Factorization of the energy–energy correlation in the two-jet limit in the massive case

Abstract

We consider non-logarithmic heavy-quark mass effects in the factorization and resummation of the Energy–Energy-Correlation (EEC) function, in the two-jet limit. We define a new partial EEC cumulant, normalized at a fixed correlation angle \(\chi _M<\pi .\) At first order, the back-to-back endpoint coefficient cancels in this ratio, while the forward endpoint does not enter. The result can therefore be obtained from the real-emission EEC distribution in \(D=4\) space-time dimensions, without determining the endpoint contributions separately. In order to determine explicitly the next-to-leading order coefficient function and the remainder function (both entering the standard resummation formula), we evaluate numerically the EEC spectrum at first order in \(\alpha _S,\) finding good agreement with previous calculations. To have a smooth massless limit, a new, improved factorization scheme is proposed, in which the coefficient function also depends on the correlation angle \(\chi .\)