Simultaneous extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation
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- CKMfitter Group, Lacker, H. & Menzel, A. J. High Energ. Phys. (2010) 2010: 6. doi:10.1007/JHEP07(2010)006
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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 GF from the muon lifetime measurement with the claimed precision of GF = 1.16637(1) × 10−5 GeV−2. We study how well GF can be extracted within the framework of four generations from leptonic and radiative μ and τ decays, as well as from Kℓ3 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, Kℓ3 decays and leptonic decays of charged pions we find a p-value of 2.6 % for the fourth generation matrix element |Ue4| = 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.