CONSTRAINT EFFECTIVE POTENTIAL AND THE SIGMA-MASS IN THE O (4) PHI-4-THEORY

GOCKELER M, JANSEN K, Neuhaus T. CONSTRAINT EFFECTIVE POTENTIAL AND THE SIGMA-MASS IN THE O (4) PHI-4-THEORY. PHYSICS LETTERS B. 1991;273(4):450-456.We present a numerical calculation of the sigma-mass from the constraint effective potential in the O (4) non-linear sigma-model in four dimensions. The sigma-mass is determined from the volume dependence of the susceptibility, which is calculated directly from the width of the effective potential. Furthermore, we compute the infinite volume value of the analogue of the pion decay constant F from the minimum of the effective potential. The extrapolation to infinite volume is based on chiral perturbation theory in combination with perturbation theory in the renormalized quartic coupling. We observe the divergence of the susceptibility of the length of the magnetization, which in four dimensions is proportional to the logarithm of the linear size of the lattice and is attributed to the pion cut of the theory. Our resulting high precision values of the renormalized quartic coupling agree very well with the work of Luscher and Weisz