Evolution of chiral-odd spin-independent fracture functions in Quantum Cromodynamics

Abstract

We construct the evolution equations for the twist-3 chiral-odd spin independent fracture functions in QCD. The Gribov-Lipatov reciprocity relation is fulfilled at the one-loop level for the quasi-partonic two-particle cut vertices only. It is found that the rang of the anomalous dimensions matrix is infinite for any given moment of the three-parton fracture function as distinguished from the case of DIS-distributions where the rang of the matrix was finite and increases with the number of the moment. In the multicolour limit $N_c \to \infty$ the evolution equation for the quark-gluon-quark correlation function decouples from another equation in the system and becomes homogeneous provided we discard the quark mass effects. This fact provides an opportunity to find its analytic solution explicitly in nonlocal form similarly to the DIS.