All-order celestial OPE in the MHV sector

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