Electroproduction of two light vector mesons in next-to-leading BFKL: study of systematic effects

TL;DR

This study analyzes the forward electroproduction of two light vector mesons within next-to-leading BFKL, focusing on the NLA amplitude and its systematic uncertainties. It compares two mathematically equivalent representations (series and exponentiated) and multiple optimization schemes (PMS, FAC, BLM), and benchmarks against a collinear-improved kernel approach. The results reveal large, opposite-sign NLA corrections and demonstrate stability of energy dependence across representations and optimizations, with typical optimal scales around μ_R ≈ 10 Q and s0 corresponding to Y0 ≈ 2. A notable discrepancy with EPSW1 in the differential cross section at minimum |t| underscores remaining theoretical uncertainties in impact factors and kernel improvements, highlighting the need for consistent NLA impact factors and collinear resummation for reliable predictions.

Abstract

The forward electroproduction of two light vector mesons is the first example of a collision process between strongly interacting colorless particles for which the amplitude can be written completely within perturbative QCD in the Regge limit with next-to-leading accuracy. In a previous paper we have given a numerical determination of the amplitude in the case of equal photon virtualities by using a definite representation for the amplitude and a definite optimization method for the perturbative series. Here we estimate the systematic uncertainty of our previous determination, by considering a different representation of the amplitude and different optimization methods of the perturbative series. Moreover, we compare our result for the differential cross section at the minimum momentum transfer with a different approach, based on collinear kernel improvement.

Figures (11)

• Figure 1: Schematic representation of the amplitude for the $\gamma^*(p)\, \gamma^*(p') \to V(p_1)\, V(p_2)$ scattering.
• Figure 2: ${\cal I}m_s ({\cal A}_{\mathrm series})Q^2/(s \, D_1 D_2)$ as a function of $Y$ for optimal choice of the energy parameters $Y_0$ and $\mu_R$ (curve labeled by "NLA"). The other curves represent the LLA result for $Y_0=2.2$ and $\mu_R=10Q$ and the Born (2-gluon exchange) limit for $\mu_R=Q$ and $\mu_R=10Q$. The photon virtuality $Q^2$ has been fixed to 24 GeV$^2$ ($n_f=5$).
• Figure 3: ${\cal I}m_s ({\cal A})Q^2/(s \, D_1 D_2)$ as a function of $Y$ at $Q^2$=24 GeV$^2$ ($n_f=5$) from series and "exponentiated" representations, in both cases with the PMS optimization method.
• Figure 4: The same as Fig. \ref{['PMSexp_vs_PMSseries']} at $Q^2$=5 GeV$^2$ ($n_f=4$).
• Figure 5: ${\cal I}m_s ({\cal A}_{\mathrm series})Q^2/(s \, D_1 D_2)$ as a function of $Y$ at $Q^2$=24 GeV$^2$ ($n_f=5$) from the series representation with PMS and FAC optimization methods.