Radiative corrections toβdecay and the possibility of a fourth generation

Abstract

Leading-logarithmic radiative corrections to β decay are summed via the renormalization group and structure-dependent O(α) effects are estimated by a form-factor analysis. These refinements reduce the Kobayashi-Maskawa quark-mixing-matrix element ‖$V_{\mathrm{ud}}$‖ by 0.13% to 0.9729±0.0012. Combined with $K_{e3}$-, hyperon-, and b-decay constraints, this implies ‖$V_{\mathrm{ud}}$ ${\Vert }^2$+‖$V_{\mathrm{us}}$ ${\Vert }^2$+‖$V_{\mathrm{ub}}$‖ 2 =0.9954±0.0025. Although consistent with unitarity at the 2σ level, our result leaves open the possibility of a fourth fermion generation which at 90% confidence level may have mixing ‖$V_{\mathrm{ub}\mathcal{’}}$‖ as large as 0.088.