Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?

TL;DR

This paper uses renormalization group improved effective potential calculations to estimate the Higgs mass in the conformal limit of the Standard Model, showing a decreasing trend in the predicted mass with higher-order corrections.

Contribution

It applies a multi-loop renormalization group summation technique in the Coleman-Weinberg scheme to estimate the Higgs mass, demonstrating slow convergence and proposing an upper bound.

Findings

Higgs mass estimates decrease from 219 GeV to 163 GeV with higher-order corrections.

The method indicates slow convergence but supports the viability of the spontaneous symmetry breaking mechanism.

163 GeV is suggested as an upper bound for the Higgs mass.

Abstract

We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $\mu$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the SU(3) gauge coupling $z$, and the $SU(2) \times U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the $N^2LL...N^4LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction (MS) scheme to their form in the CW scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is $m_{H}=219\;GeV/c^2$ decreases to $m_{H}=188\;GeV/c^2$ at $N^{2}LL$ order and $m_{H}=163\;GeV/c^2$ at $N^{4}LL$ order. No reasonable estimate of $m_H$ can be made at orders $V_{NLL}$ or $V_{N^3LL}$. This is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of $m_H$. The mass $163\;GeV/c^2$ is argued to be an upper bound on $m_H$.