Lattice QCD calculation of the pion-nucleon coupling g̅0 induced by the QCD Θ-term
Abstract
We present lattice QCD results for the CP violating pion-nucleon coupling g̅0 induced by the QCD Θ̅ term from the analysis of three 2+1+1-flavor ensembles generated with highly improved staggered quarks (HISQ) by the MILC collaboration. These ensembles are at lattice spacing a≈ 0.09 fm and pion masses of 313, 226 and 138 MeV, respectively. The coupling g̅0 is extracted in two ways. First, from the matrix element of the correlation between the pesudoscalar current and the topological charge evaluated between the nucleon ground state. The data for correlation functions with both the pseudoscalar and axial vector exhibit large contamination from the Nπ excited state. We show that these can be controlled at the leading order using chiral perturbation theory (χPT) and the axial Ward identity (AWI, also called the partially conserved axial current (PCAC) relation). The result after removing the Nπ contamination and extrapolating to the physical pion mass is, however, noisy: g̅0/(2Fπ)=−7(63)× 10−3 Θ̅. The more precise result g̅0/(2Fπ)=17.4(1.9)× 10−3 Θ̅ is obtained using low energy effective field theory methods or equivalently the AWI. Since contamination from the Nπ excited states arises in the calculation of many nucleon matrix elements, we give an extended discussion on them and the use of the AWI for controlling them in the calculation of g̅0.
Related
- Probing the nucleon axial form factor via the e⃗ + + 2H → ν̅e + p + p reaction below the pion-production threshold
- One-nucleon intermediate-state contribution to the pion-coupled four-quark condensate in the N--J/ψ interaction
- Gravitational D-form factors of the nucleon and pion with mixing between two-quark and four-quark states
- Effects of in-medium NN inelastic cross sections and the high-momentum tail of nucleon momentum distributions on pion production in heavy-ion collisions
- Local-nuclear-density dependent calculation of nucleon electromagnetic form factor ratios in finite nuclei
BibTeX
@misc{he2026lattice,
title = {{Lattice QCD calculation of the pion-nucleon coupling $\barg_0$ induced by the QCD $Θ$-term}},
author = {Fangcheng He and Tanmoy Bhattacharya and Rajan Gupta and Emanuele Mereghetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04129},
eprint = {2609.04129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04129},
note = {CC0},
}
RIS
TY - UNPB
TI - Lattice QCD calculation of the pion-nucleon coupling g̅_0 induced by the QCD Θ-term
AU - Fangcheng He
AU - Tanmoy Bhattacharya
AU - Rajan Gupta
AU - Emanuele Mereghetti
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04129
UR - https://arxiv.org/abs/2609.04129
AB - We present lattice QCD results for the CP violating pion-nucleon coupling g̅_0 induced by the QCD Θ̅ term from the analysis of three 2+1+1-flavor ensembles generated with highly improved staggered quarks (HISQ) by the MILC collaboration. These ensembles are at lattice spacing a≈ 0.09 fm and pion masses of 313, 226 and 138 MeV, respectively. The coupling g̅_0 is extracted in two ways. First, from the matrix element of the correlation between the pesudoscalar current and the topological charge evaluated between the nucleon ground state. The data for correlation functions with both the pseudoscalar and axial vector exhibit large contamination from the Nπ excited state. We show that these can be controlled at the leading order using chiral perturbation theory (χPT) and the axial Ward identity (AWI, also called the partially conserved axial current (PCAC) relation). The result after removing the Nπ contamination and extrapolating to the physical pion mass is, however, noisy: g̅_0/(2F_π)=−7(63)× 10^−3 Θ̅. The more precise result g̅_0/(2F_π)=17.4(1.9)× 10^−3 Θ̅ is obtained using low energy effective field theory methods or equivalently the AWI. Since contamination from the Nπ excited states arises in the calculation of many nucleon matrix elements, we give an extended discussion on them and the use of the AWI for controlling them in the calculation of g̅_0.
ER -