10.1103/PhysRevC.75.035202	journal	March 2007
Measurement of the neutron magnetic form factor from inclusive quasielastic scattering of polarized electrons from polarized ${}^{3}{He}$ Gao, H.; Arrington, J.; Beise, E. J. Physical Review C, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevC.50.R546	journal	August 1994
Precision Rosenbluth Measurement of the Proton Elastic Form Factors Qattan, I. A.; Arrington, J.; Segel, R. E. Physical Review Letters, Vol. 94, Issue 14 https://doi.org/10.1103/PhysRevLett.94.142301	journal	April 2005
Precise Measurement of the Neutron Magnetic Form Factor $G_{M}^{n}$ in the Few- ${GeV}^{2}$ Region Lachniet, J.; Afanasev, A.; Arenhövel, H. Physical Review Letters, Vol. 102, Issue 19 https://doi.org/10.1103/PhysRevLett.102.192001	journal	May 2009
Absolute electron-proton cross sections at low momentum transfer measured with a high pressure gas target system Simon, G. G.; Schmitt, Ch.; Borkowski, F. Nuclear Physics A, Vol. 333, Issue 3 https://doi.org/10.1016/0375-9474(80)90104-9	journal	January 1980
Measurement of the Neutron Electric to Magnetic Form Factor Ratio at $Q^{2} = 1.58 {GeV}^{2}$ Using the Reaction ${}^{3}{\vec{He}} (\vec{e}, e^{'} n) p p$ Schlimme, B. S.; Achenbach, P.; Ayerbe Gayoso, C. A. Physical Review Letters, Vol. 111, Issue 13 https://doi.org/10.1103/PhysRevLett.111.132504	journal	September 2013
Zemach moments of the proton from Bayesian inference Graczyk, Krzysztof M.; Juszczak, Cezary Physical Review C, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevC.91.045205	journal	April 2015
The ratio of proton electromagnetic form factors via recoil polarimetry at MacLachlan, G.; Aghalaryan, A.; Ahmidouch, A. Nuclear Physics A, Vol. 764 https://doi.org/10.1016/j.nuclphysa.2005.09.012	journal	January 2006
Review of Particle Physics Tanabashi, M.; Hagiwara, K.; Hikasa, K. Physical Review D, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevD.98.030001	journal	August 2018
Nuclear finite-size effects in light muonic atoms Friar, J. L. Annals of Physics, Vol. 122, Issue 1 https://doi.org/10.1016/0003-4916(79)90300-2	journal	September 1979
Proton Form Factors from Observation of Recoil Protons Frèrejacque, D.; Benaksas, D.; Drickey, D. Physical Review, Vol. 141, Issue 4 https://doi.org/10.1103/PhysRev.141.1308	journal	January 1966
Recoil correction to the proton finite-size contribution to the Lamb shift in muonic hydrogen Karshenboim, Savely G.; Korzinin, Evgeny Yu.; Shelyuto, Valery A. Physical Review D, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevD.91.073003	journal	April 2015
Differences in quasielastic cross sections of muon and electron neutrinos Day, Melanie; McFarland, Kevin S. Physical Review D, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevD.86.053003	journal	September 2012
Model-independent determination of the axial mass parameter in quasielastic neutrino-nucleon scattering Bhattacharya, Bhubanjyoti; Hill, Richard J.; Paz, Gil Physical Review D, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevD.84.073006	journal	October 2011
Measurements of electron-proton elastic cross sections for $0.4 < Q^{2} < 5.5 {(GeV ∕ c)}^{2}$ Christy, M. E.; Ahmidouch, A.; Armstrong, C. S. Physical Review C, Vol. 70, Issue 1 https://doi.org/10.1103/PhysRevC.70.015206	journal	July 2004
Measurement of the ratio of the proton form factors, GE/GM, at high momentum transfers and the question of scaling Litt, J.; Buschhorn, G.; Coward, D. H. Physics Letters B, Vol. 31, Issue 1 https://doi.org/10.1016/0370-2693(70)90015-8	journal	January 1970
First measurement of the electric formfactor of the neutron in the exclusive quasielastic scattering of polarized electrons from polarized 3He Meyerhoff, M.; Eyl, D.; Frey, A. Physics Letters B, Vol. 327, Issue 3-4 https://doi.org/10.1016/0370-2693(94)90718-8	journal	May 1994
