Study of muon-pair production at centre-of-mass energies from 20 to 136 GeV with the Aleph detector

The total cross section and the forward-backward asymmetry for the process $e^+ e^- \rightarrow \mu^+ \mu^- (n \gamma)$ are measured in the energy range 20-136 GeV by reconstructing the effective centre-of-mass energy after initial state radiation. The analysis is based on the data recorded with the ALEPH detector at LEP between 1990 and 1995, corresponding to a total integrated luminosity of 143.5 $\mathrm{pb}^{-1}$. Two different approaches are used: in the first one an exclusive selection of events with hard initial state radiation in the energy range 20-88 GeV is directly compared with the Standard Model predictions showing good agreement. In the second one, all events are used to obtain a precise measurement of the energy dependence of $\sigma^0$ and $A_{\mathrm{FB}}^0$ from a model independent fit, enabling constraints to be placed on models with extra Z bosons