Extracting alpha_s from Electron-Positron Annihilation around 10 GeV

Abstract

The total cross section for electron-positron annihilation into hadrons is calculated in the region just below the B meson threshold. QCD corrections up to third order, quark mass effects, initial state radiation, the running of alpha_QED and the tails of the Upsilon resonances are included in the prediction. For given alpha_s the prediction is accurate to 0.5 percent. An experimental measurement with the corresponding precision would allow to determine alpha_s with high accuracy at intermediate energies.

Figures (4)

• Figure 1: (a) The differential cross section ${\rm d}\sigma(e^+ e^- \to \tau^+ \tau^-)/{\rm d}z$ and (b) the cutoff dependent cross section $\sigma(z > z_0)$ in nb for the centre of mass energy $E_1 = 10.52$ GeV as functions of $z$ and $z_0$, respectively.
• Figure 2: The relative shift in $\alpha(s)$ as a function of $\sqrt{s}$ from the hadronic plus leptonic vacuum polarization as described in the text.
• Figure 3: (a) $R_{\rm had}(s)$ as defined in eq. (\ref{['eqRhad']}), and (b) only the contributions from the light ($u$, $d$ and $s$) quark currents for different values of $\alpha_s$.
• Figure 4: Dependence of the hadronic cross section $\sigma(e^+ e^- \to {\rm hadrons})$ on the cutoff in the minimal invariant mass of the hadronic system, $m_{\rm min}$, for the two energies $E_1 = 10.52$ GeV, $E_2 = 9.98$ GeV and $\alpha_s(M_Z) = 0.120$.