The possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu-Jona-Lasinio model including the Kobayashi-Maskawa-'t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi-Maskawa-'t Hooft interaction is included, due to the flavor mixing effect. It is also shown that the two kinds of tensor condensates may coexist in a certain quark chemical potential due to the flavor mixing.
A possibility of a quark spin polarization originated from a pseudovector condensate is investigated in the three-flavor Nambu-Jona-Lasinio model with the Kobayashi-Maskawa-'t Hooft interaction which leads to flavor mixing. It is shown that a pseudovector condensate related to the strange quark easily occurs compared with pseudovector condensate related to light quarks. Further, it is shown that the pseudovector condensate related to the strange quark appears at a slightly small chemical potential by the effect of the flavor mixing due to the Kobayashi-Maskawa-'t Hooft interaction.
We propose a new parametrisation of the Cabibbo-Kobayashi-Maskawa Matrix in which the approximations of the standard parametrisation, $|V_{cb}|\approx s_{23}$, $|V_{us}|\approx s_{12}$, are promoted to exact results.
Magnetic quadrupole moment of $W$-boson in Kobayashi-Maskawa model, I.B. Khriplovich and M.E. Pospelov, BUDKERINP 93--88 Due to CP-invariance violation a vector particle can acquire T- and P-odd electromagnetic moment, magnetic quadrupole one. The W-boson magnetic quadrupole moment is calculated in the Kobayashi-Maskawa model. This is the only known CP-odd moment arising in this model in two-loop approximation.
I discuss some general aspects of diagonalizing the quark mass matrices and list all possible parametrizations of the Cabibbo-Kobayashi-Maskawa matrix (CKM) in terms of three rotation angles and a phase. I systematically study the relation between the rotations needed to diagonalize the Yukawa matrices and various parametrizations of the CKM.
We explore the possible tie between the naturalness of having a very small strong CP $θ$ parameter in the Kobayashi-Maskawa Model and the flavor symmetry. We provide many examples in which the flavor symmetry group at high energy can naturally give rise to Kobayashi-Maskawa Model at low energy with a naturally small theta.
Using the on-shell scheme and the general linear R_xi gauge we have calculated the one-loop amplitude W+ -> u_I d_j. In agreement with previous work we have shown that the Cabibbo-Kobayashi-Maskawa (CKM) matrix ought to be renormalized. We show how to renormalize the CKM matrix and, at the same time, obtain a gauge independent W decay amplitude.
Based on the relation between CP-violation phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, a new constraint on the parameters of Wolfenstein's parametrization is given. The result is consistent with the relative experimental results and can be further put to the more precise tests in future.
The flavor changing charged currents of the weak sector of the Standard Model are studied in the framework of a quantum statistical approach. The quantum superposition of same-type quarks, generated by the Cabibbo-Kobayashi-Maskawa matrix, is used to define three density matrices, one for each quark family. The properties of such density matrices are analyzed, in particular, the associated von Neumann entropy. It is proven that, due to the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, the quantum mixtures of quarks resulting from the weak interaction do not increase entropy and, therefore…
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix, and found there is still not an integrated prescription to all loop levels. In this paper We propose a new prescription which is designed for all loop levels in the present perturbative theory. This new prescription will keep the unitarity of the bare CKM matrix and make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent.
The hypothesis of a real Cabibbo-Kobayashi-Maskawa matrix has been considered and found to be disfavoured by present measurements even when neglecting results from CP violation in neutral Kaon decay. The Best Linear Unbiased Estimator has been used as a statistical approach to compute the Confidence Level. A new way to take into account the information from Bs mesons oscillations has been considered, reducing considerably the error on extractions of rho and eta parameter of the Wolfenstain parametrization of the matrix.
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
We discuss the formulas for one-to-one correspondence between the two popular parametrizations of the quark mixing matrix and the confidence limits for the mixing parameters.
