Higgs boson self coupling from two-loop analysis

TL;DR

This paper uses two-loop effective potential analysis and renormalization group equations to estimate the Higgs boson self-coupling, revealing two fixed points and their dependence on top quark and strong couplings.

Contribution

It introduces a two-loop analysis of the effective potential to determine the Higgs self-coupling and identifies fixed points influenced by gauge and top quark couplings.

Findings

Identifies two real positive solutions for the scalar self-coupling.

Connects the solutions to ultraviolet and infrared fixed points.

Analyzes the dependence of the scalar coupling on top quark and strong couplings.

Abstract

The scale invariant of the effective potential of the standard model at two-loop is used as a boundary condition under the assumption that the two-loop effective potential approximates the full effective potential. This condition leads with the help of the renormalization group functions of the model at two-loop to an algebraic equation of the scalar self coupling with coefficients that depend on the gauge and the top quark couplings. It admits only two real positive solutions. One of them, in the absence of the gauge and top quark couplings, corresponds to the non-perturbative ultraviolet fixed point of the scalar renormalization group function and the other corresponds to the perturbative infrared fixed point. The dependence of the scalar coupling on the top quark and the strong couplings at two-loop radiative corrections is analyzed.