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

Based 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 Novikov et al (1980 Nucl. Phys. B 165 67, 1981 Nucl. Phys. B 191 301), 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