Naturalness and ultraviolet structure of gauge theories with massive fermions

Abstract

According to the principle of naturalness a small, with respect to the cutoff, mass parameter entering a quantum field system is natural only when it is compatible with some symmetry in the limit where it vanishes. In this paper, advantage is taken of the liberty afforded by the renormalization procedure in order to harmonize the cutoff with the physical mass in a non-Abelian gauge field theory with spin-1/2 matter fields. The ultraviolet structure of the theory, from such a vantage point, is explored at the level of the full fermionic propagator, as well as the vertex function, using the world line approach. An interplay between this ultraviolet structure and the infrared behavior of the {ital same} system, but from the customary viewpoint {open_quotes}cutoff much greater than mass,{close_quotes} is pointed out. Direct implications for open fermionic lines in the world line path integral casting of field theories are also made. {copyright} {ital 1997} {ital The American Physical Society}