NLO oriented event-shape distributions for massive quarks

Abstract

In this article we compute the cross section for the process $$ {e}^{+}{e}^{-}\to Q\overline{Q}+X $$ e + e − → Q Q ¯ + X , with Q a heavy quark, differential in a given event shape e and the angle θT between the thrust axis and the beam direction. These observables are usually referred to as oriented event shapes, and it has been shown that the θT dependence can be split in two structures, dubbed the unoriented and angular terms. Since the unoriented part is already known, we compute the differential and cumulative distributions in fixed-order for the angular part up to $$ \mathcal{O} $$ O (αs). Our results show that, for the vector current, there is a non-zero $$ \mathcal{O}\left({\alpha}_s^0\right) $$ O α s 0 contribution, in contrast to the axial-vector current or for massless quarks. This entails that for the vector current one should expect singular terms at $$ \mathcal{O} $$ O (αs) as well as infrared divergences in real- and virtual-radiation diagrams that should cancel when added up. On the phenomenological side, and taking into account that electroweak factors enhance the vector current, it implies that finite bottom-mass effects are an important correction since they are not damped by a power of the strong coupling and therefore cannot be neglected in precision studies. Finally, we show that the total angular distribution for the vector current has a Sommerfeld enhancement at threshold.