Based on the relation between weak CP phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, the ranges of rho and eta have been estimated by using the best known two KM matrix elements Vud and Vcd (or Vus). It is found that, the upper limit on eta is about 0.008 which is consistent with that estimated by Wolfenstein more than ten years ago but far small than the present popular estimation.
In 1970, Kobayashi and Maskawa concluded that an effective six-quark vertex with a determinantal form is necessary in the chiral effective models to account for the large mass of $X$ meson, which is now called the $η'$. The determinantal interaction has an $SU(3)_L \otimes SU(3)_R$ symmetry but not $U(3)_L \otimes U(3)_R$, and, hence accounts for the explicit breaking of $U(1)_A$ symmetry in quantum chromodynamics (QCD); the vertex was later derived by 't Hooft as an instanton-induced quark interaction. The vertex, which may be called the Kobayashi-Maskawa-'t Hooft (KMT) term, is widely used i…
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix at one-loop level. We emphasize at one prescription which is formulated with reference to the case of no mixing of quark's generations and point out that it doesn't make the physical amplitude involving quark mixing ultraviolet finite. We then propose a revised prescription to solve this problem and simultaneously keep the unitarity of the CKM matrix. Through explicit calculations we also prove that in order to keep the CKM matrix gauge independent the unitarity of the CKM matrix must be pr…
We examine the problem of three generation quark flavor mixing in realistic, superstring derived standard--like models, constructed in the free fermionic formulation. We study the sources of family mixing in these models and discuss the necessary conditions to obtain a realistic Cabibbo--Kobayashi--Maskawa (CKM) mixing matrix. In a specific model, we estimate the mixing angles and discuss the weak CP violating phase. We argue that the superstring standard--like models can produce a realistic CKM mixing matrix. We discuss the possible textures of quark mass matrices that may be obtained in thes…
We have investigated the present renormalization prescriptions of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Based on one prescription which is formulated by comparing with the fictitious case of no mixing of quark generations, we propose a new prescription which can make the physical amplitude involving quark's mixing gauge independent and ultraviolet finite. Compared with the previous prescriptions this prescription is very simple and suitable for actual calculations. Through analytical calculations we also give a strong Proof for the important hypothesis that in order to keep …
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix. When considering the prescription which is formulated with reference to the case of zero mixing we find it doesn't satisfy the unitary condition of the bare CKM matrix. After added a delicate patch this problem can be solved at one-loop level. In this paper We generalize this prescription to all loop levels and keep the unitarity of the bare CKM matrix, simultaneously make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent. We also find t…
A piece of the Standard Model presently undergoing intense experimental scrutiny is the Cabibbo Kobayashi Maskawa matrix. Several different measurements are planned to enrich the spectrum of experimental constraints and thus provide one of the most stringent tests of Standard Model validity. The success of this program is closely related to theoretical progress in evaluating QCD matrix elements in a non-perturbative regime, as we need to extract fundamental quark properties from observations on decays involving hadrons. This interplay between experimental and theoretical progress will be illus…
By use of the one-loop renormalization group equations and current experimental data, we study the off-diagonal asymmetries of the Cabibbo-Kobayashi-Maskawa (CKM) matrix at the GUT scale in the framework of the standard model as well as its two Higgs and supersymmetric extensions. It is concluded that the possibility of a symmetric CKM matrix at the GUT scale has almost been ruled out.
In this paper we give a geometric parametrization to the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and the Jarlskog invariant, which is based on two flag manifolds $SU(3)/U(1)^{2}$. To treat a fourth generation of quarks on CP violation we generalize the parametrization to one based on two flag manifolds $SU(4)/U(1)^{3}$.
