Renormalization of Scalar and Yukawa Field Theories with Lorentz Violation

TL;DR

This paper investigates the renormalization properties of scalar and Yukawa field theories incorporating Lorentz-violating operators, demonstrating their renormalizability at one-loop order and providing a framework for higher-order calculations.

Contribution

It explicitly shows the renormalizability of Lorentz-violating scalar and Yukawa theories at one-loop and offers a method to extend calculations to higher orders.

Findings

Renormalizability confirmed at one-loop order.

Framework for higher-order and finite term calculations.

Extension of scalar sector analysis to more complex scenarios.

Abstract

We consider a theory of scalar and spinor fields, interacting through Yukawa and phi^4 interactions, with Lorentz-violating operators included in the Lagrangian. We compute the leading quantum corrections in this theory. The renormalizability of the theory is explicitly shown up to one-loop order. In the pure scalar sector, the calculations can be generalized to higher orders and to include finite terms, because the theory can be solved in terms of its Lorentz-invariant version.