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  • Letter
  • Open Access

Weak-charge form-factor determination at the electron-ion collider

Hooman Davoudiasl1, Hongkai Liu1, Sonny Mantry2, and Ethan T. Neil3

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Phys. Rev. D 113, L051301 – Published 26 March, 2026

DOI: https://doi.org/10.1103/lnqv-bltq

Abstract

Determining the weak charge form factor, FW(Q2), of nuclei over a continuous range of momentum transfers, 0≲Q2≲0.1  GeV2, is essential for mapping out the distribution of neutrons in nuclei. The neutron density distribution has significant implications for a broad range of areas, including studies of nuclear structure, neutron stars, and physics beyond the Standard Model. Currently, our knowledge of FW(Q2) comes primarily from fixed target experiments that measure the parity-violating asymmetry in coherent elastic electron-ion scattering. Fixed target experiments, such as CREX and PREX-1,2, have provided high-precision weak charge form factor extractions for the Ca48 and Pb208 nuclei, respectively. However, a major limitation of fixed target experiments is that they each provide data only at a single value of Q2. With the proposed electron-ion collider (EIC) on the horizon, we explore its potential to impact the determination of the weak charge form factor. While it cannot compete with the precision of fixed target experiments, it can provide data over a wide and continuous range of Q2 values, and for a wide variety of nuclei. We show that with data corresponding to an integrated luminosity of L∼500/A  fb−1, where A is the nucleus atomic weight, the EIC can significantly impact constraints by lifting degeneracies in theoretical models of the neutron density distribution. Ensuring EIC detector coverage at low Q2 and large negative pseudorapidities will be essential for such FW(Q2) measurements.

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References (97)

