Chiral Extrapolation of Lattice QCD Data: Baryon Spectroscopy
CSSM Collaboration: B. Crouch, D. B. Leinweber, D. Morel, and A. W. Thomas
[4mm]Centre for the Subatomic Structure of Matter and Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA 5005, Australia

The chiral extrapolation of hadron masses is a topic of great current interest because of the well known non-analytic behaviour with quark mass and the need to incorporate the consequent, model independent constraints of chiral symmetry. For the octet and decuplet baryons as well as the rho-meson this problem has been studied extensively and the technique for extracting model independent physical masses is well understood. The aim of this work is to generalise those results to excited baryon states.

Morel and Capstick (MC) have recently made an extensive study of the baryon masses, including the contribution of meson self-energy loops. For our purposes, only the pion loops are of interest, as only they are expected to show any rapid, non-analytic variation as the quark masses go to zero. We have therefore re-examined the MC analysis in order to ascertain which $BB'\pi$ couplings are large enough to make a significant self-energy contribution to the mass of each baryon excited state $B$ which is amenable to lattice simulation.

Having determined the most important nearby excited states one can then evaluate the corresponding self-energy contributions as a function of pion mass, $\sigma(m_\pi,\Lambda)$ (where $\Lambda$ is a finite-range regulator mass), and fit the lattice data with the functional form

$$M_R = a^R_0 + a^R_2 m_\pi^2 + a_4^R m_\pi^4 + \sigma_R(m_\pi,\Lambda) \, .$$ (1)

The parameters, $a^R_i$ and $\Lambda$, are, in principle, to be determined by fitting the available results from lattice QCD simulations. In practice, it turns out that existing data are too high in pion mass to optimize $\Lambda$ and even $a^R_4$ is usually not well determined and therefore set to zero, until more extensive lattice results become available. Nevertheless, one can already learn a great deal about the possible size of the chiral corrections as $m_\pi \rightarrow 0$. The latest results will be presented.