We propose that the CP violating phase in the CKM mixing matrix is identical to the CP phases responsible for the spontaneous CP violation in the Higgs potential. A specific multi-Higgs model with Peccei-Quinn (PQ) symmetry is constructed to realize this idea. The CP violating phase does not vanish when all Higgs masses become large. There are flavor changing neutral current (FCNC) interactions mediated by neutral Higgs bosons at the tree level. However, unlike general multi-Higgs models, the FCNC Yukawa couplings are fixed in terms of the quark masses and CKM mixing angles. Implications for meson-anti-meson mixing, including recent data on $D-\bar D$ mixing, and neutron electric dipole moment (EDM) are studied. We find that the neutral Higgs boson masses can be at the order of one hundred GeV. The neutron EDM can be close to the present experimental upper bound.
The CKM matrix describing quark mixing with three generations can be parameterized by three mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP violating quantities, $α$, $β$ or $γ$ in the unitarity triangle as the phase in the CKM matrix, and construct explicit $α$, $β$ and $γ$ parameterizations. Approximate Wolfenstein-like expressions are also suggested.
The CKM matrix describing quark mixing with three generations can be parameterized by three Euler mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use the most accurately measured CP violating angle $β$ in the unitarity triangleas the phase in the CKM matrix, and construct an explicit $β$ parameterization. We also derive an approximate Wolfenstein-like expression for this parameterization.
The current analysis of the Cabibbo-Kobayashi-Maskawa(CKM) quark mixing matrix uses the standard parametrisation by 3 mixing angles and the CP-violating KM phase. However it would be more convenient to express these mixing angle parameters in terms of the known CKM matrix elements like $V_{ud}$, $ V_{us}$, $ V_{ub}$, $V_{cb}$ and the CP-violating phase $δ$. The other CKM matrix elements are then expressed in terms of these known matrix elements instead of the standard mixing angles. In this paper, using $V_{ud}$, $ V_{us}$, $ V_{ub}$ and $V_{cb}$ from the current global fit, we show that the m…
The Standard Model for CP violation, the CKM model, works very well in explaining all laboratory experimental data. However, this model does not address the question that where it comes from. The origin of CP violation is still a mystery. In this talk I discuss a model\cite{model} addressing this problem in which the CP violating phase in the CKM matrix is identical to the phase in the Higgs potential resulting from spontaneous CP violation.
The first principle derivation of kinetic transport equations suggests that a CP-violating mass term during the electroweak phase transition can induce axial vector currents. Since the important terms are of first order in gradients there is a possibility to construct new rephasing invariants that are proportional to the CP phase in the Cabibbo-Kobayashi-Maskawa matrix and to circumvent the upper bound of CP-violating contributions in the Standard Model, the Jarlskog invariant. Qualitative arguments are given that these new contributions still fail to explain electroweak baryogenesis in extens…
The picture of CP-violation in orbifold compactifications in which the $T$-modulus is at a complex fixed point of the modular group is studied. CP-violation in the neutral kaon system and in the neutron electric dipole moment are both discussed. The situation where the $T$-modulus takes complex values on the unit circle which are not at a fixed point is also discussed.