  1. W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81, 1 (1966).
  2. C. J. Horowitz, J. Piekarewicz, and B. Reed, Phys. Rev. C 102, 044321 (2020).
  3. B.-A. Li, B.-J. Cai, L.-W. Chen, and J. Xu, Prog. Part. Nucl. Phys. 99, 29 (2018).
  4. C. J. Horowitz, E. F. Brown, Y. Kim, W. G. Lynch, R. Michaels, A. Ono, J. Piekarewicz, M. B. Tsang, and H. H. Wolter, J. Phys. G 41, 093001 (2014).
  5. M. Baldo and G. F. Burgio, Prog. Part. Nucl. Phys. 91, 203 (2016).
  6. G. Hagen et al., Nat. Phys. 12, 186 (2015).
  7. F. J. Fattoyev, J. Piekarewicz, and C. J. Horowitz, Phys. Rev. Lett. 120, 172702 (2018).
  8. C. J. Horowitz, Ann. Phys. (Amsterdam) 411, 167992 (2019).
  9. J. Piekarewicz and F. J. Fattoyev, Phys. Today 72 (7), 30 (2019).
  10. J.-B. Wei, J.-J. Lu, G. F. Burgio, Z. H. Li, and H. J. Schulze, Eur. Phys. J. A 56, 63 (2020).
  11. B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Phys. Rev. Lett. 126, 172503 (2021).
  12. B.-A. Li, B.-J. Cai, W.-J. Xie, and N.-B. Zhang, Universe 7, 182 (2021).
  13. G. F. Burgio, H. J. Schulze, I. Vidana, and J. B. Wei, Prog. Part. Nucl. Phys. 120, 103879 (2021).
  14. B. P. Abbott et al. (LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRAWITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF (Deeper Wider Faster Program), AST3, CAASTRO, VINROUGE, MASTER, J-GEM, GROWTH, JAGWAR, CaltechNRAO, TTU-NRAO, NuSTAR, Pan-STARRS, MAXI Team, TZAC Consortium, KU, Nordic Optical Telescope, ePESSTO, GROND, Texas Tech University, SALT Group, TOROS, BOOTES, MWA, CALET, IKI-GW Follow-up, H.E.S.S., LOFAR, LWA, HAWC, Pierre Auger, ALMA, Euro VLBI Team, Pi of Sky, Chandra Team at McGill University, DFN, ATLAS Telescopes, High Time Resolution Universe Survey, RIMAS, RATIR, and SKA South Africa/MeerKAT Collaborations), Astrophys. J. Lett. 848, L12 (2017).
  15. S. Ascenzi, V. Graber, and N. Rea, Astropart. Phys. 158, 102935 (2024).
  16. D. Z. Freedman, Phys. Rev. D 9, 1389 (1974).
  17. D. Akimov et al. (COHERENT Collaboration), Science 357, 1123 (2017).
  18. D. Akimov et al. (COHERENT Collaboration), Phys. Rev. Lett. 126, 012002 (2021).
  19. M. Abdullah et al., arXiv:2203.07361.
  20. M. Cadeddu, F. Dordei, and C. Giunti, Europhys. Lett. 143, 34001 (2023).
  21. P. Danielewicz, R. Lacey, and W. G. Lynch, Science 298, 1592 (2002).
  22. M. Pospelov, Phys. Rev. D 84, 085008 (2011).
  23. R. Harnik, J. Kopp, and P. A. N. Machado, J. Cosmol. Astropart. Phys. 07 (2012) 026.
  24. D. G. Cerdeño, M. Fairbairn, T. Jubb, P. A. N. Machado, A. C. Vincent, and C. Bœhm, J. High Energy Phys. 05 (2016) 118; 09 (2016) 048.
  25. J. Liao and D. Marfatia, Phys. Lett. B 775, 54 (2017).
  26. B. Dutta, S. Liao, L. E. Strigari, and J. W. Walker, Phys. Lett. B 773, 242 (2017).
  27. Y. Farzan, M. Lindner, W. Rodejohann, and X.-J. Xu, J. High Energy Phys. 05 (2018) 066.
  28. P. B. Denton, Y. Farzan, and I. M. Shoemaker, J. High Energy Phys. 07 (2018) 037.
  29. T. Han, J. Liao, H. Liu, and D. Marfatia, J. High Energy Phys. 11 (2019) 028.
  30. D. Aristizabal Sierra, B. Dutta, S. Liao, and L. E. Strigari, J. High Energy Phys. 12 (2019) 124.
  31. P. B. Denton and J. Gehrlein, J. High Energy Phys. 04 (2021) 266.
  32. T. Han, J. Liao, H. Liu, and D. Marfatia, J. High Energy Phys. 07 (2020) 207.
  33. I. M. Shoemaker, Y.-D. Tsai, and J. Wyenberg, Phys. Rev. D 104, 115026 (2021).
  34. G. Herrera, J. High Energy Phys. 05 (2024) 288.
  35. S.-y. Xia, Nucl. Phys. B1009, 116738 (2024).
  36. A. Majumdar, D. K. Papoulias, H. Prajapati, and R. Srivastava, Phys. Rev. D 111, 073006 (2025).
  37. V. De Romeri, D. K. Papoulias, and C. A. Ternes, J. Cosmol. Astropart. Phys. 05 (2025) 012.
  38. P. Blanco-Mas, P. Coloma, G. Herrera, P. Huber, J. Kopp, I. M. Shoemaker, and Z. Tabrizi, J. High Energy Phys. 08 (2025) 043.
  39. S. Carey and V. Pandey, arXiv:2510.14015.
  40. J. Billard, L. Strigari, and E. Figueroa-Feliciano, Phys. Rev. D 89, 023524 (2014).
  41. C. A. J. O’Hare, Phys. Rev. Lett. 127, 251802 (2021).
  42. Z. Bo et al. (PandaX Collaboration), Phys. Rev. Lett. 133, 191001 (2024).
  43. E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 133, 191002 (2024).
  44. K. Patton, J. Engel, G. C. McLaughlin, and N. Schunck, Phys. Rev. C 86, 024612 (2012).
  45. C. G. Payne, S. Bacca, G. Hagen, W. Jiang, and T. Papenbrock, Phys. Rev. C 100, 061304 (2019).
