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

Abstract

Several recent studies performed on constraints of a fourth generation of quarks and leptons suffer from the ad-hoc assumption that 3 × 3 unitarity holds for the first three generations in the neutrino sector. Only under this assumption is one able to determine the Fermi constant G F from the muon lifetime measurement with the claimed precision of G F = 1.16637(1) × 10−5 GeV−2. We study how well G F can be extracted within the framework of four generations from leptonic and radiative μ and τ 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. In the combined fit to leptonic and radiative μ and τ 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 e4| = 0 of the neutrino mixing matrix. 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.