Spin-dependent fermion potentials from mixed tensor couplings of massive spin-1 and spin-2 bosons
Abstract
Searches for weak spin-dependent forces are commonly interpreted in terms of a basis of sixteen rotationally invariant two-fermion potentials, including potentials which violate parity (P) and time-reversal (T) invariance. We derive finite-range coordinate-space potentials generated by a massive spin-1 boson with vector, axial-vector, tensor, and pseudotensor couplings to Dirac fermions. In addition to the familiar vector--vector, vector--axial-vector, and axial-vector--axial-vector interactions, we obtain the mixed vector--tensor, vector--pseudotensor, axial-vector--tensor, and axial-vector--pseudotensor potentials, together with tensor--tensor, tensor--pseudotensor, and pseudotensor--pseudotensor terms. We retain the contact terms needed in atomic-scale applications and give compact expressions that include both orderings of inequivalent fermion vertices. We then extend the analysis to a massive spin-2 mediator described by a symmetric Fierz--Pauli field. Besides the conventional coupling to the conserved fermion energy--momentum tensor, we consider a symmetric axial-tensor current. Its nonconservation for massive fermions makes the longitudinal spin-2 helicities contribute to axial-tensor--axial-tensor exchange. The leading minimal spin-2 interactions are either P,T even or P odd and T even; in particular, they do not generate a T-odd potential. We map the resulting interactions onto the sixteen-potential Dobrescu--Mocioiu basis and use this mapping to translate existing experimental constraints into numerical limits on spin-1 and spin-2 coupling products in the small- and large-mediator-mass regimes, together with representative limits at finite mediator masses. The derived relations between the boson-exchange coupling constants and the coefficients of the basis potentials also allow published exclusion curves to be rescaled to arbitrary mediator masses.
Related
- Localized orbitals and tunnel couplings from general confinement potentials in gate-defined quantum-dot arrays
- Fermion-Boson Stars in Scalar-Tensor Gravity
- Quasi-bound states and late-time evolution of a massive fermion around a Reissner-Nordström black hole
- Numerically exact simulation of open quantum networks with strong system-bath couplings using tensor network path integrals
- Gödel-type universes in Lorentz-violating Kalb-Ramond gravity with Ricci- and Riemann-tensor nonminimal couplings
BibTeX
@misc{khadka2026spindependent,
title = {{Spin-dependent fermion potentials from mixed tensor couplings of massive spin-1 and spin-2 bosons}},
author = {D. Khadka and V. V. Flambaum},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30240},
eprint = {2608.30240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30240},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-dependent fermion potentials from mixed tensor couplings of massive spin-1 and spin-2 bosons
AU - D. Khadka
AU - V. V. Flambaum
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.30240
UR - https://arxiv.org/abs/2608.30240
AB - Searches for weak spin-dependent forces are commonly interpreted in terms of a basis of sixteen rotationally invariant two-fermion potentials, including potentials which violate parity (P) and time-reversal (T) invariance. We derive finite-range coordinate-space potentials generated by a massive spin-1 boson with vector, axial-vector, tensor, and pseudotensor couplings to Dirac fermions. In addition to the familiar vector--vector, vector--axial-vector, and axial-vector--axial-vector interactions, we obtain the mixed vector--tensor, vector--pseudotensor, axial-vector--tensor, and axial-vector--pseudotensor potentials, together with tensor--tensor, tensor--pseudotensor, and pseudotensor--pseudotensor terms. We retain the contact terms needed in atomic-scale applications and give compact expressions that include both orderings of inequivalent fermion vertices. We then extend the analysis to a massive spin-2 mediator described by a symmetric Fierz--Pauli field. Besides the conventional coupling to the conserved fermion energy--momentum tensor, we consider a symmetric axial-tensor current. Its nonconservation for massive fermions makes the longitudinal spin-2 helicities contribute to axial-tensor--axial-tensor exchange. The leading minimal spin-2 interactions are either P,T even or P odd and T even; in particular, they do not generate a T-odd potential. We map the resulting interactions onto the sixteen-potential Dobrescu--Mocioiu basis and use this mapping to translate existing experimental constraints into numerical limits on spin-1 and spin-2 coupling products in the small- and large-mediator-mass regimes, together with representative limits at finite mediator masses. The derived relations between the boson-exchange coupling constants and the coefficients of the basis potentials also allow published exclusion curves to be rescaled to arbitrary mediator masses.
ER -