Energy-Energy Correlation in the back-to-back region at N$^3$LL+NNLO in QCD

Abstract

We consider the Energy-Energy Correlation (EEC) function in high-energy electron-positron annihilation to hadrons. In the back-to-back (two-jet) region, we perform the all-order resummation of the logarithmically-enhanced contributions in QCD perturbation theory up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. Away from the back-to-back region, we consistently combine resummed predictions with the known fixed-order results up to next-to-next-to-leading order (NNLO) and we are able to obtain an accurate fit of the $\mathcal{O}(\alpha_S^3)$ remainder function from the numerical QCD computation of the full spectrum. All perturbative terms up to order $\alpha_S^3$ are included in our calculation and a non-trivial cross-check in the back-to-back region is obtained by comparing the SCET analytic calculation against the corresponding numerical QCD computation. In particular, the values of the $\mathcal{O}(\alpha_S^3)$ resummation coefficients have been numerically verified. We regularize the Landau singularity of the QCD coupling within the so-called Minimal Prescription and we discuss the reduction of the perturbative scale dependence of distributions at higher orders, as a means to estimate the corresponding residual perturbative uncertainty. Finally, after introducing within a dispersive approach non-perturbative power corrections, we are able to obtain an accurate description of experimental data at LEP and SLC accelerators.