NLO Corrections to the γ* Impact Factor: First Numerical Results for the Real Corrections to γ*_L

TL;DR

The paper tackles the challenge of NLO corrections to the γ* impact factor by focusing on the real corrections for longitudinal polarization. It develops finite, analytic expressions for the real-emission contributions through a detailed Feynman-parameter treatment and a subtraction scheme to regulate soft, collinear, and central regions, with the remaining parameter integrals evaluated numerically using VEGAS. The authors provide a complete computational framework, including MATHEMATICA/FORTRAN code, and demonstrate that the results are independent of the collinear regulator $\Lambda$ while exposing the $s_0$-dependence of the real corrections. They find that the real corrections are negative and grow in magnitude as $s_0$ decreases, consistent with expectations for the interplay with virtual pieces and the BFKL evolution, and they set the stage for extending the method to transverse polarization and broader NLO analyses within the BFKL framework.

Abstract

We analytically perform the transverse momentum integrations in the real corrections to the longitudinal γ*_L impact factor. The resulting integrals are Feynman parameter integrals, and we provide a MATHEMATICA file which contains the integrands. The remaining integrals are carried out numerically. We perform a numerical test, and we compute those parts of the impact factor which depend upon the energy scale s_0: they are found to be negative and, with decreasing values of s_0, their absolute value increases.

Figures (5)

• Figure 1: Kinematics of the process $\gamma^*+q' \to q\bar{q}g + q'$.
• Figure 2: The diagrams contributing to $\Gamma_{{\gamma^*}\to q\bar{q}g}$
• Figure 3: The dependence of the real corrections on $\Lambda$ (with $\bm r^2 = s_0 = 1$)
• Figure 4: $\Phi'_{\gamma^*}$ at different different values of $s_0$
• Figure 5: The ratio $\Phi'_{\gamma^*} /(g^2 \Phi^{(0)}_{\gamma^*})$ at different $s_0$