All-order celestial OPE in the MHV sector

TL;DR

This paper uses twistor string theory to derive all-order celestial operator product expansions for MHV gluon scattering, including regular contributions, providing new formulas for collinear splitting functions and OPE coefficients.

Contribution

It introduces a twistor string theory approach to compute all-order celestial OPEs for MHV gluon scattering, capturing regular terms in the collinear limit.

Findings

Derived all-order celestial OPE expressions including regular terms.

Provided new formulas for collinear splitting functions in momentum space.

Obtained celestial OPE coefficients for various helicity configurations.

Abstract

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.