Lattice QCD calculation of the $\eta$ and $\eta^{\prime}$ meson masses at the physical point using rooted staggered fermions

TL;DR

This paper reports a lattice QCD calculation of the $ta$ and $ta'$ meson masses at the physical point using rooted staggered fermions, providing results consistent with experimental data and supporting the validity of the method.

Contribution

First lattice QCD calculation of $ta$ and $ta'$ masses at the physical point using rooted staggered fermions, validating the fourth root procedure.

Findings

Masses are consistent with experimental values.

Supports the validity of the rooted staggered fermion approach.

Lays groundwork for calculating transition form factors.

Abstract

We present a lattice calculation of the $\eta$ and $\eta^{\prime}$ meson masses at the physical point and in the continuum limit, based on $N_f = 2+1+1$ flavors of rooted staggered quarks. Our analysis includes gauge ensembles at the physical pion and kaon masses spread over six lattice spacings in the range [0.064-0.1315]~fm. Our main results read $m_{\eta} = 543.5(5.6)~$MeV and $m_{\eta^{\prime}} = 986(38)~$MeV, consistent with the experimental values. This is an important numerical test that supports the validity of the fourth root procedure used in the staggered quark formalism. This calculation was the first step towards extracting the pseudoscalar transition form factors of the $\eta$ and $\eta^{\prime}$ mesons that play a crucial role in the hadronic light-by-light contribution to the muon $g-2$.