Skip to main content
SpringerLink
Log in

Charge radii of the nucleon from its flavor dependent Dirac form factors

  • Letter
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

We have determined the proton and the neutron charge radii from a global analysis of the proton and the neutron elastic form factors, after first performing a flavor decomposition of these form factors under charge symmetry in the light cone frame formulation. We then extracted the transverse mean-square radii of the flavor dependent quark distributions. In turn, these are related in a model-independent way to the proton and neutron charge radii but allow us to take into account motion effects of the recoiling nucleon for data at finite but high momentum transfer. In the proton case we find \(\langle r_p \rangle = 0.852 \pm 0.002_{\mathrm{(stat.)}} \pm 0.009_{\mathrm{(syst.)}}~({\mathrm{fm}})\), consistent with the proton charge radius obtained from muonic hydrogen spectroscopy [1, 2]. The current method improves on the precision of the \(\langle r_p \rangle \) extraction based on the form factor measurements. Furthermore, we find no discrepancy in the \(\langle r_p \rangle \) determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a value that is consistent with the smallest \(\langle r_p \rangle \) extraction from the electron scattering measurements [3]. Concerning the neutron case, past results relied solely on the neutron-electron scattering length measurements, which suffer from an underestimation of underlying systematic uncertainties inherent to the extraction technique. Utilizing the present method we have performed the first extraction of the neutron charge radius based on nucleon form factor data, and we find \(\langle r_n^2 \rangle = -0.122 \pm 0.004_\mathrm{(stat.)} \pm 0.010_\mathrm{(syst.)}~(\mathrm{fm}^2)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The proton and neutron elastic form factor data used in this work are publicly available in their original publications cited in this paper. The flavor dependent Dirac form factors derived in this work can be found at: https://github.com/fizikci0147/flav_dec_ff_data. All data, codes, and parametrizations used in this work are available from the authors upon request.]

References

  1. R. Pohl et al., The size of the proton. Nature 466, 213–216 (2010)

    Article  ADS  Google Scholar 

  2. A. Antognini et al., Proton structure from the measurement of 2S–2P transition frequencies of muonic hydrogen. Science 339, 417–420 (2013)

    Article  ADS  Google Scholar 

  3. W. Xiong et al., A small proton charge radius from an electron-proton scattering experiment. Nature 575(7781), 147–150 (2019)

    Article  ADS  Google Scholar 

  4. R. Pohl et al., Muonic hydrogen and the proton radius puzzle. Ann. Rev. Nucl. Part. Sci. 63, 175–204 (2013)

    Article  ADS  Google Scholar 

  5. J. Bernauer, R. Pohl, The proton radius problem. Sci. Am. 310, 32–39 (2014)

    Article  Google Scholar 

  6. H. Fleurbaey et al., New measurement of the 1S–3S transition frequency of hydrogen: contribution to the proton charge radius puzzle. Phys. Rev. Lett. 120, 182001 (2018)

    Article  Google Scholar 

  7. N. Bezginov et al., A measurement of the atomic hydrogen Lamb shift and the proton charge radius. Science 365, 1007 (2019)

    Article  ADS  Google Scholar 

  8. J.C. Bernauer et al., High-precision determination of the electric and magnetic form factors of the proton. Phys. Rev. Lett. 105, 242001 (2010)

    Article  ADS  Google Scholar 

  9. V.E. Krohn, G.R. Ringo, Reconsiderations of the electron–neutron scattering length as measured by the scattering of thermal neutrons by noble gases. Phys. Rev. D 8, 1305–1307 (1973)

    Article  ADS  Google Scholar 

  10. YuA Aleksandrov et al., Neutron rms radius and electric polarizability from data on the interaction of slow neutrons with bismuth. Sov. J. Nucl. Phys. 44, 900–902 (1986)

    Google Scholar 

  11. L. Koester et al., Neutrino electron scattering length and electric polarizability of the neutron derived from cross-sections of bismuth and of lead and its isotopes. Phys. Rev. C 51, 3363–3371 (1995)

    Article  ADS  Google Scholar 

  12. S. Kopecky et al., Neutron charge radius determined from the energy dependence of the neutron transmission of liquid Pb-208 and Bi-209. Phys. Rev. C 56, 2229–2237 (1997)

