Fixed-Point Structure of Scalar Fields

TL;DR

This paper explores extended scalar field theories with arbitrary self-couplings, revealing a continuum of fixed points including a Higgs-mass-related maximum, and identifies directions leading to asymptotically free theories.

Contribution

It introduces a broader class of renormalizable scalar theories with arbitrary powers of self-coupling and characterizes their fixed point structure, including the Gaussian fixed point.

Findings

A continuum of fixed points including Gaussian fixed point.

Maximum fixed point density at Higgs mass ~2700 GeV.

Existence of asymptotically free theories in certain directions.

Abstract

We search for alternatives to the trivial $\phi^4$ field theory by including arbitrary powers of the self-coupling. Such theories are renormalizable when the natural cutoff dependencies of the coupling constants are taken into account. We find a continuum of fixed points, which includes the well-known Gaussian fixed point. The fixed point density has a maximum at a location corresponding to a theory with a Higgs mass of approximately 2700 GeV. The Gaussian fixed point is UV stable in some directions in the extended parameter space. Along such directions we obtain non-trivial asymptotically free theories.