We show that in a Complementary two-Higgs doublet model(C2HDM) the CP violating phase in the CKM matrix can be generated spontaneously, dangerous FCNC can be naturally suppressed and the strong CP problem can also be avoided. The two Higgs doublets in the model are complementary in the sense that none of them is enough to describe masses of a given type of quarks. We find that the strength of FCNC is suppressed by the strength of Yukawa couplings of the first generation quark and the tree-level FCNC is sufficiently small. Using an explicit example, we show that radiative correction to the assu…
It is pointed out that the recent measurement of the angle $γ$ of the unitarity triangle, providing irrefutable evidence for a complex Cabibbo-Kobayashi-Maskawa (CKM) matrix, presents a great challenge for supersymmetric models with spontaneous CP violation. We construct a new minimal extension of the minimal supersymmetric standard model (MSSM), with spontaneous CP breaking, which leads to a complex CKM matrix, thus conforming to present experimental data. This is achieved through the introduction of two singlet chiral superfields and a vector-like quark chiral superfield which mixes with the…
We study the influence of penguin (especially, electroweak penguin) effects on some methods of measuring the angles $α$, $β$, and $γ$ in the CKM unitarity triangle. We use next-to-leading order effective Hamiltonian, and present numerical estimates based on the factorization approximation. We find that some techniques suggested in the literature, especially for $α$ determination, are not workable in light of the electroweak penguin effects. Nevertheless, there are methods that would work for each angle determination. For angle $β$ we consider $B \rightarrow D^{+} D^{-}$ mode and estimate the p…
We propose a new method to extract the CP violating weak phase $γ$ (the phase of $V_{ub}^*$) in the CKM paradigm of the Standard Model, using $B^- \rightarrow D^0 π^- \rightarrow f π^-$ and $B^- \rightarrow \bar D^0 π^- \rightarrow f π^-$ decays, where $f$ are final states such as $K^+ π^-$, $K^+ ρ^-$, $K ππ$, {\it etc.} We also study the experimental feasibility of our new method. With possibility of new phases in the CKM matrix, we re-examine some of the previously proposed methods to determine $γ$, and find that it would be in principle possible to identify $γ$ and a new phase angle $θ$ sep…
A shape of the unitary triangle versus a CP violating parameter δdepends on the phase conventions of the CKM matrix, because the CP violating parameter δcannot directly be observed, so that it is not rephasing-invariant. In order to seek for a clue to the quark mass matrix structure and the origin of the CP violation, the dependence of the unitary triangle shape on the parameter δis systematically investigated.
We use the perturbative QCD methods of Lepage and Brodsky to calculate the rate for B-bar_s -> rho K_s, with an eye toward the CP violating unitarity triangle angle gamma. We show that, although the penguins are large, there are regions of the allowed parameter space of the Cabibbo-Kobayashi-Maskawa mixing matrix wherein gamma is measurable in the sense that penguins change the value of sin(2gamma) one would extract from the attendant time dependent asymmetry measurement by less than 29 per cent, so that a 3sigma measurement of sin(2gamma) as being different from 0 is allowed by the correspond…
We analyse the general constraints on unified gauge models with spontaneous CP breaking that satisfy the conditions that (i) CP violation in the quark sector is described by a realistic complex CKM matrix, and (ii) there is no significant flavor changing neutral current effects in the quark sector. We show that the crucial requirement in order to conform to the above conditions is that spontaneous CP breaking occurs at a very high scale by complex vevs of standard model singlet Higgs fields. Two classes of models are found, one consisting of pure Higgs extensions and the other one involving fe…
The standard CKM model can be tested and New Physics detected using only CP-violating phase measurements in B decays. This requires the measurement of a phase factor which is small in the Standard Model, in addition to the usual large phases $β$ and $γ$. We also point out that identifying violations of the unitarity of the CKM matrix is rather difficult, and cannot be done with phase measurements alone.
The first principle derivation of kinetic transport equations suggests that a CP-violating mass term during the electroweak phase transition can induce axial vector currents. Since the important terms are of first order in gradients there is a possibility to construct new rephasing invariants that are proportional to the CP phase in the Cabibbo-Kobayashi-Maskawa matrix and to circumvent the upper bound of CP-violating contributions in the Standard Model, the Jarlskog invariant.
The 3 X 3 CKM matrix defines six unitarity triangles in the complex plane, which will be carefully explored in the LHCb experiment and at the Super-B factory. We calculate the running effects of nine different inner angles and eighteen different sides of the six triangles from the electroweak scale to a superhigh-energy scale by using the one-loop renormalization-group equations, and demonstrate that all the nine angles are stable against radiative corrections. In particular, we find that the CP-violating angle αis most insensitive to the changes of energy scales.
