Improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi β decay

Abstract

We report new shell-model calculations of the isospin-symmetry-breaking correction δ C to superallowed 0 + → 0 + nuclear β decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pickup reactions. In addition, where new sets of effective interactions have become available since our last calculation, we now include them; this leads to small changes in δ NS as well. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent "inner" radiative term, V R , and a nucleus-dependent "outer" term, δ R . We tabulate the new values for δ C , δ NS , and δ R for 20 superallowed transitions, including the 13 currently well-studied cases. With these new correction terms, the corrected Ft values for the 13 cases are statistically consistent with one another, and the anomalousness of the 46 V result disappears. These new calculations lead to a lower average Ft value and a higher value for V ud . The sum of squares of the top-row elements of the Cabibbo-Kobayashi-Maskawa matrix now agrees exactly with unitarity.

Beta-Decay Studies in N ≈ Z Nuclei Using No-Core Configuration-Interaction Model

“…It is gratifying to see that also individual DFT values of δ C are consistent within 2σ with the values calculated in Ref. [11] (see Fig. 7 of Ref.…”

Isospin-breaking corrections to superallowed Fermiβdecay in isospin- and angular-momentum-projected nuclear density functional theory

“…In turn, it is also the most precise source of the matrix element V ud = G V /G µ of the Cabibbo-Kobayashi-Maskawa (CKM) three-generation quark mixing matrix [2,[7][8][9]. This is so because the leptonic coupling constant, G µ /( c) 3 = 1.16637(1) × 10 −5 GeV −2 , is well known from the muon decay [9].…”

“…In Eq. (3), ∆ V R = 2.361(38)% stands for the nucleusindependent part of the radiative correction [5], δ ′ is a transition-dependent (Z-dependent) but nuclearstructure-independent part of the radiative correction [2,5], and δ NS denotes the nuclear-structure-dependent part of the radiative correction [2,6].…”

“…[1][2][3][4] and references cited therein. Since these corrections are small, of the order of a percent, they can be approximately factorized and arranged in the following way:…”

“…For precise tests of the Standard Model, only these transitions that have f t-values known with a relative precision better than a fraction of a percent are acceptable. Currently, 13 "canonical" transitions spreading over a wide range of nuclei from A = 10 to A = 74 meet this criterion (have f t-values measured with accuracy of order of 0.3% or better) and are used to evaluate the values of G V and V ud [2].…”