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Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both $theta_{13}$ and $theta_{23}$ or only $theta_{13}$ are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The $Z_7$ symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the $Delta(6N^2)$ series are also briefly discussed.
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This report contains the results of the Workshop on the CKM Unitarity Triangle, held at CERN on 13-16 February 2002 to study the determination of the CKM matrix from the available data of K, D, and B physics. This is a coherent document with chapters covering the determination of CKM elements from tree level decays and K and B meson mixing and the global fits of the unitarity triangle parameters. The impact of future measurements is also discussed.
We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $lambda^2$, from $lambda^2$ to $lambda^8$. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics.
In this letter we propose a multi-Higgs extension of the standard model with Abelian and non-Abelian discrete symmetries in which the mass matrices of the charged fermions obtained from renormalizable interactions are diagonal. Corrections induced by non-renormalizable interactions deviate these matrices from the diagonal form. Active neutrinos acquire mass only from non-renormalizable interactions. The main entries of the neutrino mass matrix arise only through dimension five operators, while the diagonal entries arise only from dimension six operators.
Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional parameters, which limit the predictive power of this scheme. In this work, we introduce the scheme of quasi-eclectic flavor symmetries as a simple fix. These symmetries are the direct product of a modular and a traditional flavor symmetry, which are spontaneously broken to a diagonal modular flavor subgroup. This allows us to construct a version of Feruglios model with the Kaehler terms under control. At the same time, the starting point is reminiscent of what one obtains from explicit string models.
We compute the renormalization of the complete CKM matrix in the MSbar scheme and perform a renormalization group analysis of the CKM parameters. The calculation is simplified by studying only the Higgs sector, which for the beta-function of the CKM matrix is at one loop the same as in the full Standard Model. The renormalization group flow including QCD corrections can be computed analytically using the hierarchy of the CKM parameters and the large mass differences between the quarks. While the evolution of the Cabibbo angle is tiny V_{ub} and V_{cb} increase sizably. We compare our results with the ones in the full Standard Model.
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