Baryon masses from lattice QCD: Beyond the perturbative chiral regime

Abstract

Consideration of the analytic properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the N π threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting to lattice data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory to the extrapolation of lattice QCD results.

Chiral Extrapolation of Lattice Moments of Proton Quark Distributions

“…Even at the lowest quark mass accessed on the lattice, the pion mass is over 300 MeV. Earlier studies of chiral extrapolations of lattice data for hadron masses [14], magnetic moments [15], and charge radii [16] have shown that for quark masses above 50 -60 MeV, hadron properties behave very much as one would expect in a constituent quark model, with relatively slow, smooth behavior as a function of the quark mass. However, for m q & 50 MeV one typically finds the rapid, nonlinear variation expected from the nonanalytic behavior of Goldstone boson loops [17].…”

“…Experience with the chiral behavior of masses and magnetic moments shows that the LNA terms alone are not sufficient to describe lattice data for m p * 200 MeV [14,15], so that extrapolation of lattice data to m p ϳ 0, through the chiral transition region, requires a formula which is consistent with both the heavy quark and chiral limits of QCD. In order to fit the lattice data at larger m p , while preserving the correct chiral behavior of moments as m p !…”

Nucleon electromagnetic form factors

“…This method was found successful when applying it to the calculation of the m π dependence of nucleon and ∆(1232) masses, see e.g. [Lei00,Lei04]. For r 2 V 1 , one may try in this spirit a modification of the χPT formula of Eq.…”

Strange-quark asymmetry in the proton in chiral effective theory

“…Regularization with the help of a finiterange regulator has been advocated [58][59][60] as a practical method which reflects the finite size of the baryon to which the chiral field couples. The effectiveness of the various prescriptions in providing accurate results for expansions of various static properties of hadrons away from the chiral regime have been discussed in Refs.…”