Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point
David Chu (Department of Electrophysics, National Chiao-Tung University, Hsinchu, 30010, Taiwan); Karl Jansen (NIC, DESY Zeuthen, Zeuthen, D-15738, Germany); Bastian Knippschild (HISKP, Universität Bonn, Bonn, D-53115, Germany); C.J. Lin (Institute of Physics, National Chiao-Tung University, Hsinchu, 30010, Taiwan, Centre for High Energy Physics, Chung-Yuan Christian University, Chung-Li, 32023, Taiwan)
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.