Multijet production at low $x_{\rm Bj}$ in deep inelastic scattering at HERA

TL;DR

This study measures dijet and trijet production in deep inelastic $ep$ scattering at HERA in the region $10<Q^2<100$ GeV$^2$ and $10^{-4}<x_{ m Bj}<10^{-2}$ using the ZEUS detector, focusing on low-$x_{ m Bj}$ dynamics through jet correlations in the hadronic centre-of-mass frame. Jets are reconstructed with the $k_T$ algorithm, and cross sections are provided as functions of $Q^2$, $x_{ m Bj}$, jet $E_T$, and jet $\\eta$, along with multi-differential correlations. Next-to-leading order QCD predictions, including $\,\mathcal{O}(\\alpha_s^{3})$ terms and hadronisation corrections, describe the data well and improve upon $\,\mathcal{O}(\\alpha_s^{2})$ results, especially for low $x_{ m Bj}$ and unbalanced jets. The results demonstrate the importance of higher-order corrections in the low-$x_{ m Bj}$ regime and test parton dynamics beyond DGLAP, providing insights applicable to high-energy hadron colliders like the LHC.

Abstract

Inclusive dijet and trijet production in deep inelastic $ep$ scattering has been measured for $10<Q^2<100$ GeV$^2$ and low Bjorken $x$, $10^{-4}<x_{\rm Bj}<10^{-2}$. The data were taken at the HERA $ep$ collider with centre-of-mass energy $\sqrt{s} = 318 \gev$ using the ZEUS detector and correspond to an integrated luminosity of $82 {\rm pb}^{-1}$. Jets were identified in the hadronic centre-of-mass (HCM) frame using the $k_{T}$ cluster algorithm in the longitudinally invariant inclusive mode. Measurements of dijet and trijet differential cross sections are presented as functions of $Q^2$, $x_{\rm Bj}$, jet transverse energy, and jet pseudorapidity. As a further examination of low-$x_{\rm Bj}$ dynamics, multi-differential cross sections as functions of the jet correlations in transverse momenta, azimuthal angles, and pseudorapidity are also presented. Calculations at $\mathcal{O}(α_{s}^3)$ generally describe the trijet data well and improve the description of the dijet data compared to the calculation at $\mathcal{O}(α_{s}^2)$.

Figures (12)

• Figure 1: Inclusive dijet and trijet cross sections as functions of (a) $Q^{2}$ and (c) $x_{Bj}$. Figures (b) and (d) show the ratios of the trijet to dijet cross sections. The bin-averaged differential cross sections are plotted at the bin centers. The inner error bars represent the statistical uncertainties. The outer error bars represent the quadratic sum of statistical and systematic uncertainties not associated with the jet energy scale. The shaded band indicates the jet energy scale uncertainty. The predictions of perturbative QCD at NLO, corrected for hadronisation effects and using the CTEQ6 parameterisations of the proton PDFs, are compared to data. The lower parts of the plots show the relative difference between the data and the corresponding theoretical prediction. The hatched band represents the renormalisation-scale uncertainty of the QCD calculation.
• Figure 2: Inclusive dijet (a) and trijet (b) cross sections as functions of $E_{T,{\rm HCM}}^{\rm jet}$ with the jets ordered in $E_{T,{\rm HCM}}^{\rm jet}$. The cross sections of the second and third jet were scaled for readability. Other details as in the caption to Fig. 1.
• Figure 3: The inclusive dijet (a) and trijet (c) cross sections as functions of $\eta^{\rm jet}_{{\rm LAB}}$ with the jets ordered in $\eta^{\rm jet}_{{\rm LAB}}$: $\eta_{{\rm LAB}}^{\rm jet 1} > \eta_{{\rm LAB}}^{\rm jet 2} > \eta_{{\rm LAB}}^{\rm jet 3}$. The cross sections of the second and third jet were scaled for readability. Figures (b) and (d) show the dijet and trijet cross sections as functions of $|\Delta\eta_{{\rm HCM}}^{\rm jet 1,2}|$ between the two jets with highest $E_{T,\rm HCM}^{\rm jet}$. Other details as in the caption in Fig. 1.
• Figure 4: Dijet cross sections as functions of $\Delta E_{T,{\rm HCM}}^{\rm jet 1,2}$. The NLOjet calculations at $\mathcal{O}(\alpha_s^{2})$$(\mathcal{O}(\alpha_s^{3}))$ are shown as dashed (solid) lines. The lower parts of the plots show the relative difference between the data and the $\mathcal{O}(\alpha_s^{3})$ predictions. The boundaries for the bins in $\Delta E_{T,{\rm HCM}}^{\rm jet 1,2}$ are given in Table \ref{['bin_borders_tab']}. Other details as in the caption to Fig. 1.
• Figure 5: Trijet cross sections as functions of $\Delta E_{T,{\rm HCM}}^{\rm jet 1,2}$. The measurements are compared to NLOjet calculations at $\mathcal{O}(\alpha_s^{3})$. The boundaries for the bins in $\Delta E_{T,{\rm HCM}}^{\rm jet 1,2}$ are given in Table \ref{['bin_borders_tab']}. Other details as in the caption to Fig. 1.