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

TL;DR

This paper investigates transverse energy-energy correlations in deep inelastic scattering at HERA, calculating them at LO and NLO in QCD, and analyzes their sensitivity to parton distributions and QCD parameters for potential use in data analysis.

Contribution

The study provides the first NLO QCD calculations of TEEC and ATEEC functions in DIS at HERA, including their dependence on PDFs, scales, and $oldsymbol{oldsymbol{oldsymbol{oldsymbol{ ext{Q}}}}}$CD parameters.

Findings

TEEC and ATEEC functions are stable against scale and PDF variations.

Correlations depend on the renormalization scale $oldsymbol{oldsymbol{oldsymbol{oldsymbol{ ext{μ}}}}}_R$.

Results are useful for $oldsymbol{oldsymbol{oldsymbol{oldsymbol{ ext{α}}}}}_s(M_Z)$ determination.

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 $-0.8 \leq \cos \phi \leq 0.8$, 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 $0 \leq x \leq 1$, $0.2 \leq y \leq 0.6$, and the pseudo-rapidity variable in the laboratory frame $(\eta^{\rm {lab}})$ to the range $-1 \leq \eta^{\rm {lab}} \leq 2.5$. The TEEC and ATEEC functions are worked out for two ranges in $Q^2$, defined by $5.5~{\rm GeV}^2 \leq Q^2 \leq 80~{\rm GeV}^2$, called the low-$Q^2$-range, and $150~{\rm GeV}^2 \leq Q^2 \leq 1000~{\rm GeV}^2$, 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.