Muon-to-positron conversion from light Majorana neutrino exchange: nuclear responses and pion-pole-improved multipoles
Abstract
We study muon-to-positron conversion in nuclei that is mediated by light Majorana neutrinos, which probes lepton-number violation in the electron-muon sector. As the second paper in a series, this work extends our study of local dimension-nine interactions to the mass mechanism. We derive the conversion amplitude from the second-order effective four-Fermi interaction and express it in terms of nuclear responses in the one-body impulse approximation. Using phenomenological nucleon form factors, we retain convection, axial charge, weak magnetism, and the longitudinal pion-pole current in a specified pion-pole-improved prescription. The two physical time orderings and the distinct momentum transfers are derived in the intermediate-state response. We complete its angular reduction and derive the corresponding closure operator, including spin-gradient terms. Both the symmetric (scalar) and antisymmetric (vector) lepton-hadron Lorentz contractions contribute to the spin-averaged, angle-integrated rate. For 0+ →0+ transitions we give explicit formulas in terms of two coherent radial amplitudes, without restricting the intermediate nuclei to spin zero. This provides an interface to nuclear calculations of the required nuclear matrix elements. However, in this work, no isotope-specific numerical predictions are attempted. The present treatment uses approximate lepton wavefunctions and recoil-free nuclear propagation. Two-body weak currents and systematic chiral effective-field-theory matching are left for future work.
Related
- Muon-to-positron conversion from local dimension-nine operators: pion-pole-improved nuclear multipoles
- Electromagnetic multipoles of Majorana spin-3/2 dark matter particles and implications for direct detection
- When can decoherence reveal a Majorana phase? A phase-covariance no-go theorem for two-flavor neutrino oscillations
- Majorana Neutrino Physics and Matter-Antimatter Asymmetry in Type IIA String Theory
- Neutrino Mass in Left-Right Symmetry: From Majorana Signals to Dirac Predictions
BibTeX
@misc{liao2026muontopositron,
title = {{Muon-to-positron conversion from light Majorana neutrino exchange: nuclear responses and pion-pole-improved multipoles}},
author = {Yi Liao and Hao-Lin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39135},
eprint = {2610.39135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39135},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Muon-to-positron conversion from light Majorana neutrino exchange: nuclear responses and pion-pole-improved multipoles
AU - Yi Liao
AU - Hao-Lin Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39135
UR - https://arxiv.org/abs/2610.39135
AB - We study muon-to-positron conversion in nuclei that is mediated by light Majorana neutrinos, which probes lepton-number violation in the electron-muon sector. As the second paper in a series, this work extends our study of local dimension-nine interactions to the mass mechanism. We derive the conversion amplitude from the second-order effective four-Fermi interaction and express it in terms of nuclear responses in the one-body impulse approximation. Using phenomenological nucleon form factors, we retain convection, axial charge, weak magnetism, and the longitudinal pion-pole current in a specified pion-pole-improved prescription. The two physical time orderings and the distinct momentum transfers are derived in the intermediate-state response. We complete its angular reduction and derive the corresponding closure operator, including spin-gradient terms. Both the symmetric (scalar) and antisymmetric (vector) lepton-hadron Lorentz contractions contribute to the spin-averaged, angle-integrated rate. For 0^+ →0^+ transitions we give explicit formulas in terms of two coherent radial amplitudes, without restricting the intermediate nuclei to spin zero. This provides an interface to nuclear calculations of the required nuclear matrix elements. However, in this work, no isotope-specific numerical predictions are attempted. The present treatment uses approximate lepton wavefunctions and recoil-free nuclear propagation. Two-body weak currents and systematic chiral effective-field-theory matching are left for future work.
ER -