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تسجيل مستخدم جديدThe CKM Matrix and the Unitarity Triangle
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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.
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Some fine differences between the twin $b$-flavored unitarity triangles are calculated by means of a generalized Wolfenstein parametrization of the CKM matrix, and a possibility of experimentally establishing the second triangle is briefly discussed.
We find that the apexes of these two triangles, characterized respectively by $(overline{rho}, overline{eta})$ and $(widetilde{rho}, widetilde{eta})$, are located on the same circular arc in the complex plane. This observation provides us with a new way to test consistency of the CKM picture of CP violation in the quark sector and probe possible new physics. The differences between the apexes (i.e., $widetilde{rho} - overline{rho}$ and $widetilde{eta} - overline{eta}$) are found to be of ${cal O}(lambda^2)$ with $lambda simeq 0.22$ being the Wolfenstein expansion parameter, and the shapes of these two triangles are found to be insensitive to the two-loop renormalization-group-equation running effects up to the accuracy of ${cal O}left(lambda^4right)$.
We give a review of the status of the global effort to measure the sides of the CKM Unitarity Triangle.
We present an update of the Unitarity Triangle (UT) analysis, within the Standard Model (SM) and beyond. Within the SM the main novelties are the inclusion in epsilon_K of the contributions of xi and phi_epsilon eq pi/4 pointed out by A.J. Buras and
D. Guadagnoli, and an accurate prediction of BR(B -> tau nu), by using the indirect determination of |V_ub| from the UT fit, which can be compared to the present experimental result. In the generalization of the UT analysis to investigate New Physics (NP) effects, the estimate of xi is more delicate and only the effect of phi_epsilon eq pi/4 has been included. We confirm an hint of NP in the B_s-bar B_s mixing at the 2.9 sigma level, which makes a comparison with new experimental data certainly desired.
We present the status of the Unitarity Triangle Analysis (UTA), within the Standard Model (SM) and beyond, with experimental and theoretical inputs updated for the ICHEP 2010 conference. Within the SM, we find that the general consistency among all t
he constraints leaves space only to some tension (between the UTA prediction and the experimental measurement) in BR(B -> tau nu), sin(2 beta) and epsilon_K. In the UTA beyond the SM, we allow for New Physics (NP) effects in (Delta F)=2 processes. The hint of NP at the 2.9 sigma level in the B_s-bar B_s mixing turns out to be confirmed by the present update, which includes the new D0 result on the dimuon charge asymmetry but not the new CDF measurement of phi_s, being the likelihood not yet released.
We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in
the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (Delta M)_d/(Delta M)_s and sin(2 beta) measured first through the CP asymmetry in B_d^0 to psi K_S and later in K to pi nu nubar decays. Also suitable ratios of the branching ratios for B to X_{d,s} nu nubar and B_{d,s} to mu^+ mu^- and the angle gamma measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the non-universal triangles extracted in each model using epsilon, (Delta M)_d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.
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