    Article  ADS  Google Scholar 

  13. J.C. Bernauer et al., Electric and magnetic form factors of the proton. Phys. Rev. C 90(1), 015206 (2014)

    Article  ADS  Google Scholar 

  14. V. Punjabi et al., Proton elastic form-factor ratios to \(Q^2\) = 3.5 \(GeV^2\) by polarization transfer. Phys. Rev. C71, 055202 (2005)

    ADS  Google Scholar 

  15. O. Gayou et al., Measurements of the elastic electromagnetic form factor ratio \({\mu }_{p}{G}_{\rm Ep{}{/G}_{\rm Mp}}\) via polarization transfer. Phys. Rev. C 64, 038202 (2001)

    Article  ADS  Google Scholar 

  16. S. Strauch, et al., Polarization Transfer in the \(^{4}{{\rm H}}{{\rm e}} (\stackrel{\rightarrow }{e},{e}^{{\prime }}\stackrel{\rightarrow }{p})^{3}{{\rm H}}\) Reaction up to \({Q}^{2}=2.6 ({{\rm G}} {{\rm e}} {{\rm V}} /c)^{2}\), Phys. Rev. Lett. 91 (2003) 052301

  17. B. D. Milbrath, et al., Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron [Phys. Rev. Lett. 80, 452 (1998)], Phys. Rev. Lett. 82 (1999) 2221–2221

  18. T. Pospischil et al., Measurement of \(G_{Ep}/G_{Mp}\) via polarization transfer at \(Q^2\) = 0.4 \((GeV/c)^2\). Eur. Phys. J A12, 125–127 (2001)

    Article  ADS  Google Scholar 

  19. C.B. Crawford et al., Measurement of the Proton’s Electric to Magnetic Form Factor Ratio from \(^{1}\vec{H}(\vec{e}, e^{\prime }p)\). Phys. Rev. Lett. 98, 052301 (2007)

    Article  ADS  Google Scholar 

  20. G. Ron et al., Measurements of the proton elastic-form-factor ratio \({\mu }_{p}{G}_{E}^{p}/{G}_{M}^{p}\) at low momentum transfer. Phys. Rev. Lett. 99, 202002 (2007)

    Article  ADS  Google Scholar 

  21. X. Zhan et al., High-precision measurement of the proton elastic form factor ratio \(\mu _pG_E/G_M\) at low \(Q^2\). Phys. Lett. B 705, 59–64 (2011)

    Article  ADS  Google Scholar 

  22. M. Paolone et al., Polarization transfer in the \(4He(e,e^{\prime }p)3H\) reaction at \(Q^2\) = 0.8 and 1.3 \((GeV/c)^2\). Phys. Rev. Lett. 105, 072001 (2010)

    Article  ADS  Google Scholar 

  23. E. Geis et al., The charge form factor of the neutron at low momentum transfer from the \(\vec{^2H} (\vec{e}, e^{\prime } n) p\) reaction. Phys. Rev. Lett. 101, 042501 (2008)

    Article  ADS  Google Scholar 

  24. C. Herberg et al., Determination of the neutron electric form-factor in the D(e, e’ n)p reaction and the influence of nuclear binding. Eur. Phys. J. A 5, 131–135 (1999)

    Article  ADS  Google Scholar 

  25. I. Passchier et al., The charge form-factor of the neutron from the reaction polarized \(^2H (\vec{e}, e, e^{\prime } n)p\). Nucl. Phys. A 663, 421–424 (2000)

    Article  ADS  Google Scholar 

  26. T. Eden et al., Electric form factor of the neutron from the \(^{2}\vec{H}\)(\(\vec{e}\),\(e^{\prime }\)n)\(^{1}H\) reaction at \(Q^{2}\)=0.255 \((GeV/c)^{2}\). Phys. Rev. C 50, R1749–R1753 (1994)

    Article  ADS  Google Scholar 

  27. D .I. Glazier et al., Measurement of the electric form-factor of the neutron at \(Q^2\) = 0.3 \((GeV/c)^2\) to 0.8 \((GeV/c)^2\), Eur. Phys. J. A24, 101–109 (2005)

