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

We derive closed expressions and useful expansions for the contributions of the tree-level W-boson propagator to 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((MMW2)-M-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.