Effect of isoscalar and isovector scalar fields on baryon semileptonic decays in nuclear matter

Abstract

The precise determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements is very important, because it could be a clue to new physics beyond Standard Theory. This is particular true of $V_{ud}$, because it is the main contribution to the unitary condition of the CKM matrix elements. The level of accuracy for the test of the unitarity involving the element $V_{ud}$ is now of the order of $10^{-4}$. Because the precise data for $V_{ud}$ is usually extracted from super-allowed nuclear $\beta$ decay, it is quite significant to investigate the breaking of SU(3) flavor symmetry on the weak vector coupling constant in nuclear matter. The purpose of this paper is to investigate how the isoscalar scalar ($\sigma$) and the isovector scalar ($\delta$ or $a_0$) mean-fields affect the weak vector and axial-vector coupling constants for semileptonic baryon (neutron, $\Lambda$ or $\Xi^-$) decay in asymmetric nuclear matter. To do so, we use the quark-meson coupling (QMC) model, where nuclear matter consists of nucleons including quark degrees of freedom bound by the self-consistent exchange of scalar and vector mesons. We pay careful attention to the center of mass correction to the quark currents in matter. We then find that, for neutron $\beta$ decay in asymmetric nuclear matter, the defect of the vector coupling constant due to the $\delta$ field can be of the order of $10^{-4}$ at the nuclear saturation density, which is the same amount as the level of the current uncertainty in the measurements. It is also interesting that, in neutron-rich matter, there exists a certain low density at which isospin symmetry is restored, that is, the $u$-$d$ quark mass difference vanishes. We conclude that the effect of the isoscalar scalar and the isovector scalar fields should be considered in baryon semileptonic decays in nuclei.