Kobayashi Maskawa Research Articles

Overview of the Cabibbo–Kobayashi–Maskawa matrix†

The current status of the determination of the elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix is reviewed. Tensions in the global fits are highlighted. Particular attention is paid to progress in, and prospects for, measurements of CP violation effects.

Charged lepton contributions to bimaximal and tri-bimaximal mixing for generating [formula omitted] and [formula omitted

Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle θ13=0 and the atmospheric angle tan2θ23=1. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of θ13 as well as deviations of θ12 and θ23 from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on θ13 and θ23 to assign θ13≠0 and tan2θ23<1 with the help of charged lepton corrections defined by UPMNS=Ul†Uν. We first consider Uν to be given separately by BM and TB mixing matrices and then find the possible forms of Ul such that the elements of PMNS matrix, finally yield θ13≠0 and tan2θ23<1 in agreement with latest observational data. To compute the values of mixing angles we assume the charged lepton correction to be of Cabibbo–Kobayashi–Maskawa (CKM) like. All the mixing matrices involved in the calculation satisfy the unitarity condition to leading order of expansion parameter. We also analyze both the mixing schemes in presence of Dirac CP phase and find expressions for the rephasing invariant quantity JCP which have been discussed in recent literature.

Microscopic calculations of isospin mixing in N≈Z nuclei and isospin-symmetry-breaking corrections to the superallowed β-decay

Recently, we applied, for the first time, the angular momentum and isospin-projected nuclear density functional theory to calculate isospin-symmetry breaking (ISB) corrections to superallowed β-decay. With the calculated set of ISB corrections, we found that |Vud|=0.97447(23) for the leading element of the Cabibbo–Kobayashi–Maskawa matrix. This is in good agreement with both the recent result of Towner and Hardy (2008 Phys. Rev. C 77 025501) and the central value deduced from the neutron decay. In this paper, we extend our calculations of the ISB corrections covering all superallowed transitions A, Iπ=0+, T=1, Tz→A, Iπ=0+, T=1 and Tz+1 where Tz=− 1, 0, and A ranges from 10 to 74.

Study of levitating nanoparticles using ultracold neutrons

Physical adsorption of atoms, molecules and clusters on the surface is well known. It is linked to many other phenomena in physics, chemistry and biology and has numerous practical applications. Due to limitations of the analytical tools usually used, studies of adsorption are limited to the particle sizes of up to ∼102–103 atoms. Following a general formalism developed in this field, we apply it to even larger objects and discover qualitatively new phenomena. A large particle is bound to the surface in a deep and broad potential well formed by van der Waals/Casimir–Polder forces appearing due to the particle and surface electric polarization. The well depth is significantly larger than the characteristic energy of a particle's thermal motion; thus such a nanoparticle is settled in long-living states. Nanoparticles in high-excited states form a two-dimensional gas of objects bound to the surface but quasi-freely traveling along the surface under certain conditions. A particularly interesting feature of this model consists in the prediction of small-energy-transfer inelastic scattering of ultracold neutrons (UCN) on solid/liquid surfaces covered by such levitating nanoparticles/nano-droplets. The change in UCN energy is due to the Doppler shift induced by UCN collisions with nanoparticles/nano-droplets; the energy change is almost as small as the UCN initial energy. We compared theoretical estimations of our model to all existing data on inelastic scattering of UCN with small