The elements of the theory of dynamical expansion of the theory of weak interaction working at the tree level, i.e. the model of dynamical analogy of Cabibbo-Kobayashi- Maskawa matrices, are given. The equation for mass difference of $K^0_1, K^0_2$ mesons or the length of $K^0, \bar K^0$ meson oscillations in the phase volume approach in the frame work of the standard model of the weak interactions and the model of dynamical analogy of Cabibbo-Kobayashi-Maskawa matrices is calculated (in this model the oscillations of $K^0, \bar K^0$ mesons arise at violation of strangeness by $B$ bosons). Com…
A parameter free, model independent analysis of quark mass matrices is carried out. We find a representation in terms of a diagonal mass matrix for the down (up) quarks and a suitable matrix for the up (down) quarks, such that the mass parameters only depend on the six quark masses and the three angles and phase appearing in the Cabibbo-Kobayashi-Maskawa matrix. The results found may also be applied to the Dirac mass matrices of the leptons.
An analysis of Wolfenstein parametrization for the Kobayashi-Maskawa matrix shows that it has a serious flaw: it depends on {\em three} independent parameters instead of {\em four} as it should be. Because this approximation is currently used in phenomenological analyzes from the quark sector, the reliability of almost all phenomenological results is called in question. Such an example is the latest PDG fit from \cite{CA}, p. 150. The parametrization cannot be fixed since even when it is brought to an exact form it has the same flaw and its use lead to many inconsistencies.
A new scenario of baryogenesis is presented, within the split fermions framework. Our model employs a first order phase transition of the localizer field. The standard model (SM), Kobayashi-Maskawa phase induces a sizable CP asymmetry. The usual suppression of CP violation which arises in the SM baryogenesis is absent due to the existence of order one Yukawa couplings before the fermions are localized in the extra dimension. Models of the above type naturally contain B-L violating operators, allowed by the SM symmetries, which induce the baryon asymmetry. Our mechanism demonstrates the followi…
In this work, the postulation that weak CP phase originates in a certain geometry, is further discussed. According to this postulation, the weak CP phase is determined by three mixing angles. So, if we can determine experimentally three elements of the Cabibbo-Kobayashi-Maskawa matrix, we can then determine the whole CKM matrix and correspondingly, the unitarity triangle. We find that the angle gamma is about pi/2 and the weak CP phase delta (delta_{13}) only can exist in the first or fourth quadrant. The conclusions coincide with the relevant analysis. Some other predictions are given in this…
Recent works show that the original Kobayashi-Maskawa (KM) form of fermion mixing matrix exhibits some advantages, especially when discussing problems such as unitarity boomerangs and maximal CP violation hypothesis. Therefore, the KM form of fermion mixing matrix is systematically studied in this paper. Starting with a general triminimal expansion of the KM matrix, we discuss the triminimal and Wolfenstein-like parametrizations with different basis matrices in detail. The quark-lepton complementarity relations play an important role in our discussions on describing quark mixing and lepton mix…
The pure electroweak three-loop mechanism for the induced electric and chromoelectric dipole moments of quarks is studied in the Kobayashi-Maskawa model with three and four generations. In the standard three generation case, this mechanism is found to produce a negligible contribution to the electric dipole moment of neutron. In the presence of the fourth heavy generation, however, pure electroweak corrections are important and might be several times larger than the corresponding QCD contribution for the masses of heaviest quarks $\sim$ 500-600 GeV. The resulting electric dipole moment of neut…
Schwinger operator method is applied for studying CP-odd pure gluonic effective Lagrangian in the Standard Model at three-loop level. The induced $θ$-term vanishes by the same reasons as EDMs of quark and W-boson to two-loop approximation. A simple way is found to demonstrate these cancellations. All other terms of the effective Lagrangian acquire non-vanishing contributions. The effective operator of dimension six, Weinberg operator, is calculated explicitly. The corresponding contribution to the EDM of neutron is much smaller than that comes from large distances.
