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.
Highlights
In the research activities described above, an important ingredient for finding physics beyond the SM is the knowledge of the fixed-point structure of candidate theories that can result in dEWSB
While it is widely accepted that the O(4) scalar theory is trivial, where no relevant operator can emerge, the situation with the Higgs-Yukawa model still requires further clarification. This is the main motivation of the current work, in which we develop a strategy for studying the fixed-point structure of the Higgs-Yukawa model by employing the technique of finite-size scaling (FSS)
It is found that near the Gaussian fixed point, the scaling laws can be derived for these moments by following the strategy outlined in ref
Summary
The extraction of anomalous dimensions (critical exponents) is of crucial importance for the study of universality classes in a field theory. For this purpose, the technique of FSS is the most commonly-employed approach. Our primary task is to establish FSS tools for a class of Higgs-Yukawa models (described in section 2.1) near the Gaussian fixed point. As explained in the rest of this section, this is achieved by extending the strategy developed for pure scalar field theories in ref. As explained in the rest of this section, this is achieved by extending the strategy developed for pure scalar field theories in ref. [73]
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