QCD description of diffractive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>meson electroproduction

Abstract

We critically review the QCD predictions for the cross sections ${\ensuremath{\sigma}}_{L}$ and ${\ensuremath{\sigma}}_{T}$ for diffractive $\ensuremath{\rho}$ meson electroproduction in longitudinally and transversely polarized states in the DESY HERA energy region. We show that both perturbative and nonperturbative approaches, which involve convolution with the $\ensuremath{\rho}$ meson wave function, predict values of ${\ensuremath{\sigma}}_{T}$ which fall off too quickly with increasing ${Q}^{2}$, in comparison with the data. We present a perturbative QCD model based on the open production of light $q\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}$ pairs and parton-hadron duality, which describes all features of the data for $\ensuremath{\rho}$ electroproduction at high ${Q}^{2}$ and, in particular, predicts a satisfactory ${Q}^{2}$ behavior of ${\ensuremath{\sigma}}_{L}/{\ensuremath{\sigma}}_{T}.$ We find that precise measurements of the latter can give valuable information on the ${Q}^{2}$ behavior of the gluon distribution at small $x$.