Upgrade of results from Monte Carlo study of the O(4) invariant λΦ4 model in the broken phase

Abstract

I summarize recent results from large scale Monte Carlo simulations of scalar O(4) theory in the broken phase. The wave function renormalization constant Z G , the mass of the scalar particle m σ and the scalar field expectation value Σ are determined. The effect of the finite lattice size on the scalar mass is estimated. The upper bound on the ratio m σ / f G is 2.6(1) at a value of the cut-off Λ cut⋍2.5 , corresponding to an triviality bound of 8.2(5) on the ratio of the Higgs mass over W mass. First results of an extensive calculation on various lattice sizes at finite small external source j and at a value of f G ⋍ .4 are presented. Taking into account the effect of the Goldstone states via analytic formulae, the scalar field expectation value Σ is determined. The agreement of this value calculated at finite j and the calculation using rotates fields at j=0 is impressive.