- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Lattice calculation of short-range contributions to neutrinoless double-beta decay π−→π+ee at physical pion mass

Peter Boyle1,2, Felix Erben3, Xu Feng4,5,6, Jonathan M. Flynn7, Nicolas Garron8,9, Taku Izubuchi1,10, Luchang Jin11, Rajnandini Mukherjee2,7, J. Tobias Tsang3,9 et al.

Xin-Yu Tuo1,*

  • *Contact author: ttxxyy.tuo@gmail.com
PDF

Phys. Rev. D 113, 054504 – Published 4 March, 2026

DOI: https://doi.org/10.1103/pf3g-kmcr

Abstract

Neutrinoless double-beta (0νββ) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the π−→π+ee process contribute at leading order in the 0νββ decay channel nn→ppee through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the π−→π+ee matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC/UKQCD Collaboration. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform nonperturbative renormalization in the regularization-independent symmetric momentum-subtraction scheme (RI/SMOM), using the (γμ,γμ) and (q,q) projectors. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. Y. Fukuda et al. (Super-Kamiokande Collaboration), Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81, 1562 (1998).
  2. Q. R. Ahmad et al. (SNO Collaboration), Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89, 011301 (2002).
  3. K. Eguchi et al. (KamLAND Collaboration), First results from KamLAND: Evidence for reactor anti-neutrino disappearance, Phys. Rev. Lett. 90, 021802 (2003).
  4. A. Strumia and F. Vissani, Neutrino masses and mixings and..., arXiv:hep-ph/0606054.
  5. M. C. Gonzalez-Garcia and Y. Nir, Neutrino masses and mixing: Evidence and implications, Rev. Mod. Phys. 75, 345 (2003).
  6. E. Majorana, Teoria simmetrica dell’elettrone e del positrone, Nuovo Cimento 14, 171 (1937).
  7. M. Agostini et al. (GERDA Collaboration), Final results of GERDA on the search for neutrinoless double-β decay, Phys. Rev. Lett. 125, 252502 (2020).
  8. I. J. Arnquist et al. (Majorana Collaboration), Final result of the Majorana demonstrator’s search for neutrinoless double-β decay in Ge76, Phys. Rev. Lett. 130, 062501 (2023).
  9. N. Abgrall et al. (LEGEND Collaboration), The Large Enriched Germanium Experiment for neutrinoless ββ Decay: LEGEND-1000 preconceptual design report, arXiv:2107.11462.
  10. S. Abe et al. (KamLAND-Zen Collaboration), First search for the Majorana nature of neutrinos in the inverted mass ordering region with KamLAND-Zen, Phys. Rev. Lett. 130, 051801 (2023).
  11. D. Q. Adams et al. (CUORE Collaboration), Search for Majorana neutrinos exploiting millikelvin cryogenics with CUORE, Nature (London) 604, 53 (2022).
  12. O. Azzolini et al. (CUPID-0 Collaboration), Search for Majoron-like particles with CUPID-0, Phys. Rev. D 107, 032006 (2023).
  13. E. Armengaud et al. (CUPID Collaboration), New limit for neutrinoless double-beta decay of Mo100 from the CUPID-Mo experiment, Phys. Rev. Lett. 126, 181802 (2021).
  14. G. Anton et al. (EXO-200 Collaboration), Search for neutrinoless double-β decay with the complete EXO-200 dataset, Phys. Rev. Lett. 123, 161802 (2019).
  15. M. A. Luty, Baryogenesis via leptogenesis, Phys. Rev. D 45, 455 (1992).
  16. S. Davidson, E. Nardi, and Y. Nir, Leptogenesis, Phys. Rep. 466, 105 (2008).
  17. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  18. K. S. Babu and C. N. Leung, Classification of effective neutrino mass operators, Nucl. Phys. B619, 667 (2001).
  19. G. Prezeau, M. Ramsey-Musolf, and P. Vogel, Neutrinoless double beta decay and effective field theory, Phys. Rev. D 68, 034016 (2003).
