Next-to-Leading-Order Corrections to Momentum Correlations in $Z^0 \to b\bar{b}$

TL;DR

The paper addresses the problem of computing next-to-leading-order QCD corrections to momentum correlations in $Z^0\to b\bar b$ to assess their impact on $R_b$ determinations. It presents a complete NLO calculation of heavy-flavour production in $e^+e^-$ annihilation including mass effects, and implements infrared-safe final states that allow a partonic event generator to be used for arbitrary shape observables; cross-checks against the massless limit and other contemporary calculations are performed. The authors derive and evaluate expansions for $ abla\langle (1-x_1)(1-x_2)\rangle$ and $\langle 1-x\rangle$ in powers of $\alpha_s$, obtaining $r = (\alpha_s/(2\pi))\, b + (\alpha_s/(2\pi))^2\,(c+2ab-a^2) + \mathcal{O}(\alpha_s^3)$ and computing $r$ and $r'$ for various heavy-quark masses and scales; numerically, radiative corrections are found to be modest (e.g., with $\alpha_s(M_Z)=0.118$, $r_{LO}\approx 0.0116$ and $r_{NLO}\approx 0.0146$). The study also discusses the smallness of potential non-perturbative power corrections via renormalon arguments, supporting the reliability of the perturbative results. Overall, the NLO corrections do not spoil the leading-order conclusions and reinforce the perturbative stability of the observable.

Abstract

We recently completed a calculation of the process $e^+e^- \to Q\bar{Q}+X$, where Q is a heavy quark, at order $O(α_s^2)$. As a first application of this calculation we compute the momentum correlations of $b\bar{b}$ pairs at next-to-leading-order. This quantity is interesting since it may affect the determination of $R_b$ as measured in $Z^0$ decays. We find that the next-to-leading corrections are of moderate size, thus confirming the conclusions that can be drawn from the leading-order calculation.

Figures (1)

• Figure 1: Some of the diagrams contributing to the process $Z\,\hbox{$\rightarrow$}\, Q\bar{Q}+X$: a Born graph (a), a virtual graph (b), a real emission graph (c), and a real emission graph with light quarks in the final state (d).