A Lower Bound on $T_{SR}/{m_{\rm H}}$ in the O(4) Model on Anisotropic Lattices

TL;DR

This paper investigates the ratio of symmetry restoration temperature to Higgs mass in the O(4) model on anisotropic lattices, finding it to be independent of anisotropy and establishing a lower bound around 0.58.

Contribution

It provides the first numerical lower bound on T_SR/m_H in the O(4) model and demonstrates the ratio's independence from lattice anisotropy.

Findings

Lower bound T_SR/m_H ≈ 0.58 ± 0.02 at m_Ha_s ≈ 0.5

Ratio is independent of anisotropy ξ

Quantum and scaling corrections to anisotropy are small

Abstract

Results of an investigation of the $O(4)$ spin model at finite temperature using anisotropic lattices are presented. In both the large $N$ approximation and numerical simulations using the Wolff cluster algorithm we find that the ratio of the symmetry restoration temperature $T_{\rm SR}$ to the Higgs mass $m_{\rm H}$ is independent of the anisotropy $\xi$. From the numerical simulations we obtain a lower bound of $T_{\rm SR} / m_{\rm H} \simeq 0.58 \pm 0.02$ at a value for the Higgs mass $m_{\rm H}a_s \simeq 0.5$, which is lowered further by about $10\%$ at $m_{\rm H}a_s \simeq 1$. Requiring certain timelike correlation functions to coincide with their spacelike counterparts, quantum and scaling corrections to the anisotropy are determined and are found to be small, i.e., the anisotropy is found to be close to the ratio of spacelike and timelike lattice spacings.