  46. J. Yang, J. A. Hernandez, and J. Piekarewicz, Phys. Rev. C 100, 054301 (2019).
  47. G. Co’, M. Anguiano, and A. M. Lallena, J. Cosmol. Astropart. Phys. 04 (2020) 044.
  48. O. Tomalak, P. Machado, V. Pandey, and R. Plestid, J. High Energy Phys. 02 (2021) 097.
  49. M. Hoferichter, J. Menéndez, and A. Schwenk, Phys. Rev. D 102, 074018 (2020).
  50. N. Van Dessel, V. Pandey, H. Ray, and N. Jachowicz, Universe 9, 207 (2023).
  51. J. Piekarewicz, Phys. Rev. C 112, 054312 (2025).
  52. I. Angeli and K. P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
  53. C. J. Horowitz, S. J. Pollock, P. A. Souder, and R. Michaels, Phys. Rev. C 63, 025501 (2001).
  54. D. Adhikari et al. (CREX Collaboration), Phys. Rev. Lett. 129, 042501 (2022).
  55. S. Abrahamyan et al., Phys. Rev. Lett. 108, 112502 (2012).
  56. D. Adhikari et al. (PREX Collaboration), Phys. Rev. Lett. 126, 172502 (2021).
  57. A. Krasznahorkay et al., Phys. Rev. Lett. 66, 1287 (1991).
  58. L.-W. Chen, C. M. Ko, and B.-A. Li, Phys. Rev. C 72, 064309 (2005).
  59. B. Klos et al., Phys. Rev. C 76, 014311 (2007).
  60. B. A. Brown, G. Shen, G. C. Hillhouse, J. Meng, and A. Trzcinska, Phys. Rev. C 76, 034305 (2007).
  61. J. Zenihiro et al., Phys. Rev. C 82, 044611 (2010).
  62. A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011).
  63. E. Friedman, Nucl. Phys. A896, 46 (2012).
  64. C. M. Tarbert et al., Phys. Rev. Lett. 112, 242502 (2014).
  65. D. M. Rossi et al., Phys. Rev. Lett. 111, 242503 (2013).
  66. T. Hashimoto et al., Phys. Rev. C 92, 031305 (2015).
  67. H. Zhang, A. Akridge, C. J. Horowitz, J. Liao, and H. Xing, arXiv:2510.07816.
  68. X.-H. Tian and L.-G. Pang, arXiv:2510.20166.
  69. S.-L. Zhang, E. Wang, X.-N. Wang, and H. Xing, arXiv:2506.10694.
  70. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  71. D. S. Armstrong et al. (G0 Collaboration), Phys. Rev. Lett. 95, 092001 (2005).
  72. D. Androic et al. (G0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 646, 59 (2011).
  73. B. Hu et al., Nat. Phys. 18, 1196 (2022).
  74. C. J. Horowitz, Phys. Rev. C 57, 3430 (1998).
  75. C. J. Horowitz, Nuovo Cimento Soc. Ital. Fis. 035C, 37 (2012).
  76. D. P. Anderle et al., Front. Phys. (Beijing) 16, 64701 (2021).
  77. J. Kim, in Proceedings of the 32nd International Workshop on Deep-Inelastic Scattering and Related Subjects (2025).
  78. See Supplemental Material at http://link.aps.org/supplemental/10.1103/lnqv-bltq for the details of differential cross section and the EIC projections for Xe132 and Ar40, which include Ref. [79].
  79. G. Duda, A. Kemper, and P. Gondolo, J. Cosmol. Astropart. Phys. 04 (2007) 012.
  80. G. A. Miller, Annu. Rev. Nucl. Part. Sci. 60, 1 (2010).
  81. A. Freese and G. A. Miller, Phys. Rev. D 105, 014003 (2022).
  82. T. W. Donnelly, J. Dubach, and I. Sick, Nucl. Phys. A503, 589 (1989).
  83. S. Klein and J. Nystrand, Phys. Rev. C 60, 014903 (1999).
  84. R. H. Helm, Phys. Rev. 104, 1466 (1956).
  85. H. De Vries, C. W. De Jager, and C. De Vries, At. Data Nucl. Data Tables 36, 495 (1987).
  86. J. Piekarewicz, A. R. Linero, P. Giuliani, and E. Chicken, Phys. Rev. C 94, 034316 (2016).
  87. D. W. L. Sprung and J. Martorell, J. Phys. A 30, 6525 (1997).
  88. B. G. Todd-Rutel and J. Piekarewicz, Phys. Rev. Lett. 95, 122501 (2005).
  89. B. Reed, Z. Jaffe, C. J. Horowitz, and C. Sfienti, Phys. Rev. C 102, 064308 (2020).
  90. I. Angeli and K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
  91. C. J. Horowitz et al., Phys. Rev. C 85, 032501 (2012).
  92. H. T. Klest, arXiv:2512.14690.
  93. E.-C. Aschenauer, A. Bazilevsky, A. Jentsch, J. Kim, A. Kiselev, B. Page, Z. Tu, T. Ullrich, and C.-P. Wong, Phys. Rev. D 111, 072013 (2025).
  94. H. Davoudiasl, R. Marcarelli, and E. T. Neil, Phys. Rev. D 108, 075017 (2023).
  95. R. Balkin, T. Coren, A. Jentsch, H. Liu, M. Ovchynnikov, Y. Soreq, and S. Trifinopoulos, arXiv:2601.00068.
  96. H. T. Klest, Phys. Rev. D 113, 033002 (2026).
  97. H. Davoudiasl, H. Liu, S. Mantry, and E. T. Neil, arXiv:2512.15865.

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Phys. Rev. D 113, L051301– Published 26 March, 2026
  • Received 15 January 2026
  • Accepted 5 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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