The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL′

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order ((NLO)-L-3) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation - the jet function - from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at (NLO)-L-3. We combine the newly obtained (NLO)-L-3 jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at (NLL)-L-3' accuracy, resulting in a factor of similar to 4 reduction of uncertainties in the peak region compared to (NLL)-L-3 predictions.

Automated summary

We present an analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order ((NLO)-L-3) in the back-to-back limit. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET). By incorporating a recently calculated jet function at (NLO)-L-3, we successfully predict the EEC in the back-to-back limit. Our analysis agrees with previous results in N = 4 supersymmetric Yang-Mills theory, and we also obtain the first resummation of the EEC in the back-to-back limit at (NLL)-L-3' accuracy.