Dijet Rapidity Gaps in Photoproduction from Perturbative QCD

TL;DR

This paper extends perturbative QCD gap-radiation resummation to photoproduction of dijets, defining gaps via interjet energy flow and factorizing the cross section into hard-scattering and soft radiation in color space. It derives process-dependent soft anomalous dimension matrices and diagonalizes them to resum leading soft-gluon logarithms, applying the formalism to direct and resolved photon contributions and comparing to ZEUS data. Numerical results show good agreement at low interjet energy thresholds (e.g., $Q_0\approx350$ MeV) and reveal quasi-singlet dominance of the soft evolution for large gap widths, with gap fractions rising with $Q_0$. The work provides a perturbative framework for predicting gap cross sections and fractions in $ep$ collisions and discusses reduced survival effects relative to hadron-hadron collisions, offering testable predictions for future measurements.

Abstract

By defining dijet rapidity gap events according to interjet energy flow, we treat the photoproduction cross section of two high transverse momentum jets with a large intermediate rapidity region as a factorizable quantity in perturbative QCD. We show that logarithms of soft gluon energy in the interjet region can be resummed to all orders in perturbation theory. The resummed cross section depends on the eigenvalues of a set of soft anomalous dimension matrices, specific to each underlying partonic process, and on the decomposition of the scattering according to the possible patterns of hard color flow. We present a detailed discussion of both. Finally, we evaluate numerically the gap cross section and gap fraction and compare the results with ZEUS data. In the limit of low gap energy, good agreement with experiment is obtained.

Figures (17)

• Figure 1: The overall dijet cross section compared with the experimental data of Ref. ZEUS.
• Figure 2: The contribution of the different partonic reactions to the dijet cross section. At $\Delta \eta = 0$ we can identify from top to bottom: the overall result (solid line); the contributions of: $\gamma +g \rightarrow q +\bar{q}$ (dotted line) , $q+g \rightarrow q+g$ (dashed line), $q+g \rightarrow g+q$ (dot dashed line), $g+g \rightarrow g+g$ (double dot dashed line), $\gamma +q(\bar{q}) \rightarrow g +q(\bar{q})$ (short dashed line), $q+q \rightarrow q+q$ (short dotted line), $q+\bar{q} \rightarrow q+\bar{q}$ (short dot dashed line). Here the two reactions $q+g \rightarrow q+g$ and $q+g \rightarrow g+q$ differ from each other by the exchange of the Mandelstam invariants $\hat{t}$ and $\hat{u}$ (see Eqs. (\ref{['qgqganalcsl']}) and (\ref{['qggqanalcsl']}) in the Appendix).
• Figure 3: The dijet cross section (solid line) and the result obtained by dropping from Fig. \ref{['figLOpart']} the contributions of the direct process $\gamma +q(\bar{q}) \rightarrow g +q(\bar{q})$, and of the resolved reaction $q+g \rightarrow g+q$ (dotted line).
• Figure 4: Real corrections to the eikonal scattering, Eq. (\ref{['eq:eikcs']}). For brevity, we only show half of the contributing cut diagrams. The remaining ones can be obtained by hermitian conjugation of each of the above graphs, i. e. , by reflection with respect to the final state cut.
• Figure 5: Virtual corrections to the eikonal scattering, Eq. (\ref{['eq:eikcs']}). For brevity, we only show half of the contributing cut diagrams. The remaining ones can be obtained by hermitian conjugation of each of the above graphs, i. e. , by reflection with respect to the final state cut.