Can the Couplings in the Fermion-Higgs Sector of the Standard Model be Strong?

TL;DR

This study investigates whether the fermion-Higgs couplings in the Standard Model can be strong by numerically analyzing a lattice model, finding that the couplings remain close to unitarity bounds and show no signs of non-triviality.

Contribution

The paper provides the first lattice simulation results for the renormalized fermion-Higgs couplings at large bare couplings, supporting the triviality of these interactions.

Findings

Renormalized couplings are close to unitarity bounds.

No evidence of non-trivial strong couplings.

Couplings exhibit expected finite volume scaling.

Abstract

We present results for the renormalized quartic self-coupling $\lambda_R$ and the Yukawa coupling $y_R$ in a lattice fermion-Higgs model with two SU(2)$_L$ doublets, mostly for large values of the bare couplings. One-component (`reduced') staggered fermions are used in a numerical simulation with the Hybrid Monte Carlo algorithm. The fermion and Higgs masses and the renormalized scalar field expectation value are computed on $L^3 24$ lattices, where $L$ ranges from $6$ to $16$. In the scaling region these quantities are found to have a $1/L^2$ dependence, which is used to determine their values in the infinite volume limit. We then calculate the $y_R$ and $\lambda_R$ from their tree level definitions in terms of the masses and renormalized scalar field expectation value, extrapolated to infinite volume. The scalar field propagators can be described for momenta up to the cut-off by one fermion loop renormalized perturbation theory and the results for $\lambda_R$ and $y_R$ come out to be close to the tree level unitarity bounds. There are no signs that are in contradiction with the triviality of the Yukawa and quartic self-coupling.