Low energy properties of SU(2) gauge theory with N_f = 3/2 flavours of adjoint fermions

TL;DR

This study numerically investigates SU(2) gauge theory with 1.5 adjoint fermion flavors, revealing infrared conformal behavior and estimating the mass anomalous dimension around 0.38, with implications for beyond Standard Model physics.

Contribution

It provides the first detailed numerical analysis of SU(2) gauge theory with 1.5 adjoint fermions, including estimates of the mass anomalous dimension and evidence of conformal behavior.

Findings

Evidence of infrared conformality in the theory.

Estimated mass anomalous dimension $oldsymbol{oxed{ ext{~0.38}}}$ at the smaller gauge coupling.

Scaling violations and lattice effects noted at different couplings.

Abstract

In this work we present the results of a numerical investigation of SU(2) gauge theory with N_f = 3/2 flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the fundamental fermion mass, represented by the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $\gamma^{\ast}$ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac operator. The difference of the estimates at the two gauge couplings should be due to scaling violations and lattice spacing effects. The more reliable estimate at the smaller gauge coupling is $\gamma^{\ast} \approx 0.38(2)$.