Extraction of the neutron magnetic form factor from quasielastic $^{3} \vec{He}$ ( $\vec{e}, e^{'}$ ) at $Q^{2} = 0.1 − 0.6 (GeV / c)^{2}$ Anderson, B.; Auberbach, L.; Averett, T. Physical Review C, Vol. 75, Issue 3 https://doi.org/10.1103/PhysRevC.75.034003	journal	March 2007
Small-Angle Electron-Proton Elastic-Scattering Cross Sections for Squared Momentum Transfers Between 10 and 105 $F^{- 2}$ Bartel, W.; Dudelzak, B.; Krehbiel, H. Physical Review Letters, Vol. 17, Issue 11 https://doi.org/10.1103/PhysRevLett.17.608	journal	September 1966
Proton elastic form factor ratios to $Q^{2} = 3.5 GeV^{2}$ by polarization transfer Punjabi, V.; Perdrisat, C. F.; Aniol, K. A. Physical Review C, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevC.71.055202	journal	May 2005
Measurements of the proton elastic form factors for $1 \leq Q^{2} \leq 3$ ${(G e V / c)}^{2}$ at SLAC Walker, R. C.; Filippone, B. W.; Jourdan, J. Physical Review D, Vol. 49, Issue 11 https://doi.org/10.1103/PhysRevD.49.5671	journal	June 1994
Measurements of $G_{E}^{n} / G_{M}^{n}$ from the ${}^{2}H (\vec{e}, e^{'} \vec{n}) {}^{1}H$ Reaction to $Q^{2} = 1.45$ $(G e V / c)^{2}$ Madey, R.; Semenov, A. Yu.; Taylor, S. Physical Review Letters, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevLett.91.122002	journal	September 2003
A measurement of the atomic hydrogen Lamb shift and the proton charge radius Bezginov, N.; Valdez, T.; Horbatsch, M. Science, Vol. 365, Issue 6457 https://doi.org/10.1126/science.aau7807	journal	September 2019
Dispersive approach to two-photon exchange in elastic electron-proton scattering Blunden, P. G.; Melnitchouk, W. Physical Review C, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevC.95.065209	journal	June 2017
Theory of the Lamb shift in muonic hydrogen Pachucki, Krzysztof Physical Review A, Vol. 53, Issue 4 https://doi.org/10.1103/PhysRevA.53.2092	journal	April 1996
Relevance of two-boson exchange effect in quasi-elastic charged current neutrino–nucleon interaction Graczyk, Krzysztof M. Physics Letters B, Vol. 732 https://doi.org/10.1016/j.physletb.2014.03.065	journal	May 2014
Backward electron-deuteron scattering below 280 MeV Ganichot, D.; Grossetête, B.; Isabelle, D. B. Nuclear Physics A, Vol. 178, Issue 2 https://doi.org/10.1016/0375-9474(72)90480-0	journal	January 1972
The neutron charge form factor and target analyzing powers from 3He(e→,e′n) scattering Bermuth, J.; Merle, P.; Carasco, C. Physics Letters B, Vol. 564, Issue 3-4 https://doi.org/10.1016/S0370-2693(03)00725-1	journal	July 2003
Two-photon exchange contribution to elastic $e^{-}$ -proton scattering: Full dispersive treatment of $π N$ states and comparison with data Tomalak, Oleksandr; Pasquini, Barbara; Vanderhaeghen, Marc Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.096001	journal	November 2017
The contribution of axial-vector mesons to hyperfine structure of muonic hydrogen Dorokhov, A. E.; Kochelev, N. I.; Martynenko, A. P. Physics Letters B, Vol. 776 https://doi.org/10.1016/j.physletb.2017.11.027	journal	January 2018
Two-photon exchange corrections to elastic $e^{-}$ -proton scattering: Full dispersive treatment of $π N$ states at low momentum transfers Tomalak, Oleksandr; Pasquini, Barbara; Vanderhaeghen, Marc Physical Review D, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevD.95.096001	journal	May 2017
Electromagnetic form factors of the peoton at low four-momentum transfer (II) Borkowski, F.; Simon, G. G.; Walther, V. H. Nuclear Physics B, Vol. 93, Issue 3 https://doi.org/10.1016/0550-3213(75)90514-3	journal	July 1975