The Standard Model fulfills the three Sakharov conditions for baryogenesis. The smallness of quark masses suppresses, however, the CP violation from the Kobayashi-Maskawa phase to a level that is many orders of magnitude below what is required to explain the observed baryon asymmetry. We point out that if, as a result of time variation in the Yukawa couplings, quark masses were large at the time of the electroweak phase transition, then the Kobayashi-Maskawa mechanism could be the source of the asymmetry. The Froggatt-Nielsen mechanism provides a plausible framework where the Yukawa couplings …
The LEP investigation of the Bd and Bs oscillations and of the Cabibbo-Kobayashi-Maskawa matrix element Vub improve the constraints on the other elements of this matrix. From a fit to the experimental data and the theory calculations it is possible to determine the vertex of the unitarity triangle as: rho = 0.155 -0.105 +0.115 eta = 0.383 -0.060 +0.063. The corresponding values of its angles, in their customary definition in terms of sines for alpha and beta, are: sin(2 alpha) = 0.08 -0.50 +0.43 sin(2 beta) = 0.75 +/- 0.10 gamma = 68 +/- 15o. The fit also yields indirect information on the com…
CP-violating interaction of quarks and W-bosons with the scalar field background is studied in the Kobayashi-Maskawa with with Standard Model content of flavors and with additional heavy generation of fermions. The corresponding two-loop induced formfactors are calculated at zero temperature. The results are generalized at large momentum transfers to take into account the CP-violating effects in the Higgs boson decay. The inclusion of this interaction into the scheme of adiabatic baryogenesis at the temperature of electroweak phase transition suffers from the uncertainties come from the poor k…
Taking use of the relation between weak CP phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, the uncertainty coming from the weak interaction can be reduced, furthermore, by means of the relation between the calculation result about mixing parameter epsilon from the box diagrams and the related experimental data in K0-K0bar system, the parameter Bk can be extracted. We take Vud, Vub and Vtb as inputs, when we let them vary in the ranges 0.9745<=Vud<=0.9760, 0.0018<=Vub<=0.0045 and 0.9991<=Vtb<=0.9993, we find the permitted window for Bk is 0.4…
We study the effects of tree-level flavor changing neutral current and its present status with Cabibbo-Kobayashi-Maskawa matrix. Especially, we remark the effects of flavor changing neutral current on the unitary triangle of Cabibbo-Kobayashi-Maskawa matrix. In the case when the unitarity is nearly conserved, we find that the allowed FCNC in the $db$ sector is $\left| {{z_d}^{db}}/{V_{CKM}^{td} {V_{CKM}^{tb}}^\ast} \right| \sim O({10}^{-2})$, from the evaluation of the present bounds for the mixing size of neutral $B$ meson ($x_d$), and the $CP$ violation parameter in the neutral $K$ meson ($ε…
We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave-function renormalization contributions, and to implement the on-shell renormalization of the former with non-diagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormali…
We show that the Kobayashi-Maskawa (KM) parametrization of the 3 X 3 lepton flavor mixing matrix is a useful language to describe the phenomenology of neutrino oscillations. In particular, it provides us with a convenient way to link the genuine flavor mixing parameters (θ_1, θ_2, θ_3 and δ_KM) to their effective counterparts in matter (\tildeθ_1, \tildeθ_2, \tildeθ_3 and \tildeδ_KM). We rediscover the Toshev-like relation sin \tildeδ_KM sin 2\tildeθ_2 = sin δ_KM sin 2θ_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matt…
A small upper-bound is obtained for the CP phase $δ$ in a CKM matrix, $|\sinδ| \le 0.44$ based on CP independent data on $|V_{ub}/V_{cb}|$ alone. Potential inconsistencies with the CKM model in existing data which need a theory beyond the standard model to overcome emerge in the analysis using this CKM matrix. In addition, all CP asymmetry measurables for the $B_d- \bar B_d$ system are expressed solely by the CP phases in the decay amplitudes. Remarkably the CP asymmetry of the bench mark process $B_d\to ψK_S$ equals sin$2δ$. This will soon be measured by BaBar and Belle to confront the above …
