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

Abstract

AbstractWe study the event shape variables, transverse energy–energy correlation TEEC $$(\cos \phi )$$ ( cos ϕ ) and its asymmetry ATEEC $$(\cos \phi )$$ ( cos ϕ ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where $$\phi $$ ϕ is the angle between two jets defined using a transverse-momentum $$(k_T)$$ ( 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 $$\sqrt{s}=314$$ s = 314 GeV. We restrict the angular region to $$-0.8 \le \cos \phi \le 0.8$$ - 0.8 ≤ cos ϕ ≤ 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, $$y=Q^2/(x s)$$ y = Q 2 / ( x s ) , where $$Q^2=-q^2$$ Q 2 = - q 2 is the negative of the momentum transfer squared $$q^2$$ q 2 , to $$0 \le x \le 1$$ 0 ≤ x ≤ 1 , $$0.2 \le y \le 0.6$$ 0.2 ≤ y ≤ 0.6 , and the pseudo-rapidity variable in the laboratory frame $$(\eta ^\mathrm{{lab}})$$ ( η lab ) to the range $$-1 \le \eta ^\mathrm{{lab}} \le 2.5$$ - 1 ≤ η lab ≤ 2.5 . The TEEC and ATEEC functions are worked out for two ranges in $$Q^2$$ Q 2 , defined by $$5.5\,\mathrm{GeV}^2 \le Q^2 \le 80\,\mathrm{GeV}^2$$ 5.5 GeV 2 ≤ Q 2 ≤ 80 GeV 2 , called the low-$$Q^2$$ Q 2 -range, and $$150\,\mathrm{GeV}^2 \le Q^2 \le 1000\,\mathrm{GeV}^2$$ 150 GeV 2 ≤ Q 2 ≤ 1000 GeV 2 , called the high-$$Q^2$$ Q 2 -range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization $$(\mu _F)$$ ( μ F ) and renormalization $$(\mu _R)$$ ( μ R ) scales, and on $$\alpha _s(M_Z^2)$$ α s ( M Z 2 ) . Of these the correlations are stable against varying the scale $$\mu _F$$ μ F and the PDFs, but they do depend on $$\mu _R$$ μ R . For the choice of the scale $$\mu _R= \sqrt{\langle E_T\rangle ^2 +Q^2}$$ μ R = ⟨ 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 $$\alpha _s(M_Z^2)$$ α s ( M Z 2 ) from the shape variables.