Polarization Transfer in the ${}^{4}{He} (\vec{e}, e^{'} \vec{p}) {}^{3}H$ Reaction at $Q^{2} = 0.8$ and $1.3 (GeV / c)^{2}$ Paolone, M.; Malace, S. P.; Strauch, S. Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.072001	journal	August 2010
Proton and neutron electromagnetic form factors and uncertainties Ye, Zhihong; Arrington, John; Hill, Richard J. Physics Letters B, Vol. 777 https://doi.org/10.1016/j.physletb.2017.11.023	journal	February 2018
Polarization transfer observables in elastic electron-proton scattering at $Q^{2} = 2.5$ , 5.2, 6.8, and $8.5 {GeV}^{2}$ Puckett, A. J. R.; Brash, E. J.; Jones, M. K. Physical Review C, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevC.96.055203	journal	November 2017
Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory Alarcón, J. M.; Higinbotham, D. W.; Weiss, C. Physical Review C, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevC.99.044303	journal	April 2019
Measurements of the electric and magnetic form factors of the proton from $Q^{2}$ =1.75 to 8.83 (GeV/ c $)^{2}$ Andivahis, L.; Bosted, P. E.; Lung, A. Physical Review D, Vol. 50, Issue 9 https://doi.org/10.1103/PhysRevD.50.5491	journal	November 1994
Review of experimental and theoretical status of the proton radius puzzle Hill, Richard J. EPJ Web of Conferences, Vol. 137 https://doi.org/10.1051/epjconf/201713701023	journal	January 2017
Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen Antognini, A.; Nez, F.; Schuhmann, K. Science, Vol. 339, Issue 6118 https://doi.org/10.1126/science.1230016	journal	January 2013
Steps towards the hyperfine splitting measurement of the muonic hydrogen ground state: pulsed muon beam and detection system characterization Adamczak, A.; Baccolo, G.; Bakalov, D. Journal of Instrumentation, Vol. 11, Issue 05 https://doi.org/10.1088/1748-0221/11/05/P05007	journal	May 2016
Two-photon exchange in elastic electron-nucleon scattering Blunden, P. G.; Melnitchouk, W.; Tjon, J. A. Physical Review C, Vol. 72, Issue 3 https://doi.org/10.1103/PhysRevC.72.034612	journal	September 2005
Electromagnetic form factors of the proton at low four-momentum transfer Borkowski, F.; Peuser, P.; Simon, G. G. Nuclear Physics A, Vol. 222, Issue 2 https://doi.org/10.1016/0375-9474(74)90392-3	journal	April 1974
The nuclear physics of hyperfine structure in hydrogenic atoms Friar, J. L.; Payne, G. L. Physics Letters B, Vol. 618, Issue 1-4 https://doi.org/10.1016/j.physletb.2005.05.015	journal	July 2005
Erratum: Polarization transfer observables in elastic electron-proton scattering at $Q^{2} = 2.5$ , 5.2, 6.8, and $8.5 {GeV}^{2}$ [Phys. Rev. C 96 , 055203 (2017)] Puckett, A. J. R.; Brash, E. J.; Jones, M. K. Physical Review C, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevC.98.019907	journal	July 2018
Radiative corrections to electron-proton scattering Maximon, L. C.; Tjon, J. A. Physical Review C, Vol. 62, Issue 5 https://doi.org/10.1103/PhysRevC.62.054320	journal	October 2000
Backward-Angle Electron-Proton Elastic Scattering and Proton Electromagnetic Form Factors Price, L. E.; Dunning, J. R.; Goitein, M. Physical Review D, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevD.4.45	journal	July 1971
Two-Photon Exchange Correction in Elastic Lepton–Proton Scattering Tomalak, Oleksandr Few-Body Systems, Vol. 59, Issue 5 https://doi.org/10.1007/s00601-018-1413-8	journal	May 2018
The RMS charge radius of the proton and Zemach moments Distler, Michael O.; Bernauer, Jan C.; Walcher, Thomas Physics Letters B, Vol. 696, Issue 4 https://doi.org/10.1016/j.physletb.2010.12.067	journal	February 2011
Quasielastic $(e, e^{'} p)$ reaction on ${}^{12}C, {}^{56}{Fe}$ , and ${}^{197}{Au}$ Dutta, D.; van Westrum, D.; Abbott, D. Physical Review C, Vol. 68, Issue 6 https://doi.org/10.1103/PhysRevC.68.064603	journal	December 2003
