The Quark Impact Factors

TL;DR

This work develops an integral representation for the next-to-leading approximation (NLA) non-forward quark impact factors in the $t$-channel for singlet and octet color states in QCD, valid in $D=4+2\epsilon$ and accommodating massive quarks, and uses it to verify the second bootstrap condition of gluon Reggeization. By decomposing the $s$-channel unitarity into one-quark and quark-gluon intermediate states and projecting onto irreducible color representations with the projector $\hat{\mathcal{P}}_{\mathcal{R}}$, the authors relate the impact factors to the Reggeized gluon trajectory $\omega(t)$ and the BFKL kernel, including the two-loop trajectory contributions $\omega^{(2)}$. They demonstrate the cancellation of the $s_{\Lambda}$ scale and confirm that both helicity-conserving $(+)$ and helicity-non-conserving $(-)$ components satisfy the bootstrap equations, strengthening the consistency of the NLA BFKL framework. In the massless-quark limit, explicit integrals are performed and results agree with prior forward-limit studies, providing practical formulas for high-energy QCD phenomenology.

Abstract

We calculate in the next-to-leading approximation the non-forward quark impact factors for both singlet and octet color representation in the $t$-channel. The integral representation of the octet impact factor in the general case of arbitrary space-time dimension and massive quark flavors is used to check the so-called "second bootstrap condition" for the gluon Reggeization at the next-to-leading logarithmic approximation in perturbative QCD. We find that it is satisfied for both helicity conserving and non-conserving parts. The integrations are then performed for the explicit calculation of the impact factors in the massless quark case.

Figures (2)

• Figure 1: Diagrammatic representation of the elastic scattering amplitude $A + B \rightarrow A' + B'$.
• Figure 2: Schematic description of the intermediate state contributions to the impact factor.