Transverse Energy-Energy Correlations of jets in the electron-proton Deep Inelastic Scattering at HERA

Abstract

We study the event shape variables, transverse energy energy correlation TEEC $(\cos \varphi )$ and its asymmetry ATEEC $(\cos \varphi )$ in deep inelastic scattering (DIS) at the electron-proton collider HERA, where $\varphi$ is the angle between two jets defined using a transverse-momentum $(k_T)$ jet algorithm. At HERA, jets are defined in the Breit frame, and the leading nontrivial transverse energy energy correlations arise from the 3-jet configurations. With the help of the NLOJET++, these functions are calculated in the leading order (LO) and the next-to-leading order (NLO) approximations in QCD at the electron-proton center-of-mass energy $\sqrt{s}=314$ GeV. We restrict the angular region to $-0.8\le \cos \varphi \le 0.8$, as the forward- and backward-angular regions require resummed logarithmic corrections, which we have neglected in this work. Following experimental jet-analysis at HERA, we restrict the DIS-variables $x$, $y=Q^2/(xs)$, where $Q^2=-q^2$ is the negative of the momentum transfer squared $q^2$, to $0\le x\le 1$, $0.2\le y\le 0.6$, and the pseudo-rapidity variable in the laboratory frame $({\eta }^{\mathrm{lab}})$ to the range $-1\le {\eta }^{\mathrm{lab}}\le 2.5$. The TEEC and ATEEC functions are worked out for two ranges in $Q^2$, defined by $5.5{\mathrm{GeV}}^2\le Q^2\le 80{\mathrm{GeV}}^2$, called the low-$Q^2$-range, and $150{\mathrm{GeV}}^2\le Q^2\le 1000{\mathrm{GeV}}^2$, called the high-$Q^2$-range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization $({\mu }_F)$ and renormalization $({\mu }_R)$ scales, and on ${\alpha }_s(M_Z)$. Of these the correlations are stable against varying the scale ${\mu }_F$ and the PDFs, but they do depend on ${\mu }_R$. These studies are useful in the analysis of the HERA data, including the determination of ${\alpha }_s(M_Z)$ from the shape variables.

Comments: 18 pages,11 figures; v2: 16 pages, accepted for publication in EPJC