Two-photon exchange on the neutron and the hyperfine splitting Tomalak, Oleksandr Physical Review D, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevD.99.056018	journal	March 2019
Comparison of Elastic Electron-Proton Scattering Cross Sections with Some Theoretical Predictions Goitein, M.; Dunning, J. R.; Wilson, Richard Physical Review Letters, Vol. 18, Issue 23 https://doi.org/10.1103/PhysRevLett.18.1018	journal	June 1967
Muonic hydrogen and the third Zemach moment Friar, J. L.; Sick, Ingo Physical Review A, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevA.72.040502	journal	October 2005
Some Recent Measurements of Proton Form Factors Albrecht, W.; Behrend, H. -J.; Dorner, H. Physical Review Letters, Vol. 18, Issue 23 https://doi.org/10.1103/PhysRevLett.18.1014	journal	June 1967
Charge Form Factor of the Neutron from the Reaction $^{2} \vec{H} (\vec{e}, e^{'} n) p$ Passchier, I.; Alarcon, R.; Bauer, Th. S. Physical Review Letters, Vol. 82, Issue 25 https://doi.org/10.1103/PhysRevLett.82.4988	journal	June 1999
Proton Form Factors from Elastic Electron-Proton Scattering Janssens, T.; Hofstadter, R.; Hughes, E. B. Physical Review, Vol. 142, Issue 4 https://doi.org/10.1103/PhysRev.142.922	journal	February 1966
Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized $^{3} He$ target Golak, J.; Ziemer, G.; Kamada, H. Physical Review C, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevC.63.034006	journal	February 2001
Measurement of the Electric Form Factor of the Neutron at $Q^{2} = 0.5$ and $1.0 {G e V}^{2} / c^{2}$ Warren, G.; Wesselmann, F.; Zhu, H. Physical Review Letters, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevLett.92.042301	journal	January 2004
Precise measurements of the neutron magnetic form factor Anklin, H.; deBever, L. J.; Blomqvist, K. I. Physics Letters B, Vol. 428, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00442-0	journal	June 1998
QED is not endangered by the proton's size De Rújula, A. Physics Letters B, Vol. 693, Issue 5 https://doi.org/10.1016/j.physletb.2010.08.074	journal	October 2010
Polarization Transfer in the ${}^{4}{H e} (\vec{e}, e^{'} \vec{p}) {}^{3}H$ Reaction up to $Q^{2} = 2.6 (G e V / c)^{2}$ Strauch, S.; Dieterich, S.; Aniol, K. A. Physical Review Letters, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevLett.91.052301	journal	July 2003
Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen Dupays, Arnaud; Beswick, Alberto; Lepetit, Bruno Physical Review A, Vol. 68, Issue 5 https://doi.org/10.1103/PhysRevA.68.052503	journal	November 2003
Measurement of the Electric Form Factor of the Neutron through $\vec{d} (\vec{e}, e^{'} n) p$ at $Q^{2} = 0.5 (GeV / c)^{2}$ Zhu, H.; Ahmidouch, A.; Anklin, H. Physical Review Letters, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevLett.87.081801	journal	August 2001
Electric and magnetic form factors of the proton Bernauer, J. C.; Distler, M. O.; Friedrich, J. Physical Review C, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevC.90.015206	journal	July 2014
Zemach moments for hydrogen and deuterium Friar, J. L.; Sick, Ingo Physics Letters B, Vol. 579, Issue 3-4 https://doi.org/10.1016/j.physletb.2003.11.018	journal	January 2004
NuSTEC 1 1Neutrino Scattering Theory Experiment Collaboration http://nustec.fnal.gov. White Paper: Status and challenges of neutrino–nucleus scattering Alvarez-Ruso, L.; Sajjad Athar, M.; Barbaro, M. B. Progress in Particle and Nuclear Physics, Vol. 100 https://doi.org/10.1016/j.ppnp.2018.01.006	journal	May 2018
Model independent extraction of the proton magnetic radius from electron scattering Epstein, Zachary; Paz, Gil; Roy, Joydeep Physical Review D, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevD.90.074027	journal	October 2014
