Q^2 dependence of diffractive vector meson electroproduction

Abstract

We give a general formula for the cross section for diffractive vector meson electroproduction, gamma^* p -> Vp. We first calculate diffractive qqbar production, and then use parton-hadron duality by projecting out the J^P = 1^- state in the appropriate mass interval. We compare the Q^2 dependence of the cross section for the diffractive production of rho and J/psi mesons with recent HERA data. We include the characteristic Q^2 dependence associated with the use of the skewed gluon distribution. We give predictions for sigma_L/sigma_T for both rho and J/psi production.

Figures (5)

• Figure 1: Schematic diagram for diffractive vector meson production at HERA, $\gamma^* p \rightarrow Vp$. The longitudinal fractions $x$ and $x^\prime$ of the ingoing and outgoing proton momentum carried by the gluons are given by Eq. (\ref{['eq:b9']}); the gluons have momenta $\pm \hbox{\boldmath $\ell$}_T$ transverse to the proton. $z$ and $1 - z$ are the longitudinal fractions of the photon momentum carried by the $q$ and $\bar{q}$, and $\pm \hbox{\boldmath $k$}_T$ are their momenta transverse to the photon. There are four possible couplings of the two gluons to the $q$ and $\bar{q}$, represented by the upper circle.
• Figure 2: The QCD predictions for the $Q^2$ dependence of the cross sections for $\gamma^* p \rightarrow \rho p$ (upper plot, $W = 75$ GeV) and $\gamma^* p \rightarrow J/\psi \, p$ (lower plot, $W = 90$ GeV) compared with the HERA data H2H3. The continuous curves are obtained using the MRST(99) gluon MRST. For the lower curve the default value $2K^2$ is chosen for the scale of $\alpha_S$ in the ${\cal K}$ factor, whereas for the upper curve the scale $K^2$ was used. The dash-dotted (dotted) curves show the results if the CTEQ(5M) CTEQ5 (KMS KMS) gluon are used. The dashed curves show our results using the MRST(99) gluon and default parameters but without the effect of skewing. All predictions contain contributions from the real part of the amplitude as discussed in the text. The data point for $J/\psi$ photoproduction in the lower plot is interpolated between H1 data for different values of $W$H4 and agrees well with the ZEUS result Z3.
• Figure 3: The data H2H3H4UH1UZ for the $\gamma^* p \rightarrow Vp$ cross sections with $V = \rho$ (circles), $J/\psi$ (triangles) and $\Upsilon(1S)$ (squares: solid ZEUS, open H1, both slightly displaced from $Q^2 = 0$ for readability) plotted versus $Q^2 + M_V^2$. The QCD predictions (with standard parameters as described in the text) are shown for comparison as continuous, dashed and dotted lines, respectively. The $J/\psi$ and $\Upsilon$ data (and errors) are corrected for (i) the different photon-quark couplings by multiplying the $J/\psi$ and $\Upsilon$ measurements by 9/8 and 9/2 respectively, (ii) the different $W$ values according to the QCD predicted energy behaviour $\sigma (J/\psi) \sim W^{1.1}$ (in agreement with the experimental measurements from H3) and $\sigma (\Upsilon) \sim W^{1.3}$. The upper dotted curve is obtained using a fixed slope parameter $b = 4$ GeV$^{-2}$, whereas the lower curve contains the slope as given in Eq. (\ref{['eq:l9']}).
• Figure 4: The upper plot shows the QCD predictions for the $Q^2$ dependence of $\sigma_L/\sigma_T$ for $\rho$ electroproduction (at $W = 75$ GeV) compared with HERA data H2H1Z1Z2, partially at slightly different (average) values of $W$ as indicated on the plot. The ZEUS measurement displayed by the open triangle is the one obtained by relaxing the $s$-channel helicity conservation condition, see Z2. The different linestyles for the different gluons are chosen as in Fig. 2. Here the steeper continuous curve corresponds to the standard choice of $2K^2$ as scale of $\alpha_S$ in the ${\cal K}$ factor, the less steeper one to $K^2$. Also displayed is the naive expectation $\sigma_L/\sigma_T = Q^2/M_{\rho}^2$ (steep dashed line). The lower plot shows $\sigma_L/\sigma_T$ for $J/\psi$ production (at $W = 90$ GeV) compared to data from H3Z1.
• Figure 5: The $W$ behaviour of $\sigma_L/\sigma_T$ for fixed values of $Q^2$ for both $\rho$ electroproduction (continuous curves) and $J/\psi$ electroproduction (dashed curves), obtained with our default parameters and the MRST(99) gluon.