NLO Corrections to the Photon Impact Factor: Combining Real and Virtual Corrections

TL;DR

This work completes the NLO QCD corrections to the photon impact factor by combining the infrared-divergent pieces of virtual corrections with the full real-emission corrections, providing finite analytic expressions for the $q\bar{q}g$ intermediate state. It details the IR structure of the virtual corrections, derives the real-emission results for both photon polarizations, and implements a subtraction scheme that isolates the central region, ensuring overall infrared finiteness. The paper also discusses ultraviolet renormalization, scale dependence, and sets up the fragmentation-scale $s_0$ for consistent separation of regions, laying the groundwork for the forthcoming numerical evaluation of the remaining finite integrals. Collectively, these results advance precise NLO predictions within the Regge/BFKL framework for photon-induced scattering at high energy.

Abstract

In this third part of our calculation of the QCD NLO corrections to the photon impact factor we combine our previous results for the real corrections with the singular pieces of the virtual corrections and present finite analytic expressions for the quark-antiquark-gluon intermediate state inside the photon impact factor. We begin with a list of the infrared singular pieces of the virtual correction, obtained in the first step of our program. We then list the complete results for the real corrections (longitudinal and transverse photon polarization). In the next step we define, for the real corrections, the collinear and soft singular regions and calculate their contributions to the impact factor. We then subtract the contribution due to the central region. Finally, we combine the real corrections with the singular pieces of the virtual corrections and obtain our finite results.

Figures (4)

• Figure 1: Kinematics for $A+B\to A'+g+B'$ with initial state momenta $p_A, p_B$ and final state momenta $k_A^i, \ell, k_B^j$. An ${\boldmath 8_A}$-reggeon is exchanged, emitting a real gluon with momentum $\ell$ which is assumed to be separated from the other final state particles by large rapidity gaps.
• Figure 2: Kinematics of the process $\gamma^*+q' \to q\bar{q} + q'$.
• Figure 3: Kinematics of the process $\gamma^*+q' \to q\bar{q}g + q'$.
• Figure :