Elastic electric and magnetic e-d scattering at low momentum transfer Simon, G. G.; Schmitt, Ch.; Walther, V. H. Nuclear Physics A, Vol. 364, Issue 2-3 https://doi.org/10.1016/0375-9474(81)90572-8	journal	July 1981
Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory Alarcón, J. M.; Weiss, C. Physics Letters B, Vol. 784 https://doi.org/10.1016/j.physletb.2018.07.060	journal	September 2018
Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: Comparison with data Tomalak, O.; Vanderhaeghen, M. The European Physical Journal A, Vol. 51, Issue 2 https://doi.org/10.1140/epja/i2015-15024-1	journal	February 2015
Proton form factor from 0.15 to 0.79 ${fm}^{- 2}$ Murphy, J. J.; Shin, Y. M.; Skopik, D. M. Physical Review C, Vol. 9, Issue 6 https://doi.org/10.1103/PhysRevC.9.2125	journal	June 1974
Lamb shift in light muonic atoms — Revisited Borie, E. Annals of Physics, Vol. 327, Issue 3 https://doi.org/10.1016/j.aop.2011.11.017	journal	March 2012
The proton radius puzzle Carlson, Carl E. Progress in Particle and Nuclear Physics, Vol. 82 https://doi.org/10.1016/j.ppnp.2015.01.002	journal	May 2015
Elastic Electron-Proton Scattering at Large Four-Momentum Transfer Kirk, P. N.; Breidenbach, M.; Friedman, J. I. Physical Review D, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevD.8.63	journal	July 1973
Measurement of Elastic Electron-Neutron Cross Sections up to $Q^{2} = 10$ ${(G e V / c)}^{2}$ Rock, S.; Arnold, R. G.; Bosted, P. Physical Review Letters, Vol. 49, Issue 16 https://doi.org/10.1103/PhysRevLett.49.1139	journal	October 1982
Measurements of the deuteron and proton magnetic form factors at large momentum transfers Bosted, P. E.; Katramatou, A. T.; Arnold, R. G. Physical Review C, Vol. 42, Issue 1 https://doi.org/10.1103/PhysRevC.42.38	journal	July 1990
Two-photon exchange in a dispersion approach Borisyuk, Dmitry; Kobushkin, Alexander Physical Review C, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevC.78.025208	journal	August 2008
Measurement of the Proton’s Electric to Magnetic Form Factor Ratio from ${}^{1}{\vec{H}} (\vec{e}, e^{'} p)$ Crawford, C. B.; Sindile, A.; Akdogan, T. Physical Review Letters, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevLett.98.052301	journal	January 2007
Measurement of the Neutron Electric Form Factor $G_{en}$ at $0.67 (GeV / c) 2$ via $^{3} \vec{He} (\vec{e}, e^{'} n)$ Rohe, D.; Bartsch, P.; Baumann, D. Physical Review Letters, Vol. 83, Issue 21 https://doi.org/10.1103/PhysRevLett.83.4257	journal	November 1999
High-precision measurement of the proton elastic form factor ratio <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>μ</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:msub><mml:mi>G</mml:mi><mml:mi>E</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:math> at low <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>Q</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> Zhan, X.; Allada, K.; Armstrong, D. S. Physics Letters B, Vol. 705, Issue 1-2 https://doi.org/10.1016/j.physletb.2011.10.002	journal	November 2011
Proton radius from electron-proton scattering and chiral perturbation theory Horbatsch, Marko; Hessels, Eric A.; Pineda, Antonio Physical Review C, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevC.95.035203	journal	March 2017
Precision Measurement of the Hydrogen-Deuterium $1 S - 2 S$ Isotope Shift Parthey, Christian G.; Matveev, Arthur; Alnis, Janis Physical Review Letters, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevLett.104.233001	journal	June 2010
Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer Tomalak, O.; Vanderhaeghen, M. Physical Review D, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevD.93.013023	journal	January 2016
