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

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.