A novel scheme for the wave function renormalization of the composite operators

TL;DR

This paper introduces a new renormalization scheme for hadronic operators, enabling precise determination of the mass anomalous dimension at an infrared fixed point in a specific gauge theory.

Contribution

The paper presents a novel coordinate-space renormalization scheme for composite operators, linking it to mass renormalization via PCAC, and applies it to compute the mass anomalous dimension at an IR fixed point.

Findings

The renormalization factor for the pseudo scalar operator is successfully computed.

The mass anomalous dimension at the IR fixed point is estimated as approximately 0.044.

The scheme provides a new method for analyzing non-Abelian gauge theories with many fermions.

Abstract

We propose a novel renormalization scheme for the hadronic operators. The renormalization factor of the operator in this scheme is normalized by the correlation function at tree level in coordinate space. If we focus on the pseudo scalar operator, then its renormalization factor is related to the mass renormalization factor of the fermion through the partially conserved axial-vector current (PCAC) relation. Using the renormalization factor for the pseudo scalar operator in our scheme, we obtain the mass anomalous dimension of the SU(3) gauge theory coupled to N_f=12 massless fundamental fermions, which has an infrared fixed point (IRFP). The mass anomalous dimension at the IRFP is estimated as gamma_m^*= 0.044_{-0.024}^{+0.025} (stat.)_{-0.032}^{+0.057} (syst.).