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" event fraction, restricted to the two-jet region and excluding the forward region, whose calculation at first order requires to consider real emission diagrams only, in $D=4$ space-time dimensions (no need to consider virtual diagrams or take $D\ne 4$). 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 $\chi$.