Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

TL;DR

This study calculates nucleon axial and pseudoscalar form factors using physical point twisted-mass fermion ensembles, confirming theoretical relations and providing precise values for key nucleon properties.

Contribution

First to use three physical point twisted-mass fermion ensembles at multiple lattice spacings to compute nucleon form factors and verify related theoretical relations.

Findings

PCAC and PPD relations are satisfied in the continuum limit.

Nucleon axial charge g_A=1.245(28)(14).

Pion-nucleon coupling g_{πNN}=13.25(67)(69).

Abstract

We compute the nucleon axial and pseudoscalar form factors using three $N_f=$2+1+1 twisted mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080 fm, 0.068 fm, and 0.057 fm, and spatial sizes 5.1 fm, 5.44 fm, and 5.47 fm, respectively, yielding $m_\pi L$>3.6. Convergence to the ground state matrix elements is assessed using multi-state fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. We find for the nucleon axial charge $g_A$=1.245(28)(14), for the axial radius $\langle r^2_A \rangle$=0.339(48)(06) fm$^2$, for the pion-nucleon coupling constant $g_{\pi NN} \equiv \lim_{Q^2 \rightarrow -m_\pi^2} G_{\pi NN}(Q^2)$=13.25(67)(69) and for $G_P(0.88m_{\mu}^2)\equiv g_P^*$=8.99(39)(49).