Abstract
The energy-energy correlator (EEC) is an event shape observable which probes the angular correlations of energy depositions in detectors at high energy collider facilities. It has been investigated extensively in the context of precision QCD. In this work, we introduce a novel definition of EEC adapted to the Breit frame in deep-inelastic scattering (DIS). In the back-to-back limit, the observable we propose is sensitive to the universal transverse momentum dependent (TMD) parton distribution functions and fragmentation functions, and it can be studied within the traditional TMD factorization formalism. We further show that the new observable is insensitive to experimental pseudorapidity cuts, often imposed in the Laboratory frame due to detector acceptance limitations. In this work the singular distributions for the new observable are obtained in soft collinear effective theory up to $\mathcal{O}(\alpha_s^3)$ and are verified by the full QCD calculations up to $\mathcal{O}(\alpha_s^2)$. The resummation in the singular limit is performed up to next-to-next-to-next-to-leading logarithmic accuracy. After incorporating non-perturbative effects, we present a comparison of our predictions to PYTHIA 8 simulations.
Highlights
Event shape observables are measures of the energy flow, multiple particle correlations, and the radiative patterns in high energy collisions
In the back-to-back limit, the observable we propose is sensitive to the universal transverse momentum dependent (TMD) parton distribution functions and fragmentation functions, and it can be studied within the traditional TMD factorization formalism
In this work we introduce a new definition of energy correlator (EEC) in the Breit frame, which is the natural frame for the study of transverse momentum dependent (TMD) physics [31]
Summary
Event shape observables (such as thrust, C-parameter, etc.) are measures of the energy flow, multiple particle correlations, and the radiative patterns in high energy collisions. For π − θ ∼ 1 the distribution is very well described by the fixed order QCD calculations, while in the back-to-back limit resummation of enhanced logarithms is required for reliable predictions To this end, in the back-to-back limit, the cross section can be factorized, within the soft-collinear effective theory (SCET) framework [32,33,34,35,36], as a convolution of TMD beam, soft, and TMD fragmentation functions, which share the same operator definitions as in the conventional single hadron semi-inclusive DIS factorization. We propose a Lorentz invariant definition of EEC in DIS in the Appendix
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