    Article  ADS  Google Scholar 

  28. M. Ostrick et al., Measurement of the neutron electric form factor \({G}_{E, n}\) in the Quasifree \(^{2}H(\stackrel{\rightarrow }{\mathit{e}},{\mathit{e}}^{{\prime }}\stackrel{\rightarrow }{\mathit{n}})\mathit{p}\) reaction. Phys. Rev. Lett. 83, 276–279 (1999)

    Article  ADS  Google Scholar 

  29. J. Golak et al., Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized \({}^{3}{{\rm He}}\) target. Phys. Rev. C 63, 034006 (2001)

    Article  ADS  Google Scholar 

  30. R. Madey et al., Measurements of \(G_{E}^n / G_{M}^n\) from the \(^2H(\vec{e},e^{\prime } \vec{n})^1H\) reaction to \(Q^2\) = 1.45 \((GeV/c)^2\). Phys. Rev. Lett. 91, 122002 (2003)

    Article  ADS  Google Scholar 

  31. H. Zhu et al., A Measurement of the electric form-factor of the neutron through \(\vec{d} (\vec{e}, e^{\prime } n)p\) at \(Q^2\) = 0.5 \((GeV/c)^2\), Phys. Rev. Lett. 87, 081801 (2001)

    Article  ADS  Google Scholar 

  32. G. Warren et al., Measurement of the electric form-factor of the neutron at \(Q^2\) = 0.5 and 1.0 \(GeV^2/c^2\). Phys. Rev. Lett 92, 042301 (2004)

    Article  ADS  Google Scholar 

  33. D. Rohe et al., Measurement of the neutron electric form-factor \(G_{(en)}\) at \(0.67 (GeV/c)^2\) via \({}^{{\bf 3}}\vec{He}(\vec{e},e^{\prime } n)\). Phys. Rev. Lett. 83, 4257–4260 (1999)

    Article  ADS  Google Scholar 

  34. J. Bermuth et al., The Neutron charge form-factor and target analyzing powers from \({}^{\vec{3}}\vec{He} (\vec{e}, e^{\prime } n)\) scattering. Phys. Lett. B 564, 199–204 (2003)

    Article  ADS  Google Scholar 

  35. V. Sulkosky et al., Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries. Phys. Rev. C 96, 065206 (2017)

    Article  ADS  Google Scholar 

  36. C. Alexandrou et al., Proton and neutron electromagnetic form factors from lattice QCD. Phys. Rev. D 100(1), 014509 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  37. M. Vanderhaeghen, T. Walcher, Long range structure of the nucleon. Nucl. Phys. News 21, 14–22 (2011)

    Article  Google Scholar 

  38. G.D. Cates et al., Flavor decomposition of the elastic nucleon electromagnetic form factors. Phys. Rev. Lett. 106, 252003 (2011)

    Article  ADS  Google Scholar 

  39. Z. Ye et al., Proton and Neutron Electromagnetic Form Factors and Uncertainties. Phys. Lett. B 777, 8–15 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  40. J.J. Kelly, Simple parametrization of nucleon form factors. Phys. Rev. C 70, 068202 (2004)

    Article  ADS  Google Scholar 

  41. S. Galster et al., Elastic electron–deuteron scattering and the electric neutron form factor at four-momentum transfers 5fm\(^{-2} < q^2 < 14\)fm\(^{-2}\). Nucl. Phys. B 32, 221–237 (1971)

    Article  ADS  Google Scholar 

  42. G.A. Miller, Charge density of the neutron and proton. Phys. Rev. Lett. 99, 112001 (2007)

    Article  ADS  Google Scholar 

  43. G.A. Miller, Defining the proton radius: a unified treatment. Phys. Rev. C 99, 035202 (2019)

    Article  ADS  Google Scholar 

  44. R. Dupré, M. Guidal, S. Niccolai, M. Vanderhaeghen, Analysis of deeply virtual compton scattering data at jefferson lab and proton tomography. Eur. Phys. J A 53, 171 (2017)

    Article  ADS  Google Scholar 

  45. C. Lorcé, Charge distributions of moving nucleons. Phys. Rev. Lett. 125, 232002 (2020)

    Article  ADS  Google Scholar 

  46. X. Yan et al., Robust extraction of the proton charge radius from electron–proton scattering data. Phys. Rev. C 98, 025204 (2018)

