Running coupling constant and mass anomalous dimension of six-flavor SU(2) gauge theory

TL;DR

This study investigates the nonperturbative behavior of the running coupling and mass anomalous dimension in six-flavor SU(2) gauge theory, aiming to understand its conformal properties relevant for dynamical electroweak symmetry breaking.

Contribution

It provides the first lattice calculation of the running coupling and mass anomalous dimension for six-flavor SU(2) gauge theory using the Schrödinger functional scheme, including continuum extrapolation.

Findings

The running coupling slows down and approaches a fixed point.

The mass anomalous dimension at the fixed point is estimated between 0.26 and 0.74.

Discretization errors are removed perturbatively.

Abstract

In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. We calculate, with the Schr\"odinger functional scheme, the running coupling constant and the mass anomalous dimension of SU(2) gauge theory with six massless Dirac fermions in the fundamental representation. The calculations are performed on $6^4$ - $24^4$ lattices over a wide range of lattice bare couplings to take the continuum limit. The discretization errors for both quantities are removed perturbatively. We find that the running slows down and comes to a stop at $0.06 \lesssim 1/g^2 \lesssim 0.15$ where the mass anomalous dimension is estimated to be $0.26 \lesssim \gamma^*_m \lesssim 0.74$.