The effect of off-diagonal parton distributions in diffractive vector meson electroproduction

Abstract

We present a simple physical description of the off-diagonal gluon distribution g (x,x^\prime,Q^2) and splitting function P_{gg}(x,x^\prime) which enter the amplitude for diffractive vector meson production. We study the off-diagonal effects both on the evolution in Q^2 and on the input distribution. We predict the ratio $R$ of the off-diagonal to the diagonal gluon density, x^\prime g(x,x^\prime,Q^2)/xg(x, Q^2), as a function of the kinematic variables.

Figures (5)

• Figure 1: A diagrammatic representation of diffractive $\rho$ meson production, $\gamma^* p \rightarrow \rho p$, via a two-gluon exchange ladder. The crosses indicate that the particles are on-mass-shell in the calculation of the imaginary part of the amplitude.
• Figure 2: The variables of the three-gluon vertex used in the vertex function of (\ref{['eq:a24']}).
• Figure 3: The ratio $R$ of the off-diagonal to diagonal gluon density as a function of $x$ for four values of $\delta x = x - x^\prime$ and three values of $Q^2$, obtained from evolving from the GRV gluon GRV with $R_0 = 1$ at $Q_0^2 = 1.5 {\rm GeV}^2$.
• Figure 4: The dependence of the ratio of the off-diagonal to diagonal gluon density on the input distribution. The dashed, continuous and dot-dashed curves are obtained by evolving from $R_0 = 1$ at $Q_0^2 = 0.4, \: 1.5$ and $4 {\rm GeV}^2$, respectively, using the GRV gluon GRV. The upper limits (represented by dots) are obtained by evolving from $R_0$(max) of (\ref{['eq:b3']}) evaluated at $Q_0^2 = 1.5 {\rm GeV}^2$. The predictions corresponding to $Q_0^2 = 4 {\rm GeV}^2$ are shown only for comparison and should not be included in a realistic estimate of the uncertainty in $R$.
• Figure 5: The predictions, together with the upper limits, based on evolution from the MRS(R2) gluon MRS compared with those obtained by evolving from the GRV gluon GRV. In each case we choose $Q_0^2 = 1.5 {\rm GeV}^2$.