Every nonsingular fermion mass matrix, by an appropriate unitary transformation of right-chiral fields, is equivalent to a triangular matrix. Using the freedom in choosing bases of right-chiral fields in the minimal standard model, reduction to triangular form reduces the well-known ambiguities in reconstructing a mass matrix to trivial phase redefinitions. Furthermore, diagonalization of the quark mass sectors can be shifted to one charge sector only, without loosing the concise and economic triangular form. The corresponding effective triangular mass matrix is reconstructed, up to trivial ph…
The structure of the mixing matrix, in the electroweak quark sector with four generations of quarks is investigated. We conclude that the area of the unitarity quadrangle is not a good choice as a possible measure of the CP~violation. In search of new physics we analyze how the existence of the 4-th quark family may influence on the values of the Cabibbo-Kobayashi-Maskawa matrix and we show that one can test for the existence of the 4-th generation using the Jarlskog invariants of the known quarks only. The analysis based on the measured unitary triangle exhibits some tension with the assumpti…
The paper is devoted to a discussion of general properties of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. First we propose a general method of a recursive construction of the CKM matrix for any number of generations. This allows to set up a parameterization with desired properties. As an application we generalize the Wolfenstein parameterization to the case of 4 generations and obtain restrictions on the CKM suppression of the fourth generation. Motivated by the rephasing invariance of the CKM observables we next consider the general phase invariant monomials built out of the CKM matrix elemen…
The CKM-matrix V is written as a linear combination of the unit matrix I and a matrix U which causes intergenerational-mixing. It is shown that such a V results from a class of quark-mass matrices. The matrix U has to be hermitian and unitary and therefore can depend at most on 4 real parameters. The available data on the CKM-matrix including CP-violation can be reproduced by $V=(I+iU)/\sqrt{2}$. This is also true for the special case when U depends on \textit{only 2 real parameters}. There is no CP-violating phase in this parametrization. Also, for such a V the invariant phase $Φ\equiv ϕ_{12}…
The elements of the theory of vacuum oscillations and the model of dynamical expansion of the theory of weak interactions works at the tree level, i.e. the model of dynamical analogy of Cabibbo-Kobayashi- Maskawa matrices and its further development, are given. It is shown that the quarks and massive vector bosons must be structural and these structural particles (subparticles) must interact to generate quark and vector boson masses. In this case the problem of singularity cancellations does not arise in this model. It is also shown that, for self consistency of the theory, the weak decays of …
The aim of the paper is to make a comparison between the unitarity condition method and the standard version of the unitarity triangle approach by using as parameters four independent moduli $|U_{ij}|$. This choice is motivated by the measurability property and leads to a simple criterion for the separation of unistochastic matrices from the double stochastic ones, whose fulfillment is the key point of any global fit for the CKM entries. In our formulation both the methods are exact, do not depend on any assumption as the smallness of some parameter and both can be used to global fits in the q…
A natural procedure is presented to measure the angle $γ$ from the decay $B^{\pm} \to π^{\pm}π^+π^-$. It is based in the Dalitz plot fitting analysis. Neither amplitudes nor strong phases have to be known a priori. We present simulations of this decay computing both statistical and theoretical uncertainties and analyze the experimental feasibility. We found that $γ$ could be measured with a combined error of the order of 20$^o$ with 90% of CL after about a couple of years of running of the first generation of B factories.
