A relation between the Barbero-Immirzi parameter and the standard model

TL;DR

This paper demonstrates that the Barbero-Immirzi parameter, induced by standard model fields, attains a UV cutoff-independent value of 1/9 within the Euclidean formalism, using heat-kernel techniques and anomaly calculations.

Contribution

It establishes a direct relation between the Barbero-Immirzi parameter and standard model fields through a novel heat-kernel approach in Euclidean space.

Findings

Barbero-Immirzi parameter is UV cutoff-independent at 1/9

Uses Schwinger's proper-time and heat-kernel expansion techniques

Draws analogy to the derivation of the ABJ chiral anomaly

Abstract

It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion.