Electroproduction of two light vector mesons in the next-to-leading approximation

TL;DR

This paper computes the forward amplitude for the electroproduction of two light vector mesons in the next-to-leading order BFKL framework, formulating it as a convolution of two $\gamma^*\to V$ impact factors with the BFKL Green's function. Using a $\nu$-space representation based on the LO BFKL eigenfunctions and including NLA kernel and impact-factor corrections, the authors provide two equivalent expressions for the amplitude: a perturbative series in $\bar{\alpha}_s$ with coefficients $b_n$ and $d_n$ and an integral form involving the Green's function. Numerical studies in the equal-virtuality regime reveal large, opposite-sign NLA corrections that necessitate optimization of the energy and renormalization scales via the Principle of Minimal Sensitivity, yielding stable results over broad parameter ranges. The work demonstrates the feasibility of a complete NLA perturbative treatment for a colorless collision process and discusses implications for $\gamma^*\gamma^*$ cross sections and the potential need for NNLA corrections in confronting experimental data.

Abstract

We calculate the amplitude for the forward electroproduction of two light vector mesons in next-to-leading order BFKL. This amplitude is written as a convolution of two impact factors for the virtual photon to light vector meson transition with the BFKL Green's function. It represents the first next-to-leading order amplitude ever calculated for a collision process between strongly interacting colorless particles.

Figures (6)

• Figure 1: Schematic representation of the amplitude for the $\gamma^*(p)\, \gamma^*(p') \to V(p_1)\, V(p_2)$ forward scattering.
• Figure 2: $\sigma/\sigma_0$ as a function of the energy logarithm $l$ for the cases of exact result of Racah, approximated result with $l_0=-A/3$ (PMS optimal choice) and $l_0=0$ (kinematical scale for energy logarithms).
• Figure 3: ${\cal I}m_s ({\cal A})Q^2/(s \, D_1 D_2)$ as a function of $Y_0$ at $\mu_R=10 Q$. The different curves are for $Y$ values of 10, 8, 6, 4 and 3. The photon virtuality $Q^2$ has been fixed to 24 GeV$^2$ ($n_f=5$).
• Figure 4: ${\cal I}m_s ({\cal A})Q^2/(s \, D_1 D_2)$ as a function of $\mu_R$ at $Y$=6. The different curves are, from above to below, for $Y_0$ values of 3, 2, 1 and 0. The photon virtuality $Q^2$ has been fixed to 24 GeV$^2$ ($n_f=5$).
• Figure 5: ${\cal I}m_s ({\cal A})Q^2/(s \, D_1 D_2)$ 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$^2$ ($n_f=5$).