Quantum effects on winding configurations in SU(2)-Higgs theory

TL;DR

This paper investigates quantum corrections to Higgs winding configurations in SU(2)-Higgs theory to determine their potential stabilization, concluding that quantum fluctuations do not stabilize such configurations within the theory's reliable regime.

Contribution

It provides a detailed calculation of quantum corrections to winding configurations in SU(2)-Higgs theory, clarifying their stability properties.

Findings

Quantum fluctuations do not stabilize winding configurations.

The static energy scales with size as described by a specific logarithmic expression.

Limitations are discussed for extremely small configurations.

Abstract

We examine the quantum corrections to the static energy for Higgs winding configurations in order to ascertain whether such corrections may stabilize solitons in the standard model. We evaluate the effective action for winding configurations in Weinberg-Salam theory without U(1)-gauge fields or fermions. For a configuration whose size, $a \ll m^{-1}$ where $m = \max{m_W,m_H}$, m_W is the W-mass, and m_H is the Higgs mass, the static energy goes like $g^{-2}m_W^2a [1+b_0g^2\ln(1/ma)]^{c_0/b_0}$ in the semiclassical limit. Here g is the SU(2)-gauge coupling constant and b_0, c_0 are positive numbers determined by renormalization-group techniques. We discuss the limitations of this result for extremely small configurations and conclude that quantum fluctuations do not stabilize winding configurations where we have confidence in SU(2)-Higgs as a renormalizable field theory.