The quark Regge trajectory at two loops

TL;DR

The paper tests the Reggeization of quarks by examining the high-energy limit of the two-loop quark–gluon scattering amplitude and demonstrates compatibility with Regge theory at leading and next-to-leading orders. By decomposing amplitudes into color and signature channels, it establishes the Reggeized-quark framework with a trajectory δ_T and Reggeon vertices, and extracts the two-loop quark trajectory through a careful comparison with known results. The findings yield a consistent j_Q(u) expansion in (D-4) near D=4 and confirm the exponentiation structure for LL/NLL terms, while highlighting unresolved NNLL contributions in certain color channels. This work extends the Reggeization program beyond gluons to fermions and provides a concrete two-loop trajectory that informs high-energy QCD phenomenology. The methods combine high-energy amplitude limits with explicit two-loop calculations, offering a precise test of Regge theory in fermionic exchange processes.

Abstract

The hypothesis of the quark Reggeization is tested by taking the high-energy limit of the two-loop amplitude for quark-gluon scattering which was recently calculated. The limit is compatible with the Reggeization in the leading and the next-to-leading orders and allows the determination of the quark trajectory in the two-loop approximation. The trajectory is presented as an expansion in powers of (D-4) for the space-time dimension $D$ tending to the physical value D=4.