Contributions of the W-boson propagator to the μ and τ leptonic decay rates

Ferroglia, Andrea; Greub, Christoph; Sirlin, Alberto; Zhang, Zhibai (2013). Contributions of the W-boson propagator to the μ and τ leptonic decay rates. Physical review. D - particles, fields, gravitation, and cosmology, 88(3), 033012. Melville, N.Y.: American Physical Society 10.1103/PhysRevD.88.033012

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We derive closed expressions and useful expansions for the contributions of the tree-level W-boson propagator to the the muon and tau leptonic decay rates. Calling M and m the masses of the initial and final charged leptons, our results in the limit m=0 are valid to all orders in M^2/M_W^2. In the terms of O(m_j^2/M_W^2) (m_j=M,m), our leading corrections, of O(M^2/M_W^2), agree with the canonical value (3/5) M^2/M_W^2, while the coefficient of our subleading contributions, of O(m^2/M_W^2), differs from that reported in the recent literature. A possible explanation of the discrepancy is presented. The numerical effect of the O(m_j^2/M_W^2) corrections is briefly discussed. A general expression, valid for arbitrary values of M_W, M and m in the range M_W>M>m, is given in the Appendix. The paper also contains a review of the traditional definition and evaluation of the Fermi constant.

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