The convergence of the chiral expansion for baryon observables

Date of Completion

January 2001


Physics, Nuclear




Chiral Perturbation Theory is an Effective Field Theory of Quantum Chromodynamics. It is currently one of the most important theoretical tools for investigating low-energy hadron properties and dynamics in the energy regime where perturbative QCD fails. In the meson sector a consistent low-energy expansion can be written in terms of the meson's four-momentum and quark masses. For processes involving only mesons the method works quite well. When the baryons are included in the theory, issues of dealing with the large, dimensionful parameter, the baryon mass, must be dealt with. Two techniques, the Heavy Baryon Formalism and “infrared regularization”, have been devised that offer systematic techniques for handling this problem. Even with these techniques it is found that the chiral expansion for baryon properties does not converge as expected from naïve dimensional analysis in most cases. ^ Presented here is an investigation into the convergence properties of the chiral expansion for five baryon obsvervables of current theoretical and experimental interest. Specifically, the baryon octet EM magnetic moments and charge radii, the baryon octet axial-current couplings, the nucleon anapole moment contributions to the radiative corrections to the proton axial form factor and the parity violating pion-nucleon-nucleon Yukawa coupling are all studied. The chiral expansion for each is carried as far as possible given the constraints of experimental data and current theoretical techniques for determining the unknown parameters that appear in the expansions. ^ We find that except in the case of the baryon magnetic moments, none of the above quantities scale as expected from power counting arguments. In some cases the depature from the expected scaling behavior is severe, as shown in the example of the axial couplings of the octet. A detailed analysis of the scaling behavior for each is presented and the impact of the convergence or non-convergence on the relevant physics issues is discussed. ^