Effect of Nucleon Structure Variation in Super-allowed Fermi Beta-decay

There is a well known anomaly between the value of the Fermi decay constant extracted from super-allowed Fermi beta-decay of nuclear isotriplets and that required by unitarity of the Cabibbo-Kobayashi-Maskawa matrix. This discrepancy remains at the level of a few tenths of a percent after the most rigorous investigation of conventional nuclear and radiative corrections. Within the framework of the quark-meson coupling model of nuclear matter, which has been previously applied successfully to phenomena such as nuclear saturation and nuclear charge symmetry violation, we show that it is possible to understand a significant fraction of the observed anomaly. [email protected] [email protected] 1 It is clearly very important to refine our understanding of the weak coupling to quarks as much as possible. Testing the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is one of the more challenging aspects of this general problem. In particular, the most accurate experimental measurement of the vector coupling constant in nuclear beta-decay comes from super-allowed 0-0 transitions between nuclear isotriplet states. However, in order to relate these precise measurements to the quark-level vector coupling, Vud, one needs to apply a number of small nuclear structure corrections [1] in addition to the relatively standard radiative corrections [2]. Despite intensive study of these nuclear “mismatch” corrections [3, 4, 5, 6] there remains a systematic difference of a few tenths of a percent between the value of Vud inferred from the vector coupling measured in muon decay, Gμ, and unitarity of the CKM matrix and those determined from the nuclear ftvalues. For recent summaries we refer to the reviews of Wilkinson [7] and Towner and Hardy [8], and also to the recent report by Savard et al. [9] of accurate data on C. Until now the nuclear corrections have been explored within the framework of conventional nuclear theory with point-like nucleons. Of course, for the nucleon itself there has been considerable investigation of the effect on the vector form-factor of the breaking of CVC caused by the small u-d mass difference in QCD. The Ademollo-Gatto theorem [10, 11] tells us that any corrections must be of second order in (md −mu) – a result that has survived [12, 13] suggestions that it might fail because of ρ-ω mixing [14]. While this is necessarily very small, the measurements of Vud and Gμ are also extremely precise. Thus we have been led to ask whether this small nuclear discrepancy might be associated with a change in the degree of non-conservation of the vector current caused by nuclear binding. In order to investigate whether nuclear binding might influence the Fermi decay constant of the nucleon itself one needs a model of nuclear structure involving explicit quark degrees of freedom which nevertheless provides an acceptable description of nuclear binding and saturation. The quark-meson coupling (QMC) model of Guichon [15] seems ideally suited to the problem. In this model, nuclear matter consists of non-overlapping