The Transverse Cross Section in Exclusive Vector Meson Production

Exclusive production of vector mesons at HERA has attracted a lot of attention in recent years because of the theoretical suggestion that this is a good way to measure the gluon distribution, as simple arguments 1 suggest that the cross section behaves as the square of xg(x). Recently, these arguments have been formalised and extended by Collins, Frankfurt and Strikman in the context of a factorisation theorem for diffractive processes. One outcome of this theorem is that the longitudinal cross section (describing the transition of a longitudinal photon to a longitudinal vector meson) is indeed proportional to the gluon distribution squared, and that the amplitude for the process can be described, after integration over transverse motion, by a convolution in longitudinal momentum of a meson wave function, a hard scattering amplitude, and a gluon distribution. Furthermore, the theorem implies that this convolution is correct at high Q for any meson, irrespective of its mass. Hence one has in principle a golden process to measure the gluon distribution directly. However, an outstanding problem has been that the theorem holds only for longitudinal vector mesons. The transverse part of the cross section can only be related to quark transversity distributions, which are so far unknown. Gauge-invariance implies that the cross section is fully transverse in Q = 0 photoproduction, but very little else was known until now about the transverse part. The näıve use of the gluon distribution in σL as in σT leads to the prediction the ratio RL/T = σL/σT of longitudinal to transverse cross sections is proportional to Q, and hence that the transverse cross section is negligible at