Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Radiative corrections to the parity-violating spin asymmetry

D. H. Jakubassa-Amundsen1,* and X. Roca-Maza2,3,4,5,†

  • *Contact author: dj@math.lmu.de
  • †Contact author: xavier.roca.maza@fqa.ub.es

Phys. Rev. C 113, 045502 – Published 29 April, 2026

DOI: https://doi.org/10.1103/2t5l-vqj8

Abstract

The parity-violating spin asymmetry Apv for elastic electron scattering from spin-zero nuclei, together with its QED corrections, is evaluated nonperturbatively within the phase-shift analysis. Dispersion corrections, taking into account low-lying transient nuclear excitations, are estimated with the help of the lowest-order γZ box diagrams. Collision energies in the range 5–500 MeV are considered, and results are provided for the C12 and Pb208 target nuclei. In addition, we have evaluated Apv at GeV energies and small scattering angles—relevant for the Pb Radius Experiment (PREx)—revealing that the low-lying nuclear excited states give no measurable dispersive contribution. However, they are important at lower energies and backward angles.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. D. Adhikari et al. (PREX Collaboration), Accurate determination of the neutron skin thickness of Pb208 through parity-violation in electron scattering, Phys. Rev. Lett. 126, 172502 (2021).
  2. D. Adhikari et al. (CREX Collaboration), Precision determination of the neutral weak form factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022).
  3. D. Androić et al. (Qweak Collaboration), Determination of the Al27 neutron distribution radius from a parity-violating electron scattering measurement, Phys. Rev. Lett. 128, 132501 (2022).
  4. S. Abrahamyan et al. (PREX Collaboration), Measurement of the neutron radius of Pb208 through parity violation in electron scattering, Phys. Rev. Lett. 108, 112502 (2012).
  5. C. J. Horowitz, Parity violating elastic electron scattering and Coulomb distortions, Phys. Rev. C 57, 3430 (1998).
  6. C. J. Horowitz, S. J. Pollock, P. A. Souder, and R. Michaels, Parity violating measurements of neutron densities, Phys. Rev. C 63, 025501 (2001).
  7. P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, Information content of the parity-violating asymmetry in Pb208, Phys. Rev. Lett. 127, 232501 (2021).
  8. T. W. Donnelly, J. Dubach, and I. Sick, Isospin dependences in parity-violating electron scattering, Nucl. Phys. A 503, 589 (1989).
  9. C. J. Horowitz et al., Weak charge form factor and radius of Pb208 through parity violation in electron scattering, Phys. Rev. C 85, 032501(R) (2012).
  10. M. Cadeddu, N. Cargioli, J. Erler, M. Gorchtein, J. Piekarewicz, X. Roca-Maza, and H. Spiesberger, Simultaneous extraction of the weak radius and the weak mixing angle from parity-violating electron scattering on C12, Phys. Rev. C 110, 035501 (2024).
  11. M. Gorchtein and C. J. Horowitz, Dispersion γZ-box correction to the weak charge of the proton, Phys. Rev. Lett. 102, 091806 (2009).
  12. M. Gorchtein, C. J. Horowitz, and M. J. Ramsey-Musolf, Model dependence of the γZ dispersion correction to the parity-violating asymmetry in elastic ep scattering, Phys. Rev. C 84, 015502 (2011).
  13. O. Koshchii, J. Erler, M. Gorchtein, C. J. Horowitz, J. Piekarewicz, X. Roca-Maza, C.-Y. Seng, and H. Spiesberger, Weak charge and weak radius of C12, Phys. Rev. C 102, 022501(R) (2020).
  14. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  15. J. L. Friar and M. Rosen, Dispersion corrections to elastic electron scattering by C12 and O16 II. On the use of the closure approximation, Ann. Phys. 87, 289 (1974).
  16. D. H. Jakubassa-Amundsen, Combined Coulombic and magnetic contributions to dispersion in e+C12 collisions, Phys. Rev. C 105, 054303 (2022).
