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

• Main Authors: J. F. S. Neto, K. A. L. Lima, P. R. S. Carvalho, M. I. Sena-Junior
• Format: Article
• Language: English
• Published: SpringerOpen 2017-12-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-017-5427-z

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) $$\lambda \phi ^{4}$$ λ ϕ 4 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.