UV/IR scale dependence in a four-derivative scalar field theory

Abstract

An analog of the standard renormalization procedure may be useful for four-derivative theories, and we illustrate it with the four-derivative scalar field theory in the $m\to 0$ limit. The renormalization scale $\mu$ appears in momentum-dependent logarithms associated with both UV and IR divergences. At one loop, the on-shell scattering amplitude satisfies an analog Callan--Symanzik equation involving the analog beta functions. These functions are determined from the combined UV and IR pole parts of the 1PI functions.

15 pages, 3 figures, added sections 4 and 5, no other changes