Super-allowed Fermi beta-decay revisited

Abstract

Analysis of J π=0 +→0 + super-allowed Fermi transitions is limited with respect to the precision of its outcome in terms of the Fermi coupling constant neither by the accuracy of the experimental input data nor by the confidence with which the radiative corrections can be applied but rather by knowledge of the nuclear mismatch: the subversion of isospin symmetry along the multiplets. Theoretical estimates of this mismatch differ considerably from author to author; their direct nuclide-by-nuclide application results in an apparent clear violation of the hypothesis of conservation of the vector current and evident inconsistency with unitary of the Cabibbo–Kobayashi–Maskawa matrix. This paper pursues and elaborates the earlier suggestion that, in these unsatisfactory circumstances, the best procedure is to look to the experimental data themselves to determine and eliminate the mismatch by appropriate extrapolation to Z≈0 where the mismatch falls away. This is done: (i) without any prior correction for mismatch; (ii) after correction for the full theoretical mismatch as estimated by various authors; (iii) after correction for nuclide-to-nuclide fluctuations in the theoretical mismatch. These three procedures are individually statistically satisfactory and mutually consistent in their extrapolation to Z≈0 despite the wide variety of the theoretical mismatches upon which they are based; they together yield: V ud 2=0.9514±0.0014 . The resultant unitarity test for the first row of the CKM matrix is V ud 2+ V us 2+ V ub 2=1.0007±0.0017 with the operational vector coupling constant G V */(ℏc) 3=(1.15138±0.00048)×10 −5 GeV −2 .