We show that the existence of a possible fourth heavy generation of quarks gives rise to a significant enhancement to the neutron electric dipole moment in comparison with the Standard Model prediction. The smaller degree of suppression in this case is linked to the presence of the operators of dimension $\leq$ 6 which enter into the effective Lagrangian with coefficients proportional to the square of the top quark mass. Numerically, the enhancement is mainly associated with chromoelectric dipole moment of the s quark which appears at three loop level, of the order $\al_s\al_w^2m_sm_t^2/m^4_w$…
Starting from a characteristic biinvariance property of Higgs potentials in gauge theories with nonunitary parallel transporters, we explain how quarks of different flavor can acquire different masses by spontaneous symmetry breaking and what is the difference between colour and flavor. We present a gauge theoretic model where the Cabbibo-Kobayashi-Maskawa matrix becomes computable in principle. The model lives on a five dimensional space time with two four dimensional boundaries R and L a small distance d apart. Right handed quarks and leptons live on R and left handed quarks and leptons on L…
Within the perturbative QCD approach, we investigated the Cabibbo-Kobayashi-Maskawa-favored $B \to \overline{D} S$ ("$S$" denoting the scalar meson) decays on the basis of the two-quark picture. Supposing the scalar mesons are the ground states or the first excited states, we calculated the the branching ratios of 72 decay modes. Most of the branching ratios are in the range $10^{-4}$ to $10^{-7}$, which can be tested in the ongoing LHCb experiment and the forthcoming Belle-II experiment. Some decays, such as $B^+ \to \overline{D}^{(*)0} a_0^+(980/1450)$ and $B^+ \to D^{(*)-} a_0^+(980/1450)$,…
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust non-diagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remai…
We report on an exact method for global fits of the CKM matrix by using the necessary and sufficient conditions the data have to satisfy in order to find a unitary matrix compatible with them, and this method can be applied to both quark and lepton CKM matrices. The key condition writes $-1\le\cosδ\le 1$ where $δ$ is the phase that encodes the CP violation, and it is obtained when one describes the CKM matrix in terms of four moduli of its entries. We use it to reconstruct many approximate unitary matrices from the PDG data, and by using the double stochasticity property of the unitary matrice…
A complete review of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and of the experimental methods for their determination is presented. A critical analysis of the relevant experimental results, and in particular of the most recent ones, allows to improve the accuracies of all the matrix elements. A chi-square minimization with the three-family unitarity constraint on the CKM matrix is performed to test the current interpretation of the CP violating phenomena inside the Standard Model. A complete and unambiguous solution satisfying all the imposed constraints is found. As a by-product of…
Rephasing Invariant Formula for CP Phase in Kobayashi-Maskawa Parametrization and Exact Sum Rule with Unitarity Triangle $δ_{\rm PDG} + δ_{\rm KM} = π- α+ γ$
Saitama University（埼玉大学）；Yokohama National University（横滨国立大学）
We study the success to describe hyperon semileptonic decays of four models that incorporate second-order SU(3) symmetry breaking corrections. The criteria to assess their success is by determining V_{us} in each of the three relevant hyperon semileptonic decays and comparing the values obtained with one another and also with the one that comes from K_{l3} decays. A strong dependence on the particular symmetry breaking model is observed. Values of V_{us} which do not agree with the one of K_{l3} are generally obtained. However, in the context of chiral perturbation theory, only the model whose…
Flavour mixing and CP violation as measured in weak decays and mixing of neutral mesons are a fundamental tool to test the Standard Model (SM) and to search for new physics. New analyses performed at the LHC experiment open an unprecedented insight into the Cabibbo-Kobayashi-Maskawa (CKM) metrology and new evidence for rare decays. Important progress has also been achieved in theoretical calculations of several hadronic quantities with a remarkable reduction of the uncertainties. This improvement is essential since previous studies of the Unitarity Triangle did show that possible contributions…
Several pieces of direct and indirect evidence now suggest that the Kobayashi-Maskawa mechanism plays a distinguished role for CP violation at the electroweak scale. This talk provides a general overview of CP violation in its various contexts, emphasizing CP violation in flavour-violating interactions, such as due to the Kobayashi-Maskawa mechanism. I then review a few recent theoretical developments relevant to the interpretation of CP violation.
In this review we present and discuss the determination of the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameter $V_{cb}$. The CKM matrix parametrizes the weak charged current interactions of quarks in the Standard Model (SM), and a precise determination of its elements has always been one of the most important targets of particle physics. The precise knowledge of the $|V_{cb}|$ value plays a pivotal role in testing the flavour sector of the SM and in the analyses of the unitarity of the CKM matrix. The SM does not predict the values of the CKM matrix elements, which have to be…
