Anisotropy beta functions

TL;DR

This paper calculates how couplings in 6D phi^3 theory change under anisotropic momentum scaling, revealing deviations from isotropic scaling that are relevant for high-energy scattering effective theories.

Contribution

It provides the first detailed computation of anisotropic beta functions in 6D phi^3 theory, highlighting differences from isotropic scaling behavior.

Findings

Coupling decreases with anisotropic momentum increase

Decreases slower than isotropic case when two momenta grow large

Results serve as tests for effective high-energy scattering theories

Abstract

The flow of couplings under anisotropic scaling of momenta is computed in $\phi^3$ theory in 6 dimensions. It is shown that the coupling decreases as momenta of two of the particles become large, keeping the third momentum fixed, but at a slower rate than the decrease of the coupling if all three momenta become large simultaneously. This effect serves as a simple test of effective theories of high energy scattering, since such theories should reproduce these deviations from the usual logarithmic scale dependence.