We investigate the sensitivity with which two angles of the "flat" unitarity triangle, defined by $V_{ub}^* V_{us} + V_{cb}^* V_{cs} + V_{tb}^* V_{ts} =0$, can possibly be measured directly at FCCee. We show that the measured errors on the angle $α_s = \arg(- V_{ub}^* V_{us} /V_{tb}^* V_{ts})$ and $β_s = \arg(-V_{tb}^* V_{ts} / V_{cb}^* V_{cs})$ should be better than $0.4^\circ$ and $0.035^\circ$, respectively. These measurements, combined with the measurement of the 3rd angle $γ_s = \arg(- V_{cb}^* V_{cs}/ V_{ub}^* V_{us})$, discussed in a different paper, will contribute to probe further the consistency of the CP sector of the Standard Model with unprecedented level of accuracy.
The great progress made recently in the sector of Flavor Physics has enabled to establish CP violation in the B-meson decays. The unitarity triangle derived from the unitarity relation $V_{ub}^* V_{ud} + V_{cb}^* V_{cd} + V_{tb}^* V_{td} = 0$ has been measured very precisely. To further asses our understanding of CP violation, it would be useful to carry out similar measurement of other triangles. In this note, we investigate the triangle derived from the relation $V_{ub}^* V_{us} + V_{cb}^* V_{cs} + V_{tb}^* V_{ts} = 0$. Two angles of this triangle ($α_s$ and $β_s$) could be measured very acc…
The angles of all unitarity triangles of the Cabibbo-Kobayashi-Maskawa matrix are determined from the experimental data. Our analysis is independent of the parameterization of the CKM matrix and it is based on the predictions of the unitarity for the angles and the areas of the unitarity triangles. We note that the lengths of the sides of the four unitarity triangles determined from the experimental data do not form a triangle. We resolve this incompatibility by performing a constrained fit, assuming the equality of the area of the unitarity triangles. We demonstrate that the measured data are…
Following analogy of the `db' triangle in the quark mixing case, we have explored the construction of the `ν_2.ν_3' leptonic unitarity triangle using the Maki-Nakagawa-Sakata matrix obtained by Bjorken {\it et al.} through generalization of the tribimaximal scenario. In particular, for the U_{e3} range 0.05-0.15, the existence of the leptonic unitarity triangle indicates a fairly good possibility of having non zero CP violation.
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…
We generalize the geometrical description of CP violation in the Standard Model in terms of a unitarity triangle. For three left-handed Majorana neutrinos CP violation in the lepton sector is determined by three unitarity triangles. With three additional right-handed neutrinos 15 quadrangles are required to characterize CP violation. We show the relation of the unitarity polygons with physical observables.
In this note I review the current determination of the unitarity triangle parameters by using the theoretical and experimental information available in summer 2000.
The quark mixing matrix is parameterised such that its "Cabibbo substructure" is emphasised. One can choose one of the parameters to be an arbitrarily chosen angle of the unitarity triangle, for example the angle $β$ (also called $Φ_1$).
We describe the present status of the Unitarity Triangle and we give an outlook for its future determinations. We discuss new sets of fundamental flavour parameters and comment briefly on new physics beyond the Standard Model.
The unitarity triangle on the first quadrant in the $ρ-η$ plane is discussed in the framework of the quark mass matrices in the NNI basis. If the quark mass matrices of the up-type is the Fritzsch one and the down-type is the one proposed by Branco et al., respectively, one gets the unitarity triangle with the vertex on the first quadrant. This simple model may be a candidate of the quark mass matrix ansatze, if the allowed region of the vertex of the unitarity triangle is restricted in the first quadrant by future experiments.
The area of the unitarity triangle is a measure of CP-violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and non-oscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish CP-violation. For different values of the CP-violating phase, $δ_D$, the required accuracy of measurements is estimated. The key elements of the method include determination of $|U_{e3}|$ and studies…
Concise variable transformations between the four angles of the CKM matrix in the standard representation advocated by the Particle Data Group and the angles of the unitarity triangles are derived. The behavior of these transformations in various limits is explored. The straightforward extension of this calculation to other representations and more generations is indicated.
