Transverse energy\u2013energy correlations of jets in the electron\u2013proton deep inelastic scattering at HERA

Abstract

We study the event shape variables, transverse energy–energy correlation TEEC (cos phi ) and its asymmetry ATEEC (cos phi ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where phi 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 phi 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/(x s), 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{langle E_Trangle ^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.