State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED

Abstract

We present a lattice analysis of the light pseudoscalar mesons with consideration for the mixing between the flavour-neutral states ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$. We extract the masses and flavour compositions of the pseudoscalar meson nonet in $n_f=1+1+1$ lattice QCD+QED around an SU(3)-flavour symmetric point, and observe flavour-symmetry features of the extracted data, along with preliminary extrapolation results for the flavour compositions at the physical point. A key result of this work is the observed mass splitting between the ${\pi }^0$ and $\eta$ on our ensembles, which is found to exhibit behaviour that is simply related to the corresponding flavour compositions.

9 pages, 4 figures. Some small changes and added discussion. Version to appear in PRD

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Cited by in corpus (4)

• Lattice QCD Calculation of the Pion Mass Splitting
• Lattice calculation of the pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$
• $1/N_c$ Nambu -- Jona-Lasinio model: ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons
• $\eta$ and ${\eta }^{\prime }$ mesons from $N_f=2+1$ lattice QCD at the physical point using topological charge operators