By using the most recent determinations of the several theoretical and experimental input parameters, we update the Unitarity Triangle analysis in the Standard Model and discuss the sensitivity to New Physics effects. We investigate the interest of measuring with a better precision the various physical quantities entering the Unitarity Triangle analysis and study in a model independent way whether, despite the undoubted success of the CKM mechanism in the Standard Model, the Unitarity Triangle analysis still allows the presence of New Physics.
After reviewing the present experimental constraints on the unitarity triangle, I discuss the various ways in which new physics can manifest itself in measurements of the parameters of the unitarity triangle. Apart from one exception, which I describe, new physics enters principally through new contributions to B0-B0(bar) mixing. Different models of new physics can be partially distinguished by looking at their effects on rare, flavour-changing $B$ penguin decays. (Invited talk given at the Symposium Twenty Beautiful Years of Bottom Physics, Chicago, IL, USA, June 29 -- July 2, 1997.)
There is no good reason to think that BSM-CP-odd phases(s) will necessarily cause large deviations in B-physics from predictions of the SM. Therefore, residual theory error in extraction of the unitarity triangle can undermine experimental efforts to search for BSM phase(s). We stress that final states containing D0 or D0-bar in decays of charged and neutral B's can yield all the angles of the unitarity triangle with negligble theory error (i.e. O(0.1%)).
Within the Standard Model, a review of the current determination of the CKM unitarity triangle parameters is presented, using experimental constraints from the measurements of |epsilon_K|, V_ub/V_cb, Delta m_d and from the limit on Delta m_s, available by end 1999.
We examine the unitarity triangle of the KM matrix by using the general quark mass matrices on the NNI basis. The Fritzsch anzätz is modified by introducing four additional parameters. The KM matrix elements are expressed in terms of quark mass ratios, two phases and four additional parameters. It is found that the vertex of the unitarity triangle is predicted to be almost in the second quadrant on the $ρ-η$ plane as far as $V_{us}\simeq -{\displaystyle \sqrt{\frac{m_d}{m_s}}e^{ip}+ \sqrt{\frac{m_u}{m_c}}e^{iq}}$ is held.
Decay rates of $B^0(t)\toπ^+π^-,~B^0\toπ^- K^+,~B^+\toπ^+ K^0~ (K_S\toπ^+π^-$) and of charge-conjugate processes are studied within flavor SU(3) symmetry and first-order SU(3) breaking. We show that these measurements can determine with a reasonable accuracy the two angles, $α$ and $γ$, of the Cabibbo-Kobayashi-Maskawa unitarity triangle.
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…
We summarize the present knowledge on the non-perturbative hadronic inputs needed in the analysis of $B^0$-$\bar B^0$ mixing and the CP-violating parameter $\varepsilon$ of the $K^0$-$\bar K^0$ system. Using this information, together with the recently determined value of the top-quark mass, we update the phenomenological constraints on the unitarity triangle.
We construct the CKM unitarity triangle from CP invariant quantities, using the coupling constant of weak decays with flavor change from b to u, and the particle - antiparticle mixing probability in the B_s and B_d systems. Also included are new measurements of the coupling V_us in Kaon decays. Of the two solutions, one agrees perfectly with the triangle constructed from CP violating processes in the K and B meson systems. The common solution yields a triangle with an area of J/2 = (1.51 +/- 0.09) x 10^{-5} and a CP violating phase gamma = 63.1^o +/- 4.0^o.
This is an opening talk for the workshop and is intended to be provocative. We take a stab at the following questions: How well do we really know the sides of the unitarity triangle? What else could we do to improve? (I propose several new measurements). What precision should we ultimately aim at in the determination of CKM elements? What have we learned so far about flavor physics? Where do we go from here?
In this presentation, I review the status of selected Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and their role in the Unitarity Triangle (UT). Since this conference concluded, many new results have been finalized and are included in the new world averages (WAs) in the 2002 edition of the PDG. I will focus here on some outstanding issues in the measurements of the CKM elements in the third row and column.
Geometric representation of CP phases $δ_{\rm PDG}, δ_{\rm KM}$ in flavor mixing matrix and its sum rule by alternative unitarity triangle and quadrangle
We study effects of SUSY particles in the unitarity triangle analysis and the CP asymmetries in b -> s decays. We consider three different SUSY models, the minimal supergravity, SU(5) SUSY GUT with right-handed neutrinos, and MSSM with U(2) flavor symmetry, and show that the patterns and correlations of deviations from the standard model will be useful to discriminate the different SUSY models in future B experiments.
