Low energy kinetic distribution on orbifolds

TL;DR

This paper analyzes fermion self-energy in a five-dimensional orbifold model, demonstrating a consistent renormalization scheme that determines bulk and brane contributions and their scale dependence, with implications for orbifold model ambiguities.

Contribution

It introduces a unique renormalization approach for fermion self-energy on orbifolds, clarifying bulk and brane contributions and their scale dependence at one-loop level.

Findings

Bulk and brane parts are uniquely determined by physical conditions.

The ratio of bulk to brane contributions varies mildly with energy.

Regularization scheme dependence does not affect the main results.

Abstract

Fermion self-energy associated with wave function renormalization is studied in a five-dimensional Yukawa theory on the orbifold S1/Z2. One-loop divergence can be subtracted with only two renormalization constants in the bulk and on the branes. We show that the bulk and brane parts of the self-energy are uniquely determined with requiring physical conditions. With this procedure, momentum-scale dependence of the renormalized self-energy is given and the distribution of the bulk and brane parts can be found at low and high energies. Despite possible higher degrees of divergence in higher dimensions, the regularization scheme dependence does not arise. A viewpoint of the regularization scheme dependence at higher-loop level is also discussed. We find that the ratio of the bulk contribution to the brane contribution depends on the momentum scale in a very mild way, so that the relative coefficient of bulk and brane kinetic terms can be regarded as approximately constant for the leading quantum effect. The physical conditions given here are applicable to remove ambiguity in various orbifold models.