Born-Oppenheimer Renormalization group for High Energy Scattering: the Setup and the Wave Function

TL;DR

This paper introduces a Born-Oppenheimer renormalization group approach to QCD high energy evolution, unifying low and high transverse momentum parton dynamics within a frequency-ordered framework.

Contribution

It develops a novel renormalization group method based on Born-Oppenheimer approximations for high energy QCD evolution, incorporating both eikonal and DGLAP-like splittings.

Findings

Derived the evolved wave function expression for hadronic states.

Formulated the frequency-ordered high energy evolution approach.

Discussed the consistent form of the S-matrix with frequency ordering.

Abstract

We develop an approach to QCD evolution based on the sequential Born-Oppenheimer approximations that include higher and higher frequency modes as the evolution parameter is increased. This Born-Oppenheimer renormalization group is a general approach which is valid for the high energy evolution as well as the evolution in transverse resolution scale $Q^2$. In the former case it yields the frequency ordered formulation of high energy evolution, which includes both the eikonal splittings which produce gluons with low longitudinal momentum, and the DGLAP-like splittings which produce partons with high transverse momentum. In this, first paper of the series we lay out the formulation of the approach, and derive the expression for the evolved wave function of a hadronic state. We also discuss the form of the $S$-matrix which is consistent with the frequency ordering.