Muon-to-positron conversion from local dimension-nine operators: pion-pole-improved nuclear multipoles
Abstract
We begin a systematic study of neutrinoless muon-to-positron conversion, μ-+(A,Z)→ e++(A,Z−2), which violates lepton number by two units and changes charged-lepton flavor. This first paper in a series constructs nuclear operators for local dimension-nine interactions containing a scalar or pseudoscalar lepton bilinear and two contracted vector or axial quark currents. The covariant nucleon currents are built with all six vector and axial form factors. For the working nuclear operator we neglect second-class currents and adopt a pion-pole-improved reduction: non-pole recoil terms generated by the displayed one-body currents are retained through second order in inverse nucleon mass, whereas the pion-pole longitudinal axial current is kept intact before the two currents are contracted. We preserve the two independent momentum transfers at the nucleon vertices and the Coulomb-shifted spatial phase of the outgoing positron. Starting from the spacetime transition element, we show explicitly how the interaction-coordinate integral fixes the sum, but not the sharing, of the two current momenta. Unequal form-factor arguments then generate relative-coordinate multipoles absent in the usually used common-momentum approximation. We give an exact recoupling into two-body nuclear tensors and specialize it to the phenomenologically important 0+→0+ transition. In this case the external nuclear rank is zero and all magnetic sums collapse, although finite-momentum internal orbital and spin tensors remain. The result is expressed in a form directly contractible with charge-changing two-body transition densities. General six-form-factor currents, arbitrary nuclear angular momenta, and power-counting qualifications are collected in appendices.
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BibTeX
@misc{liao2026muontopositron,
title = {{Muon-to-positron conversion from local dimension-nine operators: pion-pole-improved nuclear multipoles}},
author = {Yi Liao and Hao-Lin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37727},
eprint = {2609.37727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37727},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Muon-to-positron conversion from local dimension-nine operators: pion-pole-improved nuclear multipoles
AU - Yi Liao
AU - Hao-Lin Wang
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.37727
UR - https://arxiv.org/abs/2609.37727
AB - We begin a systematic study of neutrinoless muon-to-positron conversion, μ^-+(A,Z)→ e^++(A,Z−2), which violates lepton number by two units and changes charged-lepton flavor. This first paper in a series constructs nuclear operators for local dimension-nine interactions containing a scalar or pseudoscalar lepton bilinear and two contracted vector or axial quark currents. The covariant nucleon currents are built with all six vector and axial form factors. For the working nuclear operator we neglect second-class currents and adopt a pion-pole-improved reduction: non-pole recoil terms generated by the displayed one-body currents are retained through second order in inverse nucleon mass, whereas the pion-pole longitudinal axial current is kept intact before the two currents are contracted. We preserve the two independent momentum transfers at the nucleon vertices and the Coulomb-shifted spatial phase of the outgoing positron. Starting from the spacetime transition element, we show explicitly how the interaction-coordinate integral fixes the sum, but not the sharing, of the two current momenta. Unequal form-factor arguments then generate relative-coordinate multipoles absent in the usually used common-momentum approximation. We give an exact recoupling into two-body nuclear tensors and specialize it to the phenomenologically important 0^+→0^+ transition. In this case the external nuclear rank is zero and all magnetic sums collapse, although finite-momentum internal orbital and spin tensors remain. The result is expressed in a form directly contractible with charge-changing two-body transition densities. General six-form-factor currents, arbitrary nuclear angular momenta, and power-counting qualifications are collected in appendices.
ER -