The non-zero Dirac phases $δ^q$ and $δ^l$ in the CKM and PMNS mixing matrices signify CP violation. In general they are independent. Experimental data including recent T2K results show, however, that in the original KM parameterization for the mixing matrix, the sum $δ^q_{\rm KM} + δ^l_{\rm KM}$ is close to zero with $δ^q_{\rm KM}$ to be approximately $π/2$. The KM parameterization may have provided some hints that these phases are actually related and CP is maximally violated. We show that this sum rule can be accommodated in models with spontaneous CP violation where both phases originate fr…
Precise lattice QCD results for hadronic matrix elements, decay constants and form factors play a crucial role in the determination of CKM matrix elements and in the identification of possible new physics contributions to flavour violating observables. This article reviews the implications of recent lattice QCD results on the phenomenology of flavour and CP violating meson decays, and highlights some future directions for lattice QCD calculations which would have a major impact on flavour phenomenology.
This article surveys the important questions attached to unitarity tests of the Cabibbo-Kobayashi-Maskawa matrix, with a focus on the direct determinations of the magnitude of CKM matrix elements. The current CKM anomalies are discussed and the clear-cut prospects at LHCb and Belle II envisaged. The anticipated precision on $C\!P$-conserving and $C\!P$-violating observables at the projected upgrades of the LHCb and Belle~II experiments is examined from the point of view of the search for New Physics in $B$-meson mixing, addressing the bottlenecks in precision for the interpretation of the meas…
We analyze the impact of the forthcoming CP-violating observables in the $B_s\to K^+ K^-$ system, combined with the precise measurement of $\sin2β$ , in the extraction of the CKM matrix. Computing the penguin parameters $(r, θ)$ within QCD factorization yields a precise determination of $(\barρ, \barη)$, reflected by a weak dependence on $θ$, which is shown to be a second order effect. Using the SU(3)-flavour symmetry argument and the current $B$-factories data provided by the $B_d \to π^+ π^-$ modes, we complement the $B_s \to K^+ K^-$ CP-violating observables in a variety of ways, in particu…
The multi-Higgs models having spontaneous CP violation (SPCV) and natural flavor conservation (NFC) lead to a real CKM matrix $V$ contradicting current evidence in favour of a complex $V$. This contradiction can be removed by using a generalized $μ$-$τ$ (called 23) symmetry in place of the discrete symmetry conventionally used to obtain NFC. If 23 symmetry is exact then the Higgs induced flavour changing neutral currents (FCNC) vanish as in case of NFC. 23 breaking introduces SPCV, a phase in $V$ and suppressed FCNC among quarks. The FCNC couplings $F_{ij}^{d,u}$ between $i$ and $j$ generation…
CP-violating asymmetries in $B \to ππ$ and $B \to ρρ$ decays can help specify the weak phase $ϕ_2 = α$ of the Cabibbo-Kobayashi-% Maskawa (CKM) matrix. We discuss the impact of improved measurements of these processes such as will be available in the near future, finding special value in better measurement of the time-dependent CP violation parameter $S_{00}$ in $B^0 \to π^0 π^0$ and $B^0 \to ρ^0 ρ^0$. Reducing the errors on $B \to ρρ$ measurements by a factor of two can potentially lead to an error in $ϕ_2 = α$ just above $2^\circ$, at which level isospin-breaking corrections must be consider…
The CKM and PMNS matrices have been constructed based on the latest measurements, largely free from theoretical inputs as well as likely NP effects in the case of the former. To facilitate the construction of the CKM matrix in the PDG representation as well as in view of the comparatively large error in the measured value of the CP violating phase δ, the possibility of its construction from the tree level measured CKM elements has also been explored using the unitarity triangle. In view of the persistent difference between the |V_{ub}| exclusive and inclusive values, we have carried out separa…
We investigate the prediction on the lepton phases in theories with a non trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices. We show that the actual evidence, under the only assumption that the correlation matrix $V^M$ product of $CKM$ and $PMNS$ has a zero in the entry $(1,3)$, gives us a prediction for the three CP-violating invariants $J$, $S_1$, and $S_2$. A better determination of the lepton mixing angles will give a strong prediction of the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. To clarify how our pre…
We address the question of whether the CP violating phase in the CKM mixing matrix can be the only source of all CP violation. We show that in supersymmetric models with new flavour structure beyond the Yukawa matrices, the CKM phase can generate the required baryon asymmetry and also accounts for all observed results in K and B systems, in particular $ε'/ε$ and the CP asymmetry of $B \to ϕK_S$.
