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Nucleon Scalar and Tensor Charges from Lattice QCD with Light Wilson Quarks

J. R. Green, J. W. Negele, A. V. Pochinsky, S. N. Syritsyn, M. Engelhardt, S. Krieg

TL;DR

This work computes the nucleon isovector scalar and tensor charges, $g_S$ and $g_T$, using 2+1 flavor Lattice QCD with three lattice actions to enable robust extrapolations to the physical point. The forward matrix elements are extracted from ratios of three-point to two-point correlators and renormalized nonperturbatively to $\overline{MS}(2\,\text{GeV})$, with careful control of excited-state effects via multiple source-sink separations. The study finds broad cross-action consistency and, at the physical point, reports $g_S = 1.08(0.28)(0.16)$ and $g_T = 1.037(0.020)(0.012)$, highlighting small renormalization-systematics and the need for future continuum and volume studies. These results constrain beyond-Standard-Model scalar/tensor couplings in neutron decay and CP-violating hadronic interactions, and inform dark-matter coupling calculations through the nucleon sigma term.

Abstract

We present 2+1 flavor Lattice QCD calculations of the nucleon scalar and tensor charges. Using the BMW clover-improved Wilson action with pion masses between 150 and 350 MeV and three source-sink separations between 0.9 and 1.4 fm, we achieve good control over excited-state contamination and extrapolation to the physical pion mass. As a consistency check, we also present results from calculations using unitary domain wall fermions with pion masses between 300 and 400 MeV, and using domain wall valence quarks and staggered sea quarks with pion masses between 300 and 600 MeV.

Nucleon Scalar and Tensor Charges from Lattice QCD with Light Wilson Quarks

TL;DR

This work computes the nucleon isovector scalar and tensor charges, and , using 2+1 flavor Lattice QCD with three lattice actions to enable robust extrapolations to the physical point. The forward matrix elements are extracted from ratios of three-point to two-point correlators and renormalized nonperturbatively to , with careful control of excited-state effects via multiple source-sink separations. The study finds broad cross-action consistency and, at the physical point, reports and , highlighting small renormalization-systematics and the need for future continuum and volume studies. These results constrain beyond-Standard-Model scalar/tensor couplings in neutron decay and CP-violating hadronic interactions, and inform dark-matter coupling calculations through the nucleon sigma term.

Abstract

We present 2+1 flavor Lattice QCD calculations of the nucleon scalar and tensor charges. Using the BMW clover-improved Wilson action with pion masses between 150 and 350 MeV and three source-sink separations between 0.9 and 1.4 fm, we achieve good control over excited-state contamination and extrapolation to the physical pion mass. As a consistency check, we also present results from calculations using unitary domain wall fermions with pion masses between 300 and 400 MeV, and using domain wall valence quarks and staggered sea quarks with pion masses between 300 and 600 MeV.

Paper Structure

This paper contains 7 sections, 14 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Lattice methodology
  3. Results
  4. Summary and conclusions
  5. Non-perturbative renormalization of the tensor charge operator
  6. Chiral Perturbation Theory
  7. Table of results

Figures (5)

  • Figure 1: Scalar charge measured at three source-sink separations on the Wilson-clover ensembles, as enumerated in Tab. \ref{['tab:ensembles']}.
  • Figure 2: Tensor charge measured at three source-sink separations on the Wilson-clover ensembles, as enumerated in Tab. \ref{['tab:ensembles']}.
  • Figure 3: $g_S$ versus $m_\pi^2$. Error bars are purely statistical and do not include errors in renormalization factors, which are correlated across ensembles with the same action. Two chiral fits are shown: a three-parameter fit to the coarse Wilson-clover ensembles (orange) and a four-parameter fit to all shown ensembles (magenta).
  • Figure 4: $g_T$ versus $m_\pi^2$. Error bars are purely statistical and do not include errors in renormalization factors, which are correlated across ensembles with the same action. Two chiral fits are shown: a two-parameter fit to the coarse Wilson-clover ensembles (orange) and a three-parameter fit to all shown ensembles (magenta).
  • Figure 5: Extrapolations of the scale-independent (SI) ratio $(Z_T^\text{SI}/Z_V^\text{lat})$ for coarse clover-improved Wilson fermion lattice ensembles (W3, W5) (left) and fine domain wall fermion lattices (D1, D2, D3) (right).