On the Calculation of the NLO Virtual Photon Impact Factor

TL;DR

This work addresses the challenge of computing the NLO virtual photon impact factor $\Phi_{\gamma^*}$ in the BFKL framework, which is essential for precise predictions in high-energy, colorless photon scattering. The authors introduce a method based on the analytic properties of amplitudes in the Reggeized-gluon effective theory, enabling part of the NLO calculation to be bypassed by transforming s-channel discontinuities into large-circle (counterterm) contributions. They show that the total NLO impact factor can be decomposed as $\boldsymbol{\Phi}_M(\vec{q})=\boldsymbol{\Phi}_\Delta(\vec{q})-\boldsymbol{\Phi}_\Delta(0)$, with the large-circle piece $\boldsymbol{\Phi}_\Lambda$ proven to be independent of the Reggeon transverse momentum $\vec{q}$, thus removing the need to evaluate that part explicitly. The analysis relies on contour integration, Cutkosky discontinuities, and Ward identities to relate and cancel contributions across many diagrams, and is demonstrated for the Born case as a consistency check. The approach promises substantial simplifications for NLO impact-factor calculations and may extend to other NLO impact factors in QCD.

Abstract

The definition of the virtual photon impact factor involves the integration of the s-channel discontinuity of the photon-Reggeon scattering amplitude over the right cut. It permits to formulate a new approach for the calculation of the impact factor based on analytical properties of the amplitude in question. In the next-to-leading order it may give a possibility for considerable simplification of the calculation. We have shown that a part of the diagrams contributing to the impact factor can be treated without their real calculation.

Figures (8)

• Figure 1: The quark-quark-Reggeon and the gluon-gluon-Reggeon effective vertices. The zig-zag lines represent the Reggeized gluon; $t^c$ and $T^c$ are the colour group generators in the fundamental and adjoint representations respectively.
• Figure 2: Some of diagrams contributing to Eq. (\ref{['210']}).
• Figure 3: Schematic representation of analytical properties of $D_n$.
• Figure 4: The diagrams contributing to $\Phi_\Delta$.
• Figure 5: a) the diagram contributing to $\Phi_\Lambda^{(0)}$; b) prescriptions for quark and gluon lines used in Section 4; c) graphic representation of the decompositions of $D^{r}_a$; d) the Ward identities in a graphic form.