The longitudinal cross section of vector meson electroproduction

TL;DR

This work develops a handbag-based framework for light vector-meson electroproduction at small x, combining generalized parton distributions constructed from double distributions with Regge-like t' dependence and a modified perturbative approach that retains transverse quark momenta and Sudakov suppression. It shows that gluon and sea quark GPDs dominate the longitudinal cross section over a wide kinematic range, with valence quarks contributing mainly at low energies for ρ and ω. The model achieves good agreement with HERA and HERMES data, explaining energy, Q^2, and t' dependences as well as the φ/ρ cross-section ratio through flavor-breaking in the sea, and highlights the importance of including transverse effects to avoid end-point divergences. Overall, the results provide a coherent description of σ_L for γ* p → V p and establish a framework for further explorations of spin observables and refined GPD modeling.

Abstract

We analyze electroproduction of light vector mesons (V=rho, phi and omega) at small Bjorken-x in the handbag approach in which the process factorizes into general parton distributions and partonic subprocesses. The latter are calculated in the modified perturbative approach where the transverse momenta of the quark and antiquark forming the vector meson are retained and Sudakov suppressions are taken into account. Modeling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal cross sections at large photon virtualities. The results are in fair agreement with the findings of recent experiments performed at HERA and HERMES.

Figures (10)

• Figure 1: Typical lowest order Feynman graphs for the two subprocesses of meson electroproduction.
• Figure 2: Illustration of gluonic radiative corrections in axial gauge.
• Figure 3: Left: Current gluon PDFs versus $\beta$ at a scale of $4\,\,{\rm GeV}^2$cteq6MRSTalekh1-pdfzeus-pdfGRV. For the CTEQ6M solution only the band of Hessian errors is shown. Its width is typical of all PDFs. The central solid line represents the gluon PDF used in this work. Right: The intercept $\delta_g$ versus $Q^2$ at $W=75\,\,{\rm GeV}$. The fit $\delta_g=0.10+0.06\ln{Q^2/Q^2_0}$ is compared to the HERA data for $\rho$ (solid circles h1, triangles zeus98) and $\phi$ electroproduction (open circles zeus05).
• Figure 4: The GPDs $H^g$ (left), $H^s_{\rm sea}$, multiplied by $\bar{x}$, (center), and $H_{\rm val}^u$ (right) at selected values of skewness. The GPDs are shown at $t'=0$ and at a scale of $4\,\,{\rm GeV}^2$.
• Figure 5: Left: The $t'$ dependence of the gluon and the $u$-valence GPDs at $W=75\,\,{\rm GeV},\; Q^2=4\,\,{\rm GeV}^2$ (solid lines) and $W=5\,\,{\rm GeV}\,\; Q^2=3\,\,{\rm GeV}^2$ (dashed lines). Right: The slope $B_V$ of the differential cross section for $\rho$ and $\phi$ electroproduction versus $Q^2$ at $W=75\,\,{\rm GeV}$. Data are taken from Ref. h1 (solid circles) and zeus05 (open triangles). The solid line represents the fit (\ref{['slope']}), (\ref{['constant-slope']}) for the case of the $\phi$.