    Article  ADS  Google Scholar 

  47. P. Mergell, U.-G. Meißner, D. Drechsel, Dispersion theoretical analysis of the nucleon electromagnetic form-factors. Nucl. Phys. A 596, 367–396 (1996)

    Article  ADS  Google Scholar 

  48. M.A. Belushkin, H.W. Hammer, U.-G. Meißner, Dispersion analysis of the nucleon form-factors including meson continua. Phys. Rev. C 75, 035202 (2007)

    Article  ADS  Google Scholar 

  49. I.T. Lorenz, H.W. Hammer, U.-G. Meißner, The size of the proton—closing in on the radius puzzle. Eur. Phys. J. A 48, 151 (2012)

    Article  ADS  Google Scholar 

  50. I.T. Lorenz, U.-G. Meißner, H.W. Hammer, Y.B. Dong, Theoretical constraints and systematic effects in the determination of the proton form factors. Phys. Rev. D 91, 014023 (2015)

    Article  ADS  Google Scholar 

  51. D.W. Higinbotham et al., The proton radius from electron scattering data. Phys. Rev. C 93, 055207 (2016)

    Article  ADS  Google Scholar 

  52. K. Griffioen et al., Consistency of electron scattering data with a small proton radius. Phys. Rev. C 93, 065207 (2016)

    Article  ADS  Google Scholar 

  53. M. Mihovilovič et al., Reinterpretation of Classic Proton Charge Form Factor Measurements. Front. Phys. 8 (2020). https://doi.org/10.3389/fphy.2020.00036

  54. J. Alarcon et al., Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory. Phys. Rev. C 99, 044303 (2019)

    Article  ADS  Google Scholar 

  55. M. Horbatsch, Properties of the Sachs electric form factor of the proton on the basis of recent e p scattering experiments and hydrogen. Phys. Lett. B 804, 135373 (2020)

    Article  Google Scholar 

  56. J. C. Bernauer, Ph.D. thesis Johannes Gutenberg-Universität Mainz (2010)

  57. A.A. Filin et al., Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius. Phys. Rev. Lett. 124, 082501 (2020)

    Article  ADS  Google Scholar 

  58. A. Filin, et al., High-accuracy calculation of the deuteron charge and quadrupole form factors in chiral effective field theory. arXiv:2009.08911 (2020)

  59. M. Tanabashi et al., Particle data group. Phys. Rev. D 98, 030001 (2018)

    Article  ADS  Google Scholar 

  60. J.-P. Karr, D. Marchand, E. Voutier, The proton size. Nat. Rev. Phys. 2, 601–614 (2020)

    Article  Google Scholar 

  61. R. Gilman, et al., Studying the Proton “Radius” Puzzle with \(\mu \)p Elastic Scattering (2017). arXiv:1709.09753

  62. N. Sparveris, et al., Measurement of the neutron charge radius, Jefferson Lab LOI 12-20-002 (2020)

Download references

Acknowledgements

We would like to thank M. Vanderhaeghen as this work received great benefit from his input and suggestions. This work has been supported by the US Department of Energy Office of Science, office of Nuclear Physics under contract no. DE-SC0016577, DE-FG02-94ER4084 and DEAC02-06CH11357. M.C. acknowledges financial support by the U.S. Department of Energy, Office of Nuclear Physics, Early Career Award under Grant No. DE-SC0020405.

Author information

Authors and Affiliations

  1. Temple University, Philadelphia, PA, 19122, USA

    H. Atac, M. Constantinou, Z.-E. Meziani, M. Paolone & N. Sparveris

  2. Argonne National Laboratory, Lemont, IL, 60439, USA

    Z.-E. Meziani

  3. New Mexico State University, Las Cruces, NM, 88003, USA

    M. Paolone

Authors
  1. H. Atac
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Constantinou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z.-E. Meziani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Paolone
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. N. Sparveris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Sparveris.

Additional information

Communicated by Carlos Munoz Camacho

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Atac, H., Constantinou, M., Meziani, ZE. et al. Charge radii of the nucleon from its flavor dependent Dirac form factors. Eur. Phys. J. A 57, 65 (2021). https://doi.org/10.1140/epja/s10050-021-00389-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-021-00389-9

Search

Navigation