Anisotropy β functions

The flow of couplings under anisotropic scaling of momenta is computed in φ3 theory in six 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. copyright 1995 The American Physical Society