  20. A. de Gouvea and J. Jenkins, A survey of lepton number violation via effective operators, Phys. Rev. D 77, 013008 (2008).
  21. L. Lehman, Extending the standard model effective field theory with the complete set of dimension-7 operators, Phys. Rev. D 90, 125023 (2014).
  22. M. L. Graesser, An electroweak basis for neutrinoless double β decay, J. High Energy Phys. 08 (2017) 099.
  23. V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, A neutrinoless double beta decay master formula from effective field theory, J. High Energy Phys. 12 (2018) 097.
  24. J. Schechter and J. Valle, Neutrinoless Double beta decay in SU(2)×U(1) theories, Phys. Rev. D 25, 2951 (1982).
  25. V. Cirigliano, W. Dekens, E. Mereghetti, and A. Walker-Loud, Neutrinoless double-β decay in effective field theory: The light-Majorana neutrino-exchange mechanism, Phys. Rev. C 97, 065501 (2018); 100, 019903(E) (2019).
  26. V. Cirigliano, W. Dekens, J. De Vries, M. L. Graesser, E. Mereghetti, S. Pastore, and U. Van Kolck, New leading contribution to neutrinoless double-β decay, Phys. Rev. Lett. 120, 202001 (2018).
  27. W. Detmold and D. J. Murphy (NPLQCD Collaboration), Neutrinoless double beta decay from Lattice QCD: The long-distance π−→π+e−e− amplitude, arXiv:2004.07404.
  28. X. Feng, L.-C. Jin, X.-Y. Tuo, and S.-C. Xia, Light-neutrino exchange and long-distance contributions to 0ν2β decays: An exploratory study on ππ→ee, Phys. Rev. Lett. 122, 022001 (2019).
  29. X.-Y. Tuo, X. Feng, and L.-C. Jin, Long-distance contributions to neutrinoless double beta decay π−→π+ee, Phys. Rev. D 100, 094511 (2019).
  30. A. Nicholson et al., Heavy physics contributions to neutrinoless double beta decay from QCD, Phys. Rev. Lett. 121, 172501 (2018).
  31. W. Detmold, W. I. Jay, D. J. Murphy, P. R. Oare, and P. E. Shanahan, Neutrinoless double beta decay from lattice QCD: The short-distance π−→π+e−e− amplitude, Phys. Rev. D 107, 094501 (2023).
  32. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  33. C. Sturm, Y. Aoki, N. H. Christ, T. Izubuchi, C. T. C. Sachrajda, and A. Soni, Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point, Phys. Rev. D 80, 014501 (2009).
  34. P. A. Boyle, F. Erben, J. M. Flynn, N. Garron, J. Kettle, R. Mukherjee, and J. T. Tsang (RBC Collaboration and UKQCD Collaboration), Kaon mixing beyond the standard model with physical masses, Phys. Rev. D 110, 034501 (2024).
  35. P. A. Boyle, N. Garron, R. J. Hudspith, C. Lehner, and A. T. Lytle (RBC Collaboration and UKQCD Collaboration), Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions. Part 2: Non perturbative renormalisation of the ΔF=2 four-quark operators, J. High Energy Phys. 10 (2017) 054.
  36. Y. Aoki et al. (RBC Collaboration and UKQCD Collaboration), Continuum limit physics from 2+1 flavor domain wall QCD, Phys. Rev. D 83, 074508 (2011).
  37. T. Blum et al. (RBC Collaboration and UKQCD Collaboration), Domain wall QCD with physical quark masses, Phys. Rev. D 93, 074505 (2016).
  38. Y. Aoki et al., Continuum limit of BK from 2+1 flavor domain wall QCD, Phys. Rev. D 84, 014503 (2011).
  39. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG) Collaboration), FLAG review 2024, Phys. Rev. D 113, 014508 (2026).
  40. M. Gorbahn, S. Jäger, and S. Kvedaraite, RI-(S)MOM to MS¯ conversion for BK at two-loop order, J. High Energy Phys. 09 (2025) 011.

Outline

Information

Phys. Rev. D 113, 054504– Published 4 March, 2026
  • Received 15 August 2025
  • Accepted 13 February 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation