Abstract
We present the calculation of the impact factor for the $\gamma^{(*)}\to q\bar{q}$ transition with one loop accuracy in arbitrary kinematics. The calculation was done within Balitsky's high energy operator expansion. Together with our previous result for the $\gamma^{(*)}\to q\bar{q} g$ Born impact factor it allows one to derive cross-sections for 2- (one loop) and 3-jet (Born) difractive electroproduction. We write such cross sections for the 2 and 3 jet exclusive diffractive electroproduction off a proton in terms of hadronic matrix elements of Wilson lines. For the 2-jet cross section we demonstrate the cancellation of IR, collinear and rapidity singularities. Our result can be directly exploited to describe the recently analyzed data on exclusive dijet production at HERA and used for the study of jet photoproduction in ultraperipheral proton or nuclear scattering.
Highlights
For several decades diffraction has been one of the most intriguing phenomena of strong interaction
The impact factor for the transition γT∗ → ρT in the forward limit was obtained at LO in ref. [58, 59], including both the kinematical twist 3 (the so-called Wandzura Wilczek (WW) [60] contribution, where the produced meson Fock state is only made of a qq) and the genuine twist 3 contributions
The present result opens the way to a computation of LO γ∗ → ρ transitions for arbitrary polarizations and kinematics (using our γ(∗) → qqg Born order result), as well as of the next-toleading order (NLO) γ(∗) → ρ impact factor in the WW approximation, using our one-loop γ(∗) → qqresult
Summary
For several decades diffraction has been one of the most intriguing phenomena of strong interaction. For very large M 2, contributions with a strong ordering of longitudinal momenta are enhanced [16, 17] These two limiting results were combined in a single model, and applied to HERA data for DDIS in ref. We emphasize that in these results, the impact factors are computed without any soft or collinear approximation for the emitted gluon, in contrast with the results reported in the literature This presents an important step towards a consistent description of inclusive DDIS, or exclusive two-jet diffractive production, in the fragmentation region of the scattered photon, i.e. in the forward rapidity region, with NLO precision. Beyond the saturation limit, the Wilson-line operators, whose matrix element describes the t−channel exchanged state, evolve with respect to rapidity according to the Balitsky hierarchy.
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