We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is therefore also fixed. The mass matrix for neutrinos is constrained leading to constraints on the Jarlskog CP violating parameter $J$, and the effective mass $<m_{ββ}>$ for neutrinoless double beta decay. The Yuka…
Natural 4 zeros texture mass matrices recently proposed by Fritzsch and Xing have been investigated by including `non-leading'corrections in the context of latest data regarding m_t^{pole} and V_{CKM} matrix elements. Apart from accommodating m_t^{pole} in the range 175\pm15 GeV, |V_{cb}| and |V_{ub}/V_{cb}|=0.08\pm0.02, the analysis with maximal CP-violation predicts |V_{td}| = .005-.013. Further, the CP-violating phase angle δcan be restricted to the ranges (i) 22^o -45^o and (ii) 95^o - 130^o, concretizing the ambiguity regarding phase of CKM matrix. Furthermore, we find that non-leading ca…
We review the present status of the CKM matrix and we offer some visions of its future. After a brief presentation of the theoretical framework for weak decays we discuss the following topics: i) CKM matrix from tree level decays, ii) Standard analysis of the unitarity triangle, iii) CKM matrix from rare and CP violating K- and B-decays, iv) CKM matrix from CP violation in two-body B-decays. In particular we compare the CKM potentials of the standard analysis of the unitarity triangle, of the very clean K --> πν\barνdecays and of CP asymmetries in B-decays.
We show that the quark flavour structure and CP violating phenomena are strongly correlated in supersymmetric theories. For a generic pattern of supersymmetry breaking the two broad categories of Yukawa couplings, democratic and hierarchical textures, have entirely different phenomenological implications. With hierarchical Yukawas, the rephasing invariant phase, arg(V_us V_cb V_cb^* V_cs^*), in the CKM mixing matrix has to be of order unity, while the SUSY CP violating phases are severely constrained by electric dipole moments, giving rise to the so-called SUSY CP problem. With democratic Yuka…
We study the contribution to flavor changing neutral current processes from box diagrams with light higgsinos and squarks. Starting with just the Cabbibo Kobayashi Maskawa (CKM) phase, we find contributions to the $K^0$ and $B^0$ meson mass matrices that are out of phase with the Standard Model contributions in the case of substantial mixing between the up-type squarks. This difference in phase could be large enough to be detected at the proposed $B$ factories, with interesting implications for the unitarity triangle of CKM matrix elements.
Loop corrections for physics beyond the Standard Model are computed. DWe discuss the influence of new physics on CP-violating observables. Assuming the standard model gives a correct description of tree level processes, we show how a consistent procedure can determine the parameters of the standard model and check its validity also in loop induced processes. A method to include new physics in a systematic way is sketched.
Recent interest in flavour or horizontal symmetry building (mass textures) has been spurred mainly by the large top mass and, hence, the strong hierarchy in quark masses. Recently, various symmetry breaking schemes have been proposed based on the discrete, non-Abelian group S3L x S3R, which is broken according to S3L x S3R > S3_diag > S2_diag. The group S3 treats three objects symmetrically, while the hierarchical nature of the Yukawa matrices is a consequence of the representation structure, 1 + 2, of S3, which treats the generations differently. Different ansaetze for the breaking of the sub…
The Jarlskog rephasing invariant parameter $|J|$ is evaluated using one of the six Unitarity Triangles involving well known CKM matrix elements \vud, \vus,~\rub, ~\vcd, ~\vcs~ and ~\vcb. With PDG2000 values of \vud~ etc. as input, we obtain $|J|=(2.71 \pm 1.12) \times 10^{-5}$, which in the PDG representation of CKM matrix leads to the range $21^o~to~159^o$ for the CP violating phase $δ$. The CKM matrix elements evaluated using this range of $δ$ are in agreement with the PDG CKM matrix. The implications of refinements in the input on $|J|$, $δ$ and CKM matrix elements have also been studied.
