Determination of the strong coupling constant and the Collins-Soper kernel from the energy-energy correlator in $e^+e^-$ collisions

Abstract: We have conducted the first simultaneous global fit of the strong coupling constant $\alpha_s$ and the Collins-Soper (CS) kernel using the energy-energy correlators (EEC) of $e^{+} e^{-}$ collisions in the back-to-back limit. This analysis, based on the transverse-momentum-dependent (TMD) factorization of EEC at next-to-next-to-next-to-leading logarithmic ($\rm{N}^{3} \rm{LL}$) accuracy, yields $\alpha_s$ consistent with the world average. We have tested two different parametrizations for the non-perturbative CS kernel and found both to align with results obtained from lattice QCD and fits on semi-inclusive deep inelastic scattering and Drell-Yan process.