Elastic Electron-Proton Scattering Cross Sections Measured by a Coincidence Technique Goitein, M.; Budnitz, R. J.; Carroll, L. Physical Review D, Vol. 1, Issue 9 https://doi.org/10.1103/PhysRevD.1.2449	journal	May 1970
Erratum: Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron [Phys. Rev. Lett. 80, 452 (1998)] Milbrath, B. D.; McIntyre, J. I.; Armstrong, C. S. Physical Review Letters, Vol. 82, Issue 10 https://doi.org/10.1103/PhysRevLett.82.2221	journal	March 1999
Neutrino reactions at accelerator energies Llewellyn Smith, C. H. Physics Reports, Vol. 3, Issue 5 https://doi.org/10.1016/0370-1573(72)90010-5	journal	June 1972
Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding Herberg, C.; Ostrick, M.; Andresen, H. G. The European Physical Journal A, Vol. 5, Issue 2 https://doi.org/10.1007/s100500050268	journal	June 1999
Double-trap measurement of the proton magnetic moment at 0.3 parts per billion precision Schneider, Georg; Mooser, Andreas; Bohman, Matthew Science, Vol. 358, Issue 6366 https://doi.org/10.1126/science.aan0207	journal	November 2017
Third Zemach moment of the proton Cloët, Ian C.; Miller, Gerald A. Physical Review C, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevC.83.012201	journal	January 2011
Nonperturbative evaluation of some QED contributions to the muonic hydrogen $n = 2$ Lamb shift and hyperfine structure Indelicato, P. Physical Review A, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevA.87.022501	journal	February 2013
CODATA recommended values of the fundamental physical constants: 2014 Mohr, Peter J.; Newell, David B.; Taylor, Barry N. Reviews of Modern Physics, Vol. 88, Issue 3 https://doi.org/10.1103/RevModPhys.88.035009	journal	September 2016
Neutron charge form factor at large $q^{2}$ Schiavilla, R.; Sick, I. Physical Review C, Vol. 64, Issue 4 https://doi.org/10.1103/PhysRevC.64.041002	journal	September 2001
New Measurement of the Charge Radius of the Neutron Kopecky, S.; Riehs, P.; Harvey, J. A. Physical Review Letters, Vol. 74, Issue 13 https://doi.org/10.1103/PhysRevLett.74.2427	journal	March 1995
Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron Milbrath, B. D.; McIntyre, J. I.; Armstrong, C. S. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevLett.80.452	journal	January 1998
Simple parametrization of nucleon form factors Kelly, J. J. Physical Review C, Vol. 70, Issue 6 https://doi.org/10.1103/PhysRevC.70.068202	journal	December 2004
Low- $Q^{2}$ measurements of the proton form factor ratio $μ_{p} G_{E} / G_{M}$ Ron, G.; Zhan, X.; Glister, J. Physical Review C, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevC.84.055204	journal	November 2011
Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline Experiments Mosel, Ulrich Annual Review of Nuclear and Particle Science, Vol. 66, Issue 1 https://doi.org/10.1146/annurev-nucl-102115-044720	journal	October 2016
Model-independent extraction of the proton charge radius from electron scattering Hill, Richard J.; Paz, Gil Physical Review D, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevD.82.113005	journal	December 2010
Charge Form Factor of the Neutron at Low Momentum Transfer from the ${}^{2}{\vec{H}} (\vec{e}, e^{'} n) {}^{1}H$ Reaction Geis, E.; Kohl, M.; Ziskin, V. Physical Review Letters, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevLett.101.042501	journal	July 2008
Measurements of the elastic electromagnetic form factor ratio $μ_{p} G_{Ep} {/ G}_{Mp}$ via polarization transfer Gayou, O.; Wijesooriya, K.; Afanasev, A. Physical Review C, Vol. 64, Issue 3 https://doi.org/10.1103/PhysRevC.64.038202	journal	August 2001