Motivated by the recent determination of the top quark mass by the CDF collaboration, $\mt =174 \pm 10 ^{+13}_{-12}$ GeV, we review and update constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model. In performing these fits, we use inputs from the measurements of $\abseps$, the CP-violating parameter in $K$ decays, $\xd = (\delm)/Γ$, the mixing parameter in \bdbdbar\ mixing, the present measurements of the matrix elements $\absvcb$ and $\absvub$, and the $B$-hadron lifetimes. The CDF value for $\mt$ considerably reduces the CKM-parameter space previous…
We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa matrix. We show that to leading order in the mass and CKM hierarchies the scaling of the mixings $|V_{ub}|^2$, $|V_{cb}|^2$, $|V_{td}|^2$, $|V_{ts}|^2$ and of the rephase-invariant CP-violating parameter $J$ is universal to all orders in perturbation theory. In leading order the other CKM elements do not scale. Imposing the constraint $λ_b=λ_τ$ at the GUT scale determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.
These lectures give an introduction and the current status of flavour physics in the quark sector, with special attention to the CKM matrix and CP violation. We describe the measurements which contribute to the determination of the CKM matrix elements and how, together with important theoretical developments, they have significantly improved our knowledge on the flavour sector of the Standard Model. These lectures are complemented by the seminar of U. Mallik (see these proceedings) which describes in more details the most recent CP-violating related measurements by the B-factories. The results…
We discuss the usefulness of the CP violating semi-leptonic asymmetry a_{SL} not only as a signal of new physics, but also as a tool in constraining the CKM parameters. We show that this technique could yield useful results in the first years of running at the B factories. We present the analysis graphically in terms of M_{12}, the dispersive part of the B-Bbar mixing amplitude. This is complementary to the usual unitarity triangle representation and often allows a cleaner interpretation of the data.
The small quark mixing, described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model, may be a clue to reveal new physics around the TeV scale. We consider a simple scenario that extra particles in a hidden sector radiatively mediate the flavor violation to the quark sector around the TeV scale and effectively realize the observed CKM matrix. The lightest particle in the hidden sector, whose contribution to the CKM matrix is expected to be dominant, is a good dark matter (DM) candidate, so we focus on the contribution, and discuss the DM physics. In this scenario, there is an …
Recent measurements of CP violating asymmetries have led to a significant progress in our understanding of CP violation. The implications of the experimental results for the Kobayashi-Maskawa mechanism and for new physics are explained.
If CP violation in the decays of neutral kaons is due to phases in the weak couplings of quarks, as encoded in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, there are many other experimental consequences. Notable among these are CP-violating rate asymmetries and triangle relations among decay rates in $B$ meson decays, while charmed particle decays should not be a good place to see CP-violating effects. In the context of the CKM and other models of CP violation, we discuss phenomena such as electric dipole moments, the baryon asymmetry of the Universe, and the strong CP problem, and speculate on…
It is shown that the deconstruction of $[SU(2)\times U(1)]^N$ into $[SU(2)\times U(1)]$ is capable of providing all necessary ingredients to completely impliment the complex CKM mixing of quark flavors. The hierarchical structure of quark masses originates from the difference in the deconstructed chiral zero-mode distribution in theory space, while the CP-violating phase comes from the genuinely complex vacuum expectation value of link fields. The mixing is constructed in a specific model to satisfy experimental bounds on quarks' masses and CP violation.
