Callan-Symanzik equations and low-energy theorems with trace anomalies

TL;DR

This paper presents new forms of Callan-Symanzik equations and proves low-energy theorems involving trace anomalies, extending their validity across various effective field theories.

Contribution

It introduces concise forms of Callan-Symanzik equations and generalizes low-energy theorems involving trace anomalies to all consistent effective field theories.

Findings

Proved low-energy theorems as consequences of new Callan-Symanzik forms

Extended validity of trace anomaly theorems to all effective field theories

Provided discussions on related theoretical topics

Abstract

Basing on some new and concise forms of the Callan-Symanzik equations, the low-energy theorems involving trace anomalies \`a la Novikov-Shifman-Vainshtein-Zakharov, first advanced and proved in Nucl. Phys. \textbf{B165}, 67 (1980), \textbf{B191}, 301 (1981), are proved as immediate consequences. The proof is valid in any consistent effective field theories and these low-energy theorems are hence generalized. Some brief discussions about related topics are given.