Properties of the $\eta$ and $\eta^{\prime}$ mesons: Masses, decay constants and gluonic matrix elements

TL;DR

This paper provides precise lattice QCD calculations of the $ta$ and $ta^{}$ mesons' masses, decay constants, and gluonic matrix elements, including their scale dependence and higher excited states.

Contribution

First direct determination of decay constants from axialvector matrix elements without model assumptions, advancing understanding of $ta$ and $ta^{}$ meson properties.

Findings

Accurate meson masses and decay constants at physical quark masses.

Determination of gluonic matrix elements and their QCD scale dependence.

Insights into higher excited states around 1400 MeV.

Abstract

We present results for the $\eta$ and $\eta^\prime$ masses and their four independent decay constants at the physical point as well as their anomalous gluonic matrix elements $a_{\eta^{(\prime)}}$. The chiral and continuum limit extrapolation is performed on twenty-one $N_f = 2+1$ Coordinated Lattice Simulations (CLS) ensembles with non-perturbatively improved Wilson fermions at four different lattice spacings and along two trajectories in the quark mass plane, including one ensemble very close to physical quark masses. For the first time the decay constants are determined directly from the axialvector matrix elements without model assumptions. This allows us to study their QCD scale dependence and to determine all low-energy constants contributing at next-to-leading order in large-$N_c$ ChPT at a well defined QCD renormalization scale. We also discuss higher excited states in the $1400\,\mathrm{MeV}$ region.