  17. A. V. Afanasev and N. P. Merenkov, Collinear photon exchange in the beam normal polarization asymmetry of elastic electron–proton scattering, Phys. Lett. B 599, 48 (2004).
  18. M. Gorchtein and C. J. Horowitz, Analyzing power in elastic scattering of electrons off a spin-0 target, Phys. Rev. C 77, 044606 (2008).
  19. O. Koshchii, M. Gorchtein, X. Roca-Maza, and H. Spiesberger, Beam-normal single-spin asymmetry in elastic scattering of electrons from a spin-0 nucleus, Phys. Rev. C 103, 064316 (2021).
  20. N. L. Hall, P. G. Blunden, W. Melnitchouk, A. W. Thomas, and R. D. Young, Hadronic γZ box corrections in Møller scattering, Phys. Lett. B 731, 287 (2014).
  21. K. Aulenbacher, Opportunities for parity violating electron scattering experiments at the planned MESA facility, Hyperfine Interact. 200, 3 (2011).
  22. E. A. Uehling, Polarization effects in the positron theory, Phys. Rev. 48, 55 (1935).
  23. D. H. Jakubassa-Amundsen, Nonperturbative theory for the QED corrections to elastic electron-nucleus scattering, J. Phys. G 51, 035105 (2024).
  24. X. Roca-Maza and D. H. Jakubassa-Amundsen, The parity-violating asymmetry including QED corrections in high-energy electron-nucleus collisions (unpublished).
  25. Energy Density Functional Methods for Atomic Nuclei, edited by N. Schunck (IOP, Bristol, 2019).
  26. G. Colò, L.-G. Cao, N. Van Giai, and L. Capelli, Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program, Comput. Phys. Commun. 184, 142 (2013).
  27. G. Colò and X. Roca-Maza, User guide for the hfbcs-qrpa(v1) code, arXiv:2102.06562.
  28. X. Roca-Maza, M. Centelles, X. Viñas, and M. Warda, Neutron skin of Pb208, nuclear symmetry energy, and the parity radius experiment, Phys. Rev. Lett. 106, 252501 (2011).
  29. T. W. Donnelly and I. Sick, Elastic magnetic electron scattering from nuclei, Rev. Mod. Phys. 56, 461 (1984).
  30. L. W. Fullerton, G. A. Rinker, Jr., Accurate and efficient methods for the evaluation of vacuum-polarization potentials of order Zα and Zα2, Phys. Rev. A 13, 1283 (1976).
  31. Y. S. Tsai, High-energy electron-electron scattering, Phys. Rev. 120, 269 (1960).
  32. M. Vanderhaeghen, J. M. Friedrich, D. Lhuillier, D. Marchand, L. Van Hoorebeke, and J. Van de Wiele, QED radiative corrections to virtual Compton scattering, Phys. Rev. C 62, 025501 (2000).
  33. B. T. Reed and C. J. Horowitz, Comment on QED corrections to the parity violating asymmetry in high-energy electron-nucleus scattering, arXiv:2601.01615.
  34. F. Salvat, J. M. Fernández-Varea, and W. Williamson, Jr., Accurate numerical solution of the radial Schrödinger and Dirac wave equations, Comput. Phys. Commun. 90, 151 (1995).
  35. H. De Vries, C. W. De Jager, and C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering, At. Data Nucl. Data Tables 36, 495 (1987).
  36. J. Bartel, P. Quentin, M. Brack, C. Guet, and H.-B. Hakansson, Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force, Nucl. Phys. A 386, 79 (1982).
  37. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Course of Theoretical Physics Vol. 4, 2nd ed. (Elsevier, Oxford, 1982).
  38. J. Dobaczewski, H. Flocard, and J. Treiner, Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line, Nucl. Phys. A 422, 103 (1984).
  39. M. Gorshteyn (private Communication).
  40. M. Thomson, Modern Particle Physics (Cambridge University Press, Cambridge, 2013).
  41. M. A. Corona, M. Cadeddu, N. Cargidi, P. Finelli, and M. Vorabbi, Incorporating the weak mixing angle dependence to reconcile the neutron skin measurement on Pb208 by PREX-II, Phys. Rev. C 105, 055503 (2022).
  42. C. J. Horowitz and J. Piekarewicz, Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei, Phys. Rev. C 86, 045503 (2012).
  43. A. Goldberg, Magnetic dispersion corrections to elastic electron scattering, Nuovo Cimento 20, 1191 (1961).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation