High-Energy Evolution of Power-Suppressed Amplitudes

Abstract

We present a new class of evolution equations which 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 including 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/decays.

Figures (2)

• Figure 1: (a) The effective all-order Feynman diagrams representing the leading logarithmic contribution. (b) An example of topology not contributing in the next-to-leading logarithmic approximation. (c) The effective all-order Feynman diagrams corresponding to the next-to-leading logarithmic contribution. The gray circle represents the one-loop single-logarithmic corrections to the annihilation amplitude.
• Figure 2: The Feynman diagram with an arbitrary number of Sudakov gluon exchanges representing the leading logarithmic corrections to the light quark mediated $H\to gg$ amplitude. The gray circles represent the color-adjusted effective vertices.