Neutrino oscillations with three lepton families are described with a unitary mixing matrix U in analogy to the quark mixing matrix V(CKM). If U contains a nontrivial phase, there will be CP- and T-violating asymmetries at distances large compared to E/D**2, where D**2 is the largest difference of neutrino mass squares. The paper presents explicit expressions for these distance-dependent asymmetries.
The unitarity triangles of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are studied in a systematic way. We show that the phases of the nine CKM rephasing invariants are indeed the outer angles of the six unitarity triangles and measurable in the $CP$-violating decay modes of $B_{d}$ and $B_{s}$ mesons. An economical notation system is introduced for describing properties of the unitarity triangles. To test unitarity of the CKM matrix we present some approximate but useful relations among the sides and angles of the unitarity triangles, which can be confronted with the accessible exp…
The recently reported measurements of the CP asymmetry a(psi K) by the BABAR and BELLE collaborations are in good agreement with the standard model (SM) prediction, resulting from the unitarity of the CKM matrix. The so-called minimal flavour violating (MFV) supersymmetric extensions of the standard model, in which the CKM matrix remains the only flavour changing structure, predict a(psi K) similar to the one in the SM. With the anticipated precision in a(psi K) and other CP asymmetries at the B factories and hadron colliders, one hopes to pin down any possible deviation from the SM. We discus…
We review the status of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and the CP-violating phases in the CKM-unitarity triangle. The emphasis in these lecture notes is on $B$-meson physics, though we also review the current status and issues in the light quark sector of this matrix. Selected applications of theoretical methods in QCD used in the interpretation of data are given and some of the issues restricting theoretical precision on the CKM matrix elements discussed. The overall consistency of the CKM theory with the available data in flavour physics is impressive and we quantify thi…
We present a solution to the strong CP problem based on the identification of the theta angle with twice the CP violating phase present in the CKM quark matrix. This solution washes out all the unwanted issues stemming form the strong CP phase and is strongly justified by general theoretical arguments based on the partition function associated to the $θ$ vacuum. Phenomenological consequences on the quark mass matrices are discussed for this case.
Generalizing a previous model to accommodate the third quark family and CP violation, we present a $T^{'}$ model which predicts tribimaximal neutrino (PMNS) mixings while the central predictions for quark mixings are $|V_{td}/V_{ts}| = 0.245$ and $|V_{ub}/V_{cb}| = 0.237$ with a predicted CP violating KM phase $δ_{KM} = 65.8^{0}$. All these are acceptably close to experiment, including the KM phase for which the allowed values are $63^{0} < δ_{KM} < 72^{0}$, and depend only on use of symmetry $T^{'} \times Z_2$ to define the model and no additional parameters.
We consider spontaneous CP violation in the Next to Minimal Supersymmetric Standard Model, without the usual $Z_3$ discrete symmetry. CP violation can occur at tree level, raising a potential conflict with the experimental bounds on the electric dipole moments of the electron and neutron. One escape from this is to demand that the CP violating angles are small, but we find that this entails a light neutral Higgs particle. This is almost pseudoscalar, can have a high singlet content, and will be hard to detect experimentally.
We propose a simple model for the spontaneous CP violation based on $SU(2)_{L}\times U(1)_{Y}\times A_{4}\times CP\times Z_{2}$ symmetry for quarks and leptons in a seesaw framework. In our model CP is spontaneously broken at high energies, after breaking of flavor symmetry, by a complex vacuum expectation value of $A_{4}$-triplet and gauge singlet scalar field. And, certain effective dimension-5 operators are introduced in the quark Lagrangian as an equal footing, which lead the quark mixing matrix to the Cabibbo-Kobayashi-Maskawa (CKM) one in the form, while the lepton Lagrangian is renormal…
We propose a viable minimal model with spontaneous CP violation in the framework of a Two Higgs Doublet Model. The model is based on a generalised Branco-Grimus-Lavoura model with a flavoured $\mathbb{Z}_2$ symmetry, under which two of the quark families are even and the third one is odd. The lagrangian respects CP invariance, but the vacuum has a CP violating phase, which is able to generate a complex CKM matrix, with the rephasing invariant strength of CP violation compatible with experiment. The question of scalar mediated flavour changing neutral couplings is carefully studied. In particul…
We update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model using the latest experimental and theoretical results as input. We present the 95$\%$ C.L. allowed region of the unitarity triangle and the corresponding ranges for the ratio $\vert V_{td}/V_{ts} \vert$ and for the quantities $\sin 2α$, $\sin 2β$ and $\sin^2γ$, which characterize CP-violating rate asymmetries in $B$-decays. The SM prediction for the $\bs$-$\bsb$ mixing ratio $\xs$ is also presented.
