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

TL;DR

This paper investigates the two-scale-factor universality hypothesis in O(N) scalar field theories with rotation symmetry-breaking, demonstrating that amplitude ratios remain universal across different methods and symmetry-breaking parameters.

Contribution

It provides an exact, multi-method analytical evaluation of amplitude ratios under rotation symmetry-breaking, confirming their universality and generalizing results to all loop levels.

Findings

Amplitude ratios are identical across three different methods.

Amplitude ratios are unaffected by the rotation symmetry-breaking parameter.

Results are generalizable to any loop level and rooted in symmetry principles.

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($N$) $\lambda\phi^{4}$ 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.