Revisiting Scalar and Pseudoscalar Couplings with Nucleons

TL;DR

The paper revisits scalar and pseudoscalar Higgs couplings to nucleons in light of recent lattice QCD results for the strange-quark content and sigma terms, and explores SU(3) breaking in axial charges $g_A^a$ that affect $g_A^0$ and $\Delta s$. It derives the scalar coupling $g_{\phi NN}$ from the trace anomaly with heavy-quark expansion, finding a predominantly heavy-quark-driven, isospin-safe coupling $g_{\phi pp} \approx 1.1\times 10^{-3}$ and a smaller strange contribution $\sigma_s$, consistent with $\sigma_{\pi N}\approx 39-40$ MeV and $\sigma_0 \approx 36$ MeV. For the pseudoscalar sector, it assesses $E_q$ and $\langle N|G\tilde{G}|N\rangle$ via large-$N_c$ chiral-limit relations, evaluating two axial-charge sets and computing $\Delta q$ and $g_{\sigma NN}$, revealing notable isospin violation and a reduced $-\Delta s$ when $g_A^8$ decreases. The findings refine predictions for dark matter–nucleon and axion–nucleon couplings, with heavy-quark dominance in the scalar case and SU(3)-breaking–driven modifications in the pseudoscalar case.

Abstract

Certain dark matter interactions with nuclei are mediated possibly by a scalar or pseudoscalar Higgs boson. The estimation of the corresponding cross sections requires a correct evaluation of the couplings between the scalar or pseudoscalar Higgs boson and the nucleons. Progress has been made in two aspects relevant to this study in the past few years. First, recent lattice calculations show that the strange-quark sigma term $σ_s$ and the strange-quark content in the nucleon are much smaller than what are expected previously. Second, lattice and model analyses imply sizable SU(3) breaking effects in the determination on the axial-vector coupling constant $g_A^8$ that in turn affect the extraction of the isosinglet coupling $g_A^0$ and the strange quark spin component $Δs$ from polarized deep inelastic scattering experiments. Based on these new developments, we re-evaluate the relevant nucleon matrix elements and compute the scalar and pseudoscalar couplings of the proton and neutron. We also find that the strange quark contribution in both types of couplings is smaller than previously thought.