NLO oriented event-shape distributions for massive quarks

Abstract

Abstract In this article we compute the cross section for the process e + e − → Q Q ¯ + X $$ {e}^{+}{e}^{-}\to Q\overline{Q}+X $$ , with Q a heavy quark, differential in a given event shape e and the angle θ T 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 θ T 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 O $$ \mathcal{O} $$ (α s ). Our results show that, for the vector current, there is a non-zero O α s 0 $$ \mathcal{O}\left({\alpha}_s^0\right) $$ 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 O $$ \mathcal{O} $$ (α s ) 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.

Keywords

• Jets and Jet Substructure
• Quark Masses
• Top Quark