Pseudoscalar flavor-singlet mesons from lattice QCD

TL;DR

This study uses advanced lattice QCD techniques to precisely determine the masses, mixing, and decay constants of the eta and eta' mesons, providing results consistent with phenomenology and testing theoretical formulas.

Contribution

First controlled chiral and continuum extrapolation of eta and eta' meson properties in lattice QCD with variance reduction techniques.

Findings

Masses: M_eta=557(11) MeV, M_eta'=911(64) MeV

Mixing angle: 38.8(2.2) degrees

Decay constants: f_l=125(5) MeV, f_s=178(4) MeV

Abstract

We investigate the masses and mixing of $\eta$, $\eta'$ mesons in the framework of twisted mass lattice QCD with $N_f=2+1+1$ dynamical quark flavors. For the first time we perform a controlled chiral and continuum extrapolation to obtain physical results. To this end, we have analyzed 17 gauge ensembles with pion masses ranging from $220\,\mathrm{MeV}$ to $500\,\mathrm{MeV}$ and at three values of the lattice spacing. This calculation became feasible through the application of a powerful variance reduction technique for the computation of quark-disconnected diagrams together with several improvements in the final analysis, including a correction of the relevant correlation functions for residual topological finite volume effects. We obtain physical results for the masses $M_{\eta}=557(11)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $M_{\eta'}=911(64)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\phi=38.8(2.2)_\mathrm{stat}(2.4)_{\chi\mathrm{PT}}^\circ$, in excellent agreement with other results from phenomenology. Similarly, for the physical values of the decay constant parameters we find $f_l=125(5)_\mathrm{stat}(6)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $f_s=178(4)_\mathrm{stat}(1)_{\chi\mathrm{PT}}\,\mathrm{MeV}$. Finally, we present a test of the Veneziano Witten formula using our lattice data.