The study of charmless hadronic two-body decays of B mesons is one of the most fascinating topics in B physics. A construction of the unitarity triangle based on such decays is presented, which is independent of B-B(bar) and K-K(bar) mixing. It provides stringent tests of the Standard Model with small theoretical uncertainties.
Phenomenological issues of the CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard and Wolfenstein parametrization of the $CKM$ mixing matrix and unitarity triangle. We discuss the phenomenology of the CP violation in $K^{0}_{L}$ and $B_{d}^{0} (\bar B_{d}^{0})$-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the $K^{0}\leftrightarrows \bar K^{0}$, $B_{d,s}^{0}\leftrightarrows \bar B^{0}_{d,s}$ etc oscillations with neutrino oscillations. In Appendix B we derive the evolution …
We present fits to charmless hadronic B decay data from the BaBar, Belle and Cleo experiments using two theoretical models: (i) the QCD factorization model of Beneke et al. and (ii) QCD factorization complemented with the so-called charming penguins of Ciuchini et al. When we include the data from pseudoscalar-vector decays the results favor the incorporation of the charming penguin terms. We also fit results for the unitarity triangle parameters and the CP-violating asymmetries.
Within a specific texture of the quark mass matrix the notion of a maximal violation of the $CP$ symmetry can be defined. The experimental constraints from weak decays imply that in reality one is close to the case of maximal $CP$ violation, which vanishes as the mass of the $u$--quark approaches zero. The unitarity triangle of the Cabibbo--Kobayashi--Maskawa matrix elements is determined. It is related to the triangle relating the Cabibbo angle to the quark mass ratios in the complex plane. The angle $α$ describing the $CP$ violation in the decay $B_d \rightarrow π^+ π^-$ is close to 90$^{\ci…
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 …
Encouraged by the latest SNO results, we consider the lepton mixing matrix in the approximation that the nu_2 mass eigenstate is trimaximally (democratically) mixed. This suggests a new parameterization of the remaining mixing degrees of freedom, which eschews mixing angles, dealing instead, directly with the complex parameter U_e3 of the mixing matrix. Unitarity triangles then take a particularly simple form, which we hope will faciltate comparison with experiment.
We explain how a four-body amplitude analysis of the $\rm D$ decay products in the mode $\rm B^\pm \to (K^+K^-π^+π^-)_D K^\pm$ is sensitive to the unitarity triangle angle $γ$. We present results from simulation studies which show that a precision on $γ$ of $15^\circ$ is achievable with 1000 events and assuming a value of 0.10 for the parameter $r_B$.
We discuss the exclusive radiative decays B -> K* gamma and B -> rho gamma in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Phenomenological implications for branching ratios and isospin breaking effects are discussed. Special emphasis is placed on constraining the CKM unitarity triangle from these observables.
The values of the elements of the Cabibbo-Kobayashi-Maskawa matrix are constrained by direct and indirect measurements. A fit to experimental data and theory calculations allows the indirect determination of the vertex and angles of the unitarity triangle as: rho = 0.18 +/- 0.07 eta = 0.35 +/- 0.05 sin 2alpha = 0.14 +0.25 -0.38 sin 2beta = 0.73 +/- 0.07 gamma = 63 +8 -11 degrees. Information is derived on the presence of CP violation in the matrix, on non-perturbative QCD parameters and on the Bs oscillation frequency.
We present a solution to the strong CP problem based on spontaneous CP violation and discrete family symmetries. The model predicts in a natural way the almost right-angled quark unitarity triangle angle ($α\simeq 90^\circ$) by making the entries of the quark mass matrices either real or imaginary. By this choice the determinants of the mass matrices are rendered real and hence the strong CP phase vanishes. We present a toy model for the quark sector that demonstrates the viability of our approach.
