Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders

TL;DR

This paper computes quantum corrections to critical exponents in Lorentz-violating scalar field theories using unconventional minimal subtraction and Callan-Symanzik methods, testing universality and extending results to all loop orders.

Contribution

It introduces and compares unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating theories, including their consistency and all-loop level critical exponents.

Findings

Confirmed universality of critical exponents across methods

Validated the unconventional minimal subtraction scheme

Extended critical exponent calculations to all loop orders

Abstract

We present an explicit analytical computation of the quantum corrections, at next-to-leading order, to the critical exponents. We employ for that the Unconventional minimal subtraction, recently proposed, and the Callan-Symanzik methods to probe the universality hypothesis by comparing the outcomes for the critical exponents evaluated in both methods and the ones calculated previously in massless theories renormalized at different renormalization schemes. Furthermore, the consistency of the former method is investigated for the first time in literature, to our knowledge. At the end, we compute the critical exponents at any loop level by an induction process and furnish the physical interpretation of the results.