Calculated corrections to superallowed Fermiβdecay: New evaluation of the nuclear-structure-dependent terms

Abstract

The measured f t-values for superallowed 0 + → 0 + nuclear β-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-KobayashiMaskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -it still fails by more than two standard deviations -but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.

Recent developments in precision electroweak physics

“…In particular |V ud | can be determined by the ratio of G V β /G µ , where G V β and G µ are respectively the vector coupling in β decay and the µ decay constant. The most precise determination of |V ud | is from superallowed 0 + →0 + transitions, currently yielding |V ud | = 0.9740(5) [27]. Combining with |V us | from kaon and hyperon decays and |V ub | from b decays, this yields a 2.3σ discrepancy ∆ = 0.0032 (14).…”

Q value of the superallowed decay of Mg22 and the calibration of the Na21(p,γ) experiment

“…The conserved vector current (CVC) hypothesis states that the vector current interaction is not modified by the presence of the strongly interacting nuclear system so that exactly the same value of G V should be obtained from each superallowed decay. The existing set of nine precisely determined transitions confirms this CVC expectation at the 3 ϫ 10 −4 level [1]. The resultant average value of G V , together with the Fermi coupling constant from the pure-leptonic decay of the muon, yields the most precise available value for V ud , the up-down quark mixing element of the CabibboKobayashi-Maskawa (CKM) matrix.…”

“…However, the small theoretical corrections that must be applied to these data, especially those that have a dependence on nuclear structure effects, are more problematic and they contribute the bulk of the uncertainty. New superallowed emitters whose calculated structure-dependent corrections cover a wider range of values than those characterizing the currently known cases are considered to provide the most useful laboratory in which to test these corrections [1]. If the new Ft values covering a wider range of corrections still produce values of G V consis-tent with CVC, then one can be more confident of the lessscattered corrections used in the unitarity test so far.…”

“…In reality, it exhibits some effects of isospin symmetry breaking but only at the percent level, the same level at which the radiative corrections contribute to the transition. The ft value for such a decay, obtained from measurements of the lifetime, Q value, and branching ratio, can be corrected for these small effects to yield an Ft value, which has the simple form [1] Ft ϵ ft͑1…”

“…This matrix is a rotation matrix connecting the weak and mass eigenstates of the quarks and, as such, must be unitary within the standard model. Currently, the most demanding test of CKM unitarity [1,2] comes from the top-row sum,…”