NLO Oriented Event-Shape Distributions for Massive Quarks

Abstract

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

v2: references added, new section on Monte Carlo strategy added, some typos fixed, matches journal version

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Cited by in corpus (2)

• Transverse Momentum-Dependent Heavy-Quark Fragmentation at Next-to-Leading Order
• Precision $e^{+}{e}^{-}$ Hemisphere Masses in the Dijet Region with Power Corrections