Scalar glueball-$s\bar{s}$ mixing in one flavor lattice QCD

Abstract

We investigate the mixing between the lowest-lying scalar glueball and the $s\overline{s}$ meson in $N_f=1$ lattice quantum chromodynamics (QCD) utilizing an anisotropic $16^3 \times 128$ lattice ensemble at a lattice spacing $a_s\approx 0.148\,\rm{fm}$. By solving a generalized eigenvalue problem (GEVP) for the optimized glueball and $s\overline{s}$ scalar operators in the $J^\text{PC} = 0^{++}$ channel, the masses of the two lowest-lying eigenstates are determined to be $m_1 = 1.290(20)\,\mathrm{GeV}$ and $m_2 = 1.777(49)\,\mathrm{GeV}$. By extracting the couplings of these mass eigenstates to the glueball and $s\bar{s}$ operators, we determine a substantial mixing angle $|θ| \approx 40.7(2.7)^\circ$ and a large mixing energy $x_s = 239(24)$ MeV. These results indicate a strong glueball-$s\bar{s}$ mixing in the scalar sector, providing important non-perturbative inputs for understanding the nature of the experimental isoscalar scalar mesons. The continuum limit of the mixing energy and its quark mass dependence need to be investigated in the future.