Simultaneous Extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation

Several recent studies performed on constraints of a fourth generation of quarks and leptons suffer from the ad-hoc assumption that 3 x 3 unitarity holds for the first three generations in the neutrino sector. Only under this assumption one is able to determine the Fermi constant G_F from the muon lifetime measurement with the claimed precision of G_F = 1.16637 (1) x 10^-5 GeV^-2. We study how well G_F can be extracted within the framework of four generations from leptonic and radiative mu and tau decays, as well as from K_l3 decays and leptonic decays of charged pions, and we discuss the role of lepton universality tests in this context. We emphasize that constraints on a fourth generation from quark and lepton flavour observables and from electroweak precision observables can only be obtained in a consistent way if these three sectors are considered simultaneously. In the combined fit to leptonic and radiative mu and tau decays, K_l3 decays and leptonic decays of charged pions we find a p-value of 2.6% for the fourth generation matrix element |U_{e 4}|=0 of the neutrino mixing matrix.