A New Parameterization of the Nucleon Elastic Form Factors Bradford, R.; Bodek, A.; Budd, H. Nuclear Physics B - Proceedings Supplements, Vol. 159 https://doi.org/10.1016/j.nuclphysbps.2006.08.028	journal	September 2006
New Measurement of the $1 S - 3 S$ Transition Frequency of Hydrogen: Contribution to the Proton Charge Radius Puzzle Fleurbaey, Hélène; Galtier, Sandrine; Thomas, Simon Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/PhysRevLett.120.183001	journal	May 2018
Precise neutron magnetic form factors Kubon, G.; Anklin, H.; Bartsch, P. Physics Letters B, Vol. 524, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)01386-7	journal	January 2002
Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆ Glazier, D. I.; Seimetz, M.; Annand, J. R. M. The European Physical Journal A, Vol. 24, Issue 1 https://doi.org/10.1140/epja/i2004-10115-8	journal	January 2005
Zemach and magnetic radius of the proton from the hyperfine splitting in hydrogen Volotka, A. V.; Shabaev, V. M.; Plunien, G. The European Physical Journal D, Vol. 33, Issue 1 https://doi.org/10.1140/epjd/e2005-00025-9	journal	February 2005
Extraction of the proton radius from electron-proton scattering data Lee, Gabriel; Arrington, John R.; Hill, Richard J. Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.013013	journal	July 2015
Exclusive processes in perturbative quantum chromodynamics Lepage, G. Peter; Brodsky, Stanley J. Physical Review D, Vol. 22, Issue 9 https://doi.org/10.1103/PhysRevD.22.2157	journal	November 1980
Muonic Hydrogen and the Proton Radius Puzzle Pohl, Randolf; Gilman, Ronald; Miller, Gerald A. Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170627	journal	October 2013
Elastic Electron-Proton Scattering at Momentum Transfers up to 245 $F^{- 2}$ Albrecht, W.; Behrend, H. J.; Brasse, F. W. Physical Review Letters, Vol. 17, Issue 23 https://doi.org/10.1103/PhysRevLett.17.1192	journal	December 1966
Electric form factor of the neutron from the ${}^{2}H$ ( e →, $e^{’}$ n → $)^{1}$ H reaction at $Q^{2}$ =0.255 (GeV/ c $)^{2}$ Eden, T.; Madey, R.; Zhang@f, W. -M. Physical Review C, Vol. 50, Issue 4 https://doi.org/10.1103/PhysRevC.50.R1749	journal	October 1994
Measurements of the electric and magnetic form factors of the neutron from $Q^{2}$ =1.75 to 4.00 (GeV/ c $)^{2}$ Lung, A.; Stuart, L. M.; Bosted, P. E. Physical Review Letters, Vol. 70, Issue 6 https://doi.org/10.1103/PhysRevLett.70.718	journal	February 1993
Neutrino–nucleus cross sections for oscillation experiments Katori, Teppei; Martini, Marco Journal of Physics G: Nuclear and Particle Physics, Vol. 45, Issue 1 https://doi.org/10.1088/1361-6471/aa8bf7	journal	December 2017
How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data Barcus, Scott K.; Higinbotham, Douglas W.; McClellan, Randall E. Physical Review C, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevC.102.015205	journal	July 2020
Chiral structure of the Lamb shift and the definition of the proton radius Pineda, Antonio Physical Review C, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevC.71.065205	journal	June 2005
The size of the proton Pohl, Randolf; Antognini, Aldo; Nez, François Nature, Vol. 466, Issue 7303 https://doi.org/10.1038/nature09250	journal	July 2010
Electron scattering at 4° with energies of 4.5-20 GeV Stein, S.; Atwood, W. B.; Bloom, E. D. Physical Review D, Vol. 12, Issue 7 https://doi.org/10.1103/PhysRevD.12.1884	journal	October 1975
Nuclear corrections to hyperfine structure in light hydrogenic atoms Friar, J. L.; Payne, G. L. Physical Review C, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevC.72.014002	journal	July 2005
Measurement of elastic electron-neutron scattering and inelastic electron-deuteron scattering cross sections at high momentum transfer Rock, S.; Arnold, R. G.; Bosted, P. E. Physical Review D, Vol. 46, Issue 1 https://doi.org/10.1103/PhysRevD.46.24	journal	July 1992
