Quenched chiral logarithms
Abstract
I develop a diagrammatic method for calculating chiral logarithms in the quenched approximation. While not rigorous, the method is based on physically reasonable assumptions, which can be tested by numerical simulations. The main results are that, at leading order in the chiral expansion, (a) there are no chiral logarithms in quenched f_{π}, for m_{u}=m_{d}, (b) the chiral logarithms in B_{K} and related kaon B parameters are, for m_{d}=m_{s}, the same in the quenched approximation as in the full theory, and (c) for m_{π} and the condensate there are extra chiral logarithms due to loops containing the η', which lead to a peculiar nonanalytic dependence of these quantities on the bare quark mass. Following the work of Gasser and Leutwyler, I discuss how there is a predictable finite volume dependence associated with each chiral logarithm. I compare the resulting predictions with numerical results: for most quantities the expected volume dependence is smaller than the errors, but for B_{V} and B_{A} there is an observed dependence which is consistent with the predictions.
 Publication:

Physical Review D
 Pub Date:
 October 1992
 DOI:
 10.1103/PhysRevD.46.3146
 arXiv:
 arXiv:heplat/9205020
 Bibcode:
 1992PhRvD..46.3146S
 Keywords:

 12.38.Gc;
 11.10.Ef;
 14.40.Aq;
 Lattice QCD calculations;
 Lagrangian and Hamiltonian approach;
 pi K and eta mesons;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 43 page latex file, 16 postscript figures included