On the experimental determination of the leptonic decay constant of pseudoscalar mesons

The decay constant in $M_{l2\mathrm{}}$ decays cannot be determined precisely because of the presence of model dependence in the virtual radiative corrections and in the accompanying bremsstrahlung process. In a previous paper we showed that this problem can be solved, at least as far as experimental analysis is concerned, by introducing a modified decay constant and provided hard bremsstrahlung photons are discriminated. Nevertheless, the present experimental detection of energetic photons does not yet allow for the discrimination ability required by our results. In order to give our results a more immediate usefulness, we explore the possibility of relaxing the requirement on the elimination of all such photons. We find that in $M_{\mu 2}$ decays this requirement can be substantially relaxed, allowing for less restrictive experimental setups. Our results can be traced back to a theorem due to Burnett and Kroll and Bell and Van Royen.