The evaluation of V(ud) and its impact on the unitarity of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix
TL;DR: In this paper, the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vud is reviewed and theoretical radiative and isospin-symmetry breaking corrections are applied.
Abstract: The determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element Vud is reviewed. Data from 0+ → 0+ superallowed beta decay in nuclei, neutron decay, beta decay of odd-mass mirror nuclei and pion beta decay are considered. Theoretical radiative and isospin-symmetry breaking corrections are applied. The most precise result comes from the nuclear 0+ → 0+ decays, which yield a recommended value of |Vud| = 0.974 25(22). We further summarize the data leading to the CKM matrix element Vus: Kl3 decays, Kl2 decays, hyperon decays and hadronic tau decay. Again SU(3)-symmetry breaking corrections (from lattice QCD) and radiative corrections are applied. We adopt values from Kl3 decay of |Vus| = 0.2246(12) and from Kl2 decay of |Vus/Vud| = 0.2319(14). From the three data just cited, a least squares fit determines two CKM matrix elements: |Vud| = 0.974 25(22) and |Vus| = 0.225 21(94). Data leading to the third member of the top row of the CKM matrix, Vub, are summarized as well but, being of order 10−3, that matrix element contributes negligibly to the unitarity sum, |Vud|2 + |Vus|2 + |Vub|2. We find this sum to be 0.999 90(60) showing unitarity to be satisfied to a precision of 0.06%. We discuss the constraints this result places on selected extensions to the standard model.
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...In the foregoing discussion, we have used the phenomenological constraint on the mixing angle ξ obtained from tests of first row CKM unitarity[158]....
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...5× 10−4 and that | sin ξ| < ∼ 10−3 from tests of first row CKM unitarity[158], we see that |dn| < ∼ (3× 10−14e fm) ( 1− M 2 1 M(2) 2 ) cos θL cos θR sinα ....
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...Meanwhile, the Coulomb exchange ter m [311] is crucial for understanding the isospin symmetry-breaking correcti ons to the superallowed β decays [312] in order to test the unitarity of the Cabibbo-Ko bayashi-Maskawa matrix [313]....
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TL;DR: In this article, it was shown that no CP-violating interactions exist in the quartet scheme without introducing any other new fields, and that the strong interaction must be chiral SU ( 4) X SU( 4) invariant as precisely as the conservation of the third component of the iso-spin.
Abstract: In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang ing neutral current and that the quartet model is free from this difficulty. Fur thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:
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CERN1
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Abstract: An analysis of leptonic decays based on unitary symmetry for strong interactions (eightfold way) and the V-A theory for weak interactions is presented. An explanation for the observed predominance of the LAMBDA yields + e/sup -/ + nu decay over the LAMBDA /sup -/ yields n + e/sup -/ + nu decay is obtained. Branching ratios predicted for electron modes with DELTA S, 1 are presented; the ratios for the above decays agree well with experimental results. (D.C.W.)
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TL;DR: In this article, the Kobayashi-Maskawa matrix is expanded in powers of a small parameter equal to $sin{\ensuremath{\theta}}_{c}=0.22$ and the term of order is determined from the measured $B$ lifetime.
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