In a large class of models, the only significant new physics effect on the CP asymmetries in $B \to ψK_S$ and $B \to ππ$ decays is a new contribution to the $B-\bar B$ mixing amplitude. This allows a model independent construction of the CKM Unitarity Triangle (up to hadronic uncertainties). Furthermore, the contributions to the mixing from the Standard Model and from the new physics can be disentangled. A serious obstacle to this analysis is an eightfold discrete ambiguity in solving for the angles of the triangle. Several ways to reduce the ambiguity either by making further measurements, or…
In this paper we present fits to charmless hadronic B decay data from the BaBar, Belle and Cleo experiments using models by Beneke et. al. and Ciuchini et al. When we include the data from pseudo-scalar vector decays (PV) the current experimental results favour the inclusions of a so-called "charming penguin" term. We also present fit results for the Unitary Triangle parameters and the CP violating asymmetries
The status of the Unitarity Triangle beyond the Standard Model including the most recent results on Delta m_s, on dilepton asymmetries and on width differences is presented. Even allowing for general New Physics loop contributions the Unitarity Triangle must be very close to the Standard Model result. With the new measurements from the Tevatron, we obtain for the first time a significant constraint on New Physics in the B_s sector. We present the allowed ranges of New Physics contributions to Delta F=2 processes, and of the time-dependent CP asymmetry in B_s to J/Psi phi decays.
Starting from a (new physics independent) tree level determination of rhobar and etabar, we perform the Unitarity Triangle analysis in general extensions of the Standard Model with arbitrary new physics contributions to loop-mediated processes. Using a simple parameterization, we determine the allowed ranges of non-standard contributions to |Delta F|=2 processes. Remarkably, the recent measurements from B factories allow us to determine with good precision the shape of the Unitarity Triangle even in the presence of new physics, and to derive stringent constraints on non-standard contributions …
We have investigated a possible connection between the Majorana phases and geometric parameters of leptonic unitarity triangle(LUT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered two-texture zero neutrino mass model to obtain relation between Majorana phases and LUT parameters. In particular, we find that Majorana phases depend on only one of the thr…
Anticipating improved determinations of $m_t$, $|V_{cb}|$, $|V_{ub}/V_{cb}|$, $B_K$ and $F_B \sqrt{B_B}$ in the next five years we make an excursion into the future in order to find a possible picture of the unitarity triangle, of quark mixing and of CP violation around the year~2000. We then analyse what impact on this picture will result from the measurements of the four possibly cleanest quantities: $BR(K^+ \to π^+ ν\barν)$, $x_d/x_s$, $\sin(2α)$ and $\sin(2β)$. In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in the Wolfenstein p…
The unitarity triangle can be determined by means of two measurements of its sides or angles. Assuming the same relative errors on the angles $(α,β,γ)$ and the sides $(R_b,R_t)$, we find that the pairs $(γ,β)$ and $(γ,R_b)$ are most efficient in determining $(\bar\varrho,\barη)$ that describe the apex of the unitarity triangle. They are followed by $(α,β)$, $(α,R_b)$, $(R_t,β)$, $(R_t,R_b)$ and $(R_b,β)$. As the set $\vus$, $\vcb$, $R_t$ and $β$ appears to be the best candidate for the fundamental set of flavour violating parameters in the coming years, we show various constraints on the CKM m…
Motivated by the possibility of the low value of sin2βin the measurements of BABAR and BELLE collaborations, we have explored the possibilty of construction of reference unitarity triangle using the unitarity of the CKM matrix, the existence of nonzero CP violating phase δand 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 reference triangle are evaluated by finding δthrough the Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix gi…
We study effects of supersymmetric particles in various rare B decay processes as well as in the unitarity triangle analysis. We consider three different supersymmetric models, the minimal supergravity, SU(5) SUSY GUT with right-handed neutrinos, and the minimal supersymmetric standard model with U(2) flavor symmetry. In the SU(5) SUSY GUT with right-handed neutrinos, we consider two cases of the mass matrix of the right-handed neutrinos. We calculate direct and mixing-induced CP asymmetries in the b to s gamma decay and CP asymmetry in B_d to phi K_S as well as the B_s--anti-B_s mixing amplit…
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.
