The role of resolved virtual photons in the production of forward jets at HERA

TL;DR

The paper addresses forward jet measurements in DIS at small $x$ and tests whether resolved virtual photons help reconcile data with theory, given concerns about BFKL dynamics and large NLL corrections. It adopts RAPGAP to simulate direct and resolved photon processes with two DGLAP ladders toward the proton and the photon, using $\mu^2 = Q^2 + p_T^2$ as the hard-scale choice. Results show that this approach describes H1 and ZEUS forward-jet data well, with the dominant resolved channel (photon-side quark interacting with proton-side gluon) producing a quark and a gluon, and initial-state radiation providing the main enhancement; the hadronic part of the photon structure is suppressed in the relevant kinematics. The findings suggest the resolved-photon mechanism effectively captures higher-order QCD effects and may emulate aspects of BFKL dynamics, while remaining consistent with other hadronic final-state observables, indicating a robust description of small-$x$ jet production that is broadly applicable.

Abstract

The measurement of forward jet cross sections has been suggested as a promising probe of new small x parton dynamics and the question is whether the new HERA data provide an indication of this. In this paper the influence of resolved photon processes has been investigated and it has been studied to what extent the inclusion of such processes in addition to normal deep inelastic scattering leads to agreement with data. It is shown that two DGLAP evolution chains from the hard scattering process towards the proton and the photon respectively, are sufficient to describe effects observed in the HERA data, which have been attributed to BFKL dynamics.

Figures (5)

• Figure 1: Deep inelastic scattering with a resolved virtual photon and the $q_{\gamma} g_p \to q g$ partonic subprocess.
• Figure 2: The forward jet cross section as a function of $x$ for $p_{T\; jet} > 3.5$ GeV ($a$) and $p_{T\; jet} > 5$ GeV ($b$) as measured by H1 H1_fjets_data . Also shown are the RAPGAP predictions for the sum of direct and resolved processes (solid line) as well as the resolved photon contribution alone (dashed line). The RAPGAP predictions for the sum of direct and resolved processes without initial and final state parton showers (solid line), including only final state (dashed line) and only initial state parton showers (dotted line) are shown in ($c$).
• Figure 3: The ratio $R=q^2_T/p^2_T$ of the transverse momenta $q^2_T$ of partons from the initial state cascade to the transverse momentum $p^2_T$ of the partons from the hard scattering process. The solid line corresponds to the scale $\mu^2=Q^2+p_T^2$, the dotted line to $\mu^2=4 \cdot P_T^2$ and the dashed line to $\mu^2=p_T^2$. The distribution is normalized to the total number of entries. Please note the logarithmic scale on the $y$ - axis.
• Figure 4: Different contributions to the total cross section of resolved virtual photons within the cuts of the forward jet analysis H1_fjets_data. In $(a)$ is shown the ratio $R= \frac{\sigma_i}{\sigma_{res.\;tot}}$, i.e. the anomalous (pointlike) part (solid line) and the hadronic part (dashed line), respectively, of the resolved virtual photon cross section divided by the the total resolved photon cross section as a function of $x$. In $(b)$ is shown the ratio $R=\frac{\sigma_i}{\sigma_{res.\;tot}}$ as a function of $x$ for different subprocesses $i$: $qg \to qg$ (dotted line), $qq \to qq$ and $q \bar{q} \to q \bar{q}$ (upper solid line), $gg \to gg$ (dashed line), $q \bar{q} \to gg$ (dashed-dotted line) and $gg \to q \bar{q}$ (lower solid line).
• Figure 5: The cross section of forward jets as a function of $E_T^2/Q^2$ as measured by ZEUS ZEUS_fjets_pt2/q2. In $(a)$ the data are compared to the prediction of RAPGAP. The solid line shows the sum of direct and resolved virtual photon contributions, whereas the dashed line shows the resolved photon contribution alone. In $(b)$ is shown the part of the cross section coming from the anomalous component (solid line) and the one coming from the hadronic component of the virtual photon separately. In $(c)$ the RAPGAP predictions are shown for the sum of direct and resolved processes without initial and final state parton showers (solid line), including only final state (dashed line) and only initial state parton showers (dotted line).