Hadron Masses and Decay Constants with Wilson Quarks at $β=5.85$ and 6.0

Abstract

We present results of a high statistics calculation of hadron masses and meson decay constants in the quenched approximation to lattice QCD with Wilson quarks at $β=$ 5.85 and 6.0 on $24^3 \times 54$ lattices. We analyze the data paying attention in particular to the systematic errors due to the choice of fitting range and due to the contamination from excited states. We find that the systematic errors for the hadron masses with quarks lighter than the strange quark amount to 1 --- 2 times the statistical errors. When the lattice scale is fixed from the $ρ$ meson mass, the masses of the $Ω^{-}$ baryon and the $ϕ$ meson at two $β$'s agree with experiment within about one standard deviation. On the other hand, the central value of the nucleon mass at $β=6.0$ (5.85) is larger than its experimental value by about 15\% (20\%) and that of the $Δ$ mass by about 15\% (4\%): Even when the systematic errors are included, the baryon masses at $β=6.0$ do not agree with experiment. Vector meson decay constants at two values of $β$ agree well with each other and are consistent with experiment for a wide range of the quark mass, when we use current renormalization constants determined nonperturbatively by numerical simulations. The pion decay constant agrees with experiment albeit with large errors. Results for the masses of excited states of the $ρ$ meson and the nucleon are also presented.