We investigate a flexible method in which we can test the unitarity of the quark flavor mixing matrix step-by-step. Singular-Value-Decomposition (SVD) techniques are used in analyzing the mixing matrix over a broader parameter region than the unitarity region. Unitary constraints make us extract CP violating properties without any specific parametrization when the magnitudes of at least three mixing matrix elements in three generation quark mixing are given. This method can also be applied to the analysis of lepton flavor mixing, in which only a few moduli are presently measured.
The necessary complex structures needed for CP violation are not easy to generate and, indeed, CP can be a symmetry in higher dimensional theories. In 4-dimensions CP violation argues for the existence of a scalar sector and, in its simplest manifestation, leads to the CKM model. Further CP violating phases, from an extended scalar sector, are constrained by the requirement of having no FCNC. Although new CP violating phases are expected in SUSY extensions of the SM, the good agreement of data with the CKM model only provides bounds on these phases. Baryogenesis via leptogenesis requires the p…
Motivated by the recent determination of the top quark mass by the CDF collaboration, $\mt =174 \pm 10 ^{+13}_{-12}$ GeV, we review and update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model. In performing our fits, we use inputs from the measurements of the following quantities: (i) $\abseps$, the CP-violating parameter in $K$ decays, (ii) $\delmd$, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements $\absvcb$ and $\absvub$, and (iv) $B$-hadron lifetimes. We find that the allowed region of the unitarity triangle is ve…
We investigate the future determination of the CKM matrix using theoretically clean quantities, like $B(K^+\toπ^+ν\barν)$, $B(K_L\toπ^0ν\barν)$ or $\sin 2β$, $\sin 2α$ as extracted from CP violation studies in $B$ physics. The theoretical status of $K\toπν\barν$ is briefly reviewed and their phenomenological potential is compared with that of CP asymmetries in $B$ decays. We stress the unique opportunities provided by measuring the CP violating rare decay $K_L\toπ^0ν\barν$. It is pointed out that this mode is likely to offer the most precise determination of ${\rm Im}V^*_{ts}V_{td}$ and the Ja…
We present a supersymmetric D-brane model that has CP spontaneously broken by discrete torsion. The low energy physics is largely independent of the compactification scheme and the kahler metric has `texture zeros' dictated by the choice of discrete torsion. This motivates a simple ansatz for the kahler metric which results in a CKM matrix given in terms of two free parameters, hence we predict a single mixing angle and the CKM phase. The CKM phase is predicted to be close to Pi/3.
Motivated by the possibility of the low value of sin2βin the measurements of BABAR and BELLE collaborations, a reference unitarity triangle is constructed using the unitarity of the CKM matrix and the experimental values of the well known CKM elements, without involving any inputs from the processes which might include the new physics effects. The angles of the triangle are evaluated by finding the CP violating phase δthrough the Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix gives for δthe range 28^o to 152^o, which for sin2βtranslates to the …
Our knowledge of quark-flavor physics and CP violation increased tremendously over the past five years. It is confirmed that the Standard Model correctly describes the dominant parts of the observed CP-violating and flavor-changing phenomena. Not only does CP violation provide some of the most precise constraints on the flavor sector, but several measurements performed at the B-factories achieved much better precision than had been expected. We review the present status of the Cabibbo-Kobayashi-Maskawa matrix and CP violation, recollect the relevant experimental and theoretical inputs, display…
