Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point

Abstract

We analyse finite-size scaling behaviour of a four-dimensional Higgs-Yukawa model near the Gaussian infrared fixed point. Through improving the mean-field scaling laws by solving one-loop renormalisation group equations, the triviality property of this model can be manifested in the volume-dependence of moments of the scalar-field zero mode. The scaling formulae for the moments are derived in this work with the inclusion of the leading-logarithmic corrections. To test these formulae, we confront them with data from lattice simulations in a simpler model, namely the O(4) pure scalar theory, and find numerical evidence of good agreement. Our results of the finite-size scaling can in principle be employed to establish triviality of Higgs-Yukawa models, or to search for alternative scenarios in studying their fixed-point structure, if sufficiently large lattices can be reached.