Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors

The SU(3) gauge theory with $N_f=8$ nearly massless Dirac fermions has long been of theoretical and phenomenological interest due to the near-conformality arising from its proximity to the conformal window. One particularly interesting feature is the emergence of a relatively light, stable flavor-singlet scalar meson $\sigma$ $(J^{PC}=0^{++})$ in contrast to the $N_f=2$ theory QCD. In this work, we study the finite-volume dependence of the $\sigma$ meson correlation function computed in lattice gauge theory and determine the $\sigma$ meson mass and decay constant extrapolated to the infinite-volume limit. We also determine the infinite volume mass and decay constant of the flavor-nonsinglet scalar meson $a_0$.