High-Energy Evolution of Power-Suppressed Amplitudes

We present a new class of evolution equations that govern the high-energy behavior of power-suppressed scattering amplitudes. The equations can be viewed as a renormalization group flow with respect to the relevant effective field theory cutoff. A distinct feature of the method is in the use of a multidimensional cutoff to separate the relevant scales in problems characterized by a complex factorization structure. By adjusting the renormalization group variables to the geometry of the effective theory modes, our method naturally extends to a broad spectrum of physical problems that include massive, massless, small, and wide-angle scattering. We present applications to the benchmark processes of electron-positron forward annihilation and light-quark-mediated Higgs boson production and decays.