Vector meson electroproduction at small Bjorken-x and generalized parton distributions

TL;DR

The paper develops a gluon-dominated generalized parton distribution (GPD) framework for vector meson electroproduction at small $x_{ m Bj}$, modeling the gluon GPD $H^g$ via gluonic double distributions and computing the hard $\gamma^* g \to V g$ subprocess in a modified perturbative approach that includes quark transverse momentum and Sudakov suppression. The amplitudes are evaluated in impact parameter space and convolved with the GPDs to predict cross sections and spin density matrix elements for $\rho$ and $\phi$ production, with the results in fair agreement with HERA data for $Q^2 \gtrsim 4$ GeV$^2$. A key finding is the dominance of the $L\to L$ transition, the insensitivity of the results to the specific $n=1$ vs $n=2$ GPD models, and the smallness of the helicity correlation $A_{LL}$ due to the suppression of $\widetilde{H}^g$. The work also contrasts the full GPD approach with leading-twist and $\ln(1/x_{ m Bj})$ approximations, highlighting the importance of skewing effects and transverse momentum dynamics in matching experimental observables.

Abstract

We analyze electroproduction of light vector mesons at small Bjorken-x in an approach that includes the gluonic generalized parton distributions and a partonic subprocess, gamma g --> (q q-bar) g, q q-bar --> V. The subprocess is calculated to lowest order of perturbative QCD taking into account the transverse momenta of the quark and antiquark as well as Sudakov suppressions. Our approach allows to investigate the transition amplitudes for all kind of polarized virtual photons and polarized vector mesons. Modelling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal and transverse cross sections at large photon virtualities as well as the spin density matrix elements for the vector mesons. Our results are in fair agreement with the findings of recent experiments performed at HERA.

Figures (15)

• Figure 1: The handbag-type diagram for meson electroproduction off protons. The large blob represents a GPD while the small one stands for meson electroproduction off partons. The momenta of the involved particles are specified.
• Figure 2: Lowest order Feynman graphs for the subprocess $\gamma^* g\to Vg$.
• Figure 3: Model results for the GPD $H^g$ in the small $\bar{x}$ range at $t\simeq 0$ and for the case $n=1$. The solid (dashed, dash-dotted) line represents the GPD at $\xi= 5\;(1\,,\; 0.5)\, \cdot 10^{-3}$ and at the scale $2\,\,{\rm GeV}$.
• Figure 4: The differential cross section (\ref{['epcross']}) for $ep\to ep\rho$ versus $-t$ integrated over the kinematical region available to the ZEUS experiment from which the data are taken zeus98. The solid line is our fit to the data at $W = 75\,\,{\rm GeV}$ and $Q^2 = 6\,\,{\rm GeV}^2$ (see text). The dashed (dot-dashed, short-dashed) line represents the individual contributions from the $L\to L$ ($T\to T$, $T\to L$) amplitudes.
• Figure 5: The integrated cross section for $\gamma^* p\to \rho p$ (left) and $\gamma^* p\to \phi p$ (right) versus $Q^2$ at $W\simeq 75\, \,{\rm GeV}$. Data taken from h1adloff (filled squares) and zeus98zeus96 (open squares) for $\rho$ and $\phi$ production, respectively. The solid lines represent our results.