Scaling analysis of the O(4)-symmetric ${\Phi }^4$-theory in the broken phase

Abstract

We study the $O(4)$-symmetric ${\Phi }^4$-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by applying the reflection cluster algorithm. Employing the histogram method we analytically continue to a sequence of values of the hopping parameter $\kappa$ neighbouring the actually simulated ones. In the investigated vicinity of the critical point ${\kappa }_c$ finite volume effects affecting, e.g., the determination of the field expectation value $\Sigma$ and the mass $m_{\sigma }$ of the $\sigma$-particle are very well described by 1-loop renormalized perturbation theory. We carry out a detailed scaling analysis on a high level of precision. Finally we discuss the upper bound on the Higgs mass for both kinds of actions.

Comments: 34 pages, 9 PS-figures