A Mixed Action Analysis of $\eta$ and ${\eta }^{\prime }$ Mesons

Abstract

We study $\eta$ and ${\eta }^{\prime }$ mesons and their mixing angle in a mixed action approach with so-called Osterwalder-Seiler valence quarks on a Wilson twisted mass sea. The gauge configurations have been generated by ETMC for $N_f=2+1+1$ dynamical quark flavours and for three values of the lattice spacing. The main results are that differences in between the mixed action and the unitary approach vanish towards the continuum limit with the expected rate of $\mathcal{O}(a^2)$. The individual size of the lattice artifacts depends, however, strongly on the observable used to match unitary and valence actions. Moreover, we show that for the $\eta$ mass valence and valence plus sea quark mass dependence differ significantly. Hence, in this case a re-tuning of the simulation parameters in the valence sector only is not sufficient to compensate for mismatches in the original quark masses.

arXiv comment30 pages, 8 figures, version accepted for publication

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• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• ${\eta }^{\prime }$ meson mass from topological charge density correlator in QCD
• Fate of the ${\eta }^{\prime }$ in the Quark Gluon Plasma
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• A linear sigma model for multiflavor gauge theories
• Mixed action with Borici-Creutz fermions on staggered sea
• Finite temperature QCD with $N_f=2+1+1$ Wilson twisted mass fermions at physical pion, strange and charm masses
• Extracting the ${\eta }^{\prime }$ meson mass from gluonic correlators in lattice QCD