Dijet Cross Sections at O($αα_s^2$) in Photon-Proton Collisions

TL;DR

This paper addresses dijet production in photon–proton collisions at HERA, focusing on how to combine direct photon interactions with a LO-resolved photon contribution to predict the inclusive dijet cross section at $O(\alpha\alpha_s^2)$. It implements a phase-space slicing method to handle infrared and collinear singularities, applies ZEUS-like cuts (including $x_\gamma^{OBS}\ge 0.75$ and $E_T>6$ GeV) and uses the Weizsäcker–Williams photon flux along with a cone jet definition to compute $d\sigma/d\bar{\eta}$. The study explores the dependence on photon and proton parton densities, showing that the direct component is reliably predicted at NLO, while the resolved piece is highly sensitive to the photon structure function and remains uncertain. Comparison with ZEUS data indicates that the sum of NLO direct and LO resolved can describe the observed cross sections in the large-$x_\gamma$ region, highlighting the potential to constrain the photon’s quark densities near $x_\gamma=1$ and to inform the proton gluon density at small $x$. These results underscore the importance of improved NLO treatment of the resolved contribution and of precise photon PDFs for interpreting dijet photoproduction data.

Abstract

We have calculated inclusive two-jet production in low $Q^2$ $ep$ collisions at O($αα_s^2$) superimposing direct and resolved contributions. The results are compared with recent experimental data from the ZEUS collaboration at HERA.

Figures (5)

• Figure 1: Schematic diagrams for a) direct and b) resolved photoproduction
• Figure 2: d$\sigma$/d$\bar{\eta}$ for $ep \rightarrow eX + 2$ (or more) jets for direct photoproduction with $E_T > 6$ GeV, $R = 1$ as a function of $\bar{\eta}$. The full curve is the LO cross section, the dashed (dotted) curve is the NLO 2-jet (3-jet) cross section with invariant mass cut $y = 10^{-3}$.
• Figure 3: d$\sigma$/d$\bar{\eta}$ for NLO direct photoproduction with different constraints for the 3-jet contribution as a function of $\bar{\eta}$. The dashed curve is NLO from Fig. 2 with no constraints. The dotted (dot-dashed) curve is with $E_{T_1} > 6$ GeV, $E_{T_2} > 5$ GeV ($E_{T_1}, E_{T_2} > 6~\hbox{GeV},~E_{T_3} \stackrel{<}{>} 1$ GeV concerning 2- and 3-jet separation).
• Figure 4: d$\sigma$/d$\bar{\eta}$ for LO resolved photoproduction using different photon structure function parametrizations as a function of $\bar{\eta}$.
• Figure 5: Sum of NLO direct and LO resolved cross sections d$\sigma$/d$\bar{\eta}$ as a function of $\bar{\eta}$ compared to data of ref. [3]. Four curves for different photon structure functions are shown: LO (full curve), NLO with GRV ($\overline{\hbox{MS}}$ and $\hbox{DIS}_\gamma$) (dashed and dot-dashed), and NLO with GS (HO) (dotted).