A Simple Way to Estimate the Value of $\bar{\alpha}\equiv\alpha(m^2_Z)$

Abstract

To obtain the value of electromagnetic coupling constant at $q^2=m^2_Z$, $\bar{\alpha}$, which plays a key role in electroweak physics one has to integrate the cross-section of $e^+e^-$-annihilation into hadrons divided by $(s-m^2_Z)$ over $s$ from threshold to infinity. By combining, for each flavor channel, the contribution of lowest resonance with the perturbative QCD continuum, we obtain $1/\bar{\alpha} = 128.90\pm 0.06 $ a result which is close to known result obtained with purely experimental inputs, i.e. $1/\bar{\alpha} = 128.87\pm 0.12$.