The energy dependence of the hard exclusive diffractive processes in pQCD as the function of momentum transfer

Abstract

We predict the dependence on energy of photo(electro) production processes: γ(γ * )+ p → V + X with large rapidity gap at small x and large momentum −t transferred to V in pQCD. Here V is a heavy quarkonium (J/ψ, Υ) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer t, photon virtuality Q 2 and/or quarkonium mass. In the kinematical region Q 2 0 ≤ −t ≪ Q 2 + M 2 V the nontrivial energy dependence of the cross section for the vector meson production due to the photon scattering off a parton follows within QCD from the summing of the double logarithmic terms. In the second regime −t ≥ Q 2 +M 2 V within DGLAP approximation in all orders of perturbation theory the qq − parton elastic cross section is energy independent. We show that the correct account of the double logarithmic terms and of the gluon radiation including kinematical constraints removes the disagreement between pQCD calculations and recent HERA experimental data. The explicit formula for the dependence of the differential cross section d 2 σ dtdx J of these processes on s γ * N is obtained. We show that perturbative Pomeron type behavior may reveal itself only at energies significantly larger than those available at HERA. In addition we evaluate the energy dependence of DVCS processes.Within the DGLAP approximation [12][13][14] the function f DL is obtained by summing large α s (N c /2π) ln(x J /x) ln(Q 2 + M 2 V )/(Q 2 0 − t) terms, that arise in the integration over parton transverse momenta in the domain where α s ≪ 1. Here x J = −t/M 2 X is the fraction of the proton momentum carried by the parton involved in the large t elastic scattering. Variables x i are the fractions of the proton momentum carried by gluons exchanged in t channel which are attached to a parton of the proton (For the explicit definition of x 1 , x 2 see section 2.). Since at large t transverse momenta of exchanged gluons are large, x i are not vastly different.

Diffractive Phenomena in High Energy Processes

“…In the case of elastic photoproduction of J/ψ, α IP ≈ 1.2 for forward scattering and α IP ≈ 1 for −t ≈ m 2 J/ψ . Such a behavior is natural for the pQCD regime where double logarithmic terms are relevant for the interrelation between the t and s dependences [33].…”

“…A further complication is that the QCD factorization theorem [56] was derived in the limit of t = const, x = const, and Q 2 → ∞. Recent studies [33] found that the pattern of the QCD evolution changes in the kinematical domain when −t becomes comparable to the intrinsic hardness scale of the process (Q 2 eff ∼ 3 GeV 2 for J/ψ photoproduction). The DGLAP equations require modifications in this case.…”