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.
Highlights
DIAGONALIZATION ON THE LATTICETo study the FN PS mesons on the lattice one must choose a set of interpolating operators which couple to them
We present a lattice analysis of the light pseudoscalar mesons with consideration for the mixing between the flavor-neutral states π0, η and η0
A key result of this work is the observed mass splitting between the π0 and η on our ensembles, which is found to exhibit behavior that is related to the corresponding flavor compositions
Summary
To study the FN PS mesons on the lattice one must choose a set of interpolating operators which couple to them. In this work we have made the assumption that the set of states coupled to by the octet-singlet basis operators above, or some other set of operators (e.g., the quark-flavor basis) related by a simple change of basis, are a complete set of states with respect to the low-lying mass eigenstates π0, η and η0. A. Operator basis and correlation functions We employ a variational basis of six interpolating operators; the three quark-flavor basis states. Ou 1⁄4 uγ5u; Od 1⁄4 dγ5d; Os 1⁄4 sγ5s; ð2Þ with two different levels of gauge-covariant Gaussian smearing each Using these operators we construct a 6 × 6 matrix of correlation functions (correlation matrix) with elements. Where the flavors of the source and sink operators differ, such as for the off-diagonal components of our correlation matrix, the corresponding correlation function is given by CðtÞdisc. For source and sink operators of the same flavor, the diagonal components of our correlation matrix are given by CðtÞdisc þ CðtÞcon
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