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…
A new approach to the parametrization of the CKM matrix, $V$, is considered in which $V$ is written as a linear combination of the unit matrix $I$ and a non-diagonal matrix $U$ which causes intergenerational-mixing, that is $V=\cosθI+i\sinθU$. Such a $V$ depends on 3 real parameters including the parameter $θ$. It is interesting that a value of $θ=π/4$ is required to fit the available data on the CKM-matrix including CP-violation. Predictions of this fit for the angles $α$, $β$ and $γ$ for the unitarity triangle corresponding to $V_{11}V^*_{13} + V_{21} V^*_{23} +V_{31}V^*_{33} =0$, are given.…
Assuming that the Kobayashi-Maskawa mechanism gives the dominant contribution to CP violation at low energies, we propose a novel way of testing the flavour sector of the Standard Model which has the potencial for discovering New Physics. Using 3 x 3 unitarity of the V_{CKM} matrix and choosing a complete set of rephasing invariant phases, we derive a set of exact relations in terms of measurable quantities, namely moduli of V_{CKM} and arguments of rephasing invariant quartets. These tests complement the usual analysis in the ρ, ηplane and, if there is New Physics, may reveal its source.
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 formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturba…
We analyze in the four-generation model the first measurement of the branching ratio of rare kaon decay K^+\toπ^+ν\barν, using the constraints from Δm_K, ε_K, B_d-\bar{B_d} mixing, Γ(b\to sγ), B_s-\bar{B_s} mixing, D^0-\bar{D^0} mixing, B(K_L\toπ^0ν\barν) and B(K_L\toμ\barμ), and study its effects on the unitarity triangle. With the results of searching for the maximum mixing of the fourth generation, we predict that D^0-\bar{D^0} mixing Δm_D and the branching ratio of "direct" CP-violating decay process K_L\toπ^0ν\barν could attain the values 1-2 orders of magnitude larger than the prediction…
We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the B0 meson system. Antusch, King, Malinsky and Spinrath have shown that the quark mass matrices with the negligible 1-3 mixing give an interesting relation between the phase of the quark mixing matrices and CP violating measure phi_2(alpha). This approach is extended by considering the SO(10) GUT including the Pati-Salam symmetry, which links the Yukawa matrices of the quark sector to the one of the lepton sector. We discuss the relation of the CP violating phases between both quark and le…
We present here the update of the Unitarity Triangle (UT) analysis performed by the UTfit Collaboration within the Standard Model (SM) and beyond. Continuously updated flavour results contribute to improving the precision of several constraints and through the global fit of the CKM parameters and the SM predictions. We also extend the UT analysis to investigate new physics (NP) effects on $ΔF=2$ processes. Finally, based on the NP constraints, we derive upper bounds on the coefficients of the most general $ΔF=2$ effective Hamiltonian. These upper bounds can be translated into lower bounds on t…
The precise measurements of the Bd oscillation frequency and the limit on the Bs one one as well as the determination of the Cabibbo-Kobayashi-Maskawa matrix element Vub improve the constraints on the other elements of this matrix. A fit to the experimental data and the theory calculations leads to the determination of the vertex of the unitarity triangle as: rho = 0.160 -0.070 +0.094 eta = 0.381 -0.058 +0.061. The values of its angles, in their customary definition in terms of sines for alpha and beta, are found to be: sin(2 alpha) = 0.06 -0.42 +0.35 sin(2 beta) = 0.75 +/- 0.09 gamma = 68 -12…
We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, alpha approximately 90 degrees. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of alpha approximately 90 degrees by a combination of purely real or purely imaginary vacuum expectation…
In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down type 1-3 mixing angles are approximately zero, and $V_{ub}$ is generated from $V_{cb}$ as a result of 1-2 up type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., $α\approx 90^\circ$, can be accounted for by a remarkably simple scheme involving real mass matr…
Using the latest determinations of several theoretical and experimental parameters, we update the Unitarity Triangle analysis in the Standard Model. The basic experimental constraints come from the measurements of |V_ub/V_cb|, Delta M_d, the lower limit on Delta M_s, epsilon_k, and the measurement of the phase of the B_d - anti B_d mixing amplitude through the time-dependent CP asymmetry in B^0 to J/psi K^0 decays. In addition, we consider the direct determination of alpha, gamma, 2 beta + gamma and cos(2 beta) from the measurements of new CP-violating quantities, recently performed at the B f…
We discuss the exclusive radiative decays $B\to K^{*}γ$, $B \toργ$, and $B\toωγ$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\toρlν$ decay spectrum to the branching fraction of $B\toργ$. The method is based on the cancellation of soft…
