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 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.

Muon decay in orbit spectra for μ − e conversion experiments

We have determined in detail the electron spectrum in the decay of bound muons. These results are especially relevant for the upcoming μ − e conversion experiments.

The long-term stability of self-esteem: Its time-dependent decay and nonzero asymptote

How stable are individual differences in self-esteem? We examined the time-dependent decay of rank-order stability of self-esteem and tested whether stability asymptotically approaches zero or a nonzero value across long test–retest intervals. Analyses were based on 6 assessments across a 29-year period of a sample of 3,180 individuals aged 14 to 102 years. The results indicated that, as test–retest intervals increased, stability exponentially decayed and asymptotically approached a nonzero value (estimated as .43). The exponential decay function explained a large proportion of variance in observed stability coefficients, provided a better fit than alternative functions, and held across gender and for all age groups from adolescence to old age. Moreover, structural equation modeling of the individual-level data suggested that a perfectly stable trait component underlies stability of self-esteem. The findings suggest that the stability of self-esteem is relatively large, even across very long periods, and that self-esteem is a trait-like characteristic.