Hadron spectrum with Wilson fermions

Abstract

We present results of a high statistics study of the quenched spectrum using Wilson fermions at $\beta =6.0\mathrm{}$ on ${32}^3$×64 lattices. We calculate the masses of mesons and baryons composed of both degenerate and nondegenerate quarks. Using nondegenerate quark combinations allows us to study baryon mass splittings in detail. We find significant deviations from the lowest order chiral expansion, deviations that are consistent with the expectations of quenched chiral perturbation theory. We find that there is a ∼20% systematic error in the extracted value of $m_s$, depending on the meson mass ratio used to set its value. Using the largest estimate of $m_s$ we find that the extrapolated octet mass splittings are in agreement with the experimental values, as is $M_{\Delta }-M_N$, while the decuplet splittings are 30% smaller than experiment. Combining our results with data from the GF11 collaboration we find considerable ambiguity in the extrapolation to the continuum limit. Our preferred values are $\frac{M_N}{M_{\rho }}=1.38\mathrm{}\left(7\right)\mathrm{}$ and $\frac{M_{\Delta }}{m_{\rho }}=1.73\mathrm{}\left(10\right)\mathrm{}$, suggesting that the quenched approximation is good to only ∼10-15%. We also analyze the $O\left(\mathrm{ma}\right)\mathrm{}$ discretization errors in heavy quark masses.