Precise determination of low- $Q$ nucleon electromagnetic form factors and their impact on parity-violating $e$ - $p$ elastic scattering Arrington, John; Sick, Ingo Physical Review C, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevC.76.035201	journal	September 2007
A small proton charge radius from an electron–proton scattering experiment Xiong, W.; Gasparian, A.; Gao, H. Nature, Vol. 575, Issue 7781 https://doi.org/10.1038/s41586-019-1721-2	journal	November 2019
Global analysis of proton elastic form factor data with two-photon exchange corrections Arrington, J.; Melnitchouk, W.; Tjon, J. A. Physical Review C, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevC.76.035205	journal	September 2007
Deuterium target data for precision neutrino-nucleus cross sections Meyer, Aaron S.; Betancourt, Minerba; Gran, Richard Physical Review D, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevD.93.113015	journal	June 2016
New Precision Measurement for Proton Zemach Radius with Laser Spectroscopy Ma, Y.; Ishida, K.; Iwasaki, M. International Journal of Modern Physics: Conference Series, Vol. 40 https://doi.org/10.1142/S2010194516600466	journal	January 2016
The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory Peset, Clara; Pineda, Antonio Nuclear Physics B, Vol. 887 https://doi.org/10.1016/j.nuclphysb.2014.07.027	journal	October 2014
Effective field theory for large logarithms in radiative corrections to electron proton scattering Hill, Richard J. Physical Review D, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevD.95.013001	journal	January 2017
Measurements of the Electric Form Factor of the Neutron up to $Q^{2} = 3.4 {GeV}^{2}$ Using the Reaction $^{3} \vec{He} (\vec{e}, e^{'} n) p p$ Riordan, S.; Abrahamyan, S.; Craver, B. Physical Review Letters, Vol. 105, Issue 26 https://doi.org/10.1103/PhysRevLett.105.262302	journal	December 2010
Neutron charge radius determined from the energy dependence of the neutron transmission of liquid $^{208} Pb$ and $^{209} Bi$ Kopecky, S.; Harvey, J. A.; Hill, N. W. Physical Review C, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRevC.56.2229	journal	October 1997
Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c)2 Bartel, W.; Büsser, F. -W.; Dix, W. -R. Nuclear Physics B, Vol. 58, Issue 2 https://doi.org/10.1016/0550-3213(73)90594-4	journal	July 1973
Laser Spectroscopy of Muonic Hydrogen and the Puzzling Proton Pohl, Randolf Journal of the Physical Society of Japan, Vol. 85, Issue 9 https://doi.org/10.7566/JPSJ.85.091003	journal	September 2016
Higher-order nuclear-polarizability corrections in atomic hydrogen Friar, J. L.; Payne, G. L. Physical Review C, Vol. 56, Issue 2 https://doi.org/10.1103/PhysRevC.56.619	journal	August 1997
Final analysis of proton form factor ratio data at $Q^{2} = 4.0$ , 4.8, and 5.6 GeV $^{2}$ Puckett, A. J. R.; Brash, E. J.; Gayou, O. Physical Review C, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevC.85.045203	journal	April 2012
Two-photon exchange correction to the hyperfine splitting in muonic hydrogen Tomalak, Oleksandr The European Physical Journal C, Vol. 77, Issue 12 https://doi.org/10.1140/epjc/s10052-017-5435-z	journal	December 2017
Measurement of GEp/GMp via polarization transfer at Q2 = 0.4 GeV /c2 Pospischil, Th.; Bartsch, P.; Baumann, D. The European Physical Journal A, Vol. 12, Issue 1 https://doi.org/10.1007/s100500170046	journal	September 2001
Quasielastic axial-vector mass from experiments on neutrino–nucleus scattering Kuzmin, K. S.; Lyubushkin, V. V.; Naumov, V. A. The European Physical Journal C, Vol. 54, Issue 4 https://doi.org/10.1140/epjc/s10052-008-0582-x	journal	April 2008