Lattice study of the Higgs-Yukawa model in and beyond the Standard Model

Abstract

We derive finite-size scaling formulae for four-dimensional Higgs-Yukawa models near the Gaussian fixed point. These formulae will play an essential role in future, detailed investigation of such models. In particular, they can be used to determine the nature of the observed phase transitions, and confirm or rule out the possibility of having non-trivial fixed points in the Higgs-Yukawa models. Our scaling formula for Binder's cumulant is tested against lattice simulations carried out at weak couplings, and good agreement is found. As a separate project, we also present preliminary results from our study of a chirally-invariant Higgs-Yukawa model including a dimension-six operator at finite temperature. Our work provides first indications of first-order temperature-induced phase transitions near the infinite cutoff limit in this model.

Lattice gauge theory for physics beyond the Standard Model

“…Other techniques for measuring operator anomalous dimensions and extrapolating to the conformal limit have been explored [115,116]. Scaling methods have also been used successfully in lattice studies of Higgs-Yukawa theory in four dimensions [117][118][119][120][121]; the appearance of conformal fixed points in Higgs-Yukawa theory could have important implications for the Standard Model and new-physics extensions.…”

Higgs-Yukawa model on the lattice

“…In view of this, we developed a strategy, and worked out its analytic aspects, as reported in Refs. [19,20].…”

“…[19,20] is that, using the techniques established by Zinn-Justin and Brezin for scalar field theories [21], we can derive finite-size scaling formulae for various quantities in one-loop perturbation theory near the Gaussian fixed point. It is natural to include the leadingorder logarithmic corrections to the mean-field scaling law through this procedure.…”

Higgs-Yukawa model on the lattice

“…In view of this, we developed a strategy, and worked out its analytic aspects, as reported in Refs. [22,23].…”

“…The main result in Refs. [22,23] is that, using the techniques established by Zinn-Justin and Brezin for scalar field theories [24], we can derive finite-size scaling formulae for various quantities in one-loop perturbation theory near the Gaussian fixed point. It is natural to include the leadingorder logarithmic corrections to the mean-field scaling law through this procedure.…”