Eur. Phys. J. C (2017) 77: 839
https://doi.org/10.1140/epjc/s10052-017-5427-z

Regular Article - Theoretical Physics

Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

¹ Departamento de Física, Universidade Federal do Piauí, Teresina, PI, 64049-550, Brazil
² Escola Politécnica de Pernambuco, Universidade de Pernambuco, Recife, PE, 50720-001, Brazil
³ Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, 57072-900, Brazil

^* e-mail: prscarvalho@ufpi.edu.br

Received: 24 August 2017
Accepted: 27 November 2017
Published online: 7 December 2017

Abstract

We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N) scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas.