Eur. Phys. J. C (2020) 80: 1096
https://doi.org/10.1140/epjc/s10052-020-08614-3

Regular Article - Theoretical Physics

Transverse energy–energy correlations of jets in the electron–proton deep inelastic scattering at HERA

¹ Deutsches Elektronen-Synchrotron DESY, 22607, Hamburg, Germany
² Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusets Amherst, 01003, Amherst, MA, USA
³ INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, MOE Key Laboratory for Particle Astrophysics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China

^c wei.wang@sjtu.edu.cn

Received: 6 August 2020
Accepted: 29 October 2020
Published online: 30 November 2020

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 ${\alpha }_s(M_Z^2)$. Of these the correlations are stable against varying the scale ${\mu }_F$ and the PDFs, but they do depend on ${\mu }_R$. For the choice of the scale ${\mu }_R=\sqrt{{⟨E_T⟩}^2+Q^2}$, advocated in earlier jet analysis at HERA, the shape variables TEEC and ATEEC are found perturbatively robust. These studies are useful in the analysis of the HERA data, including the determination of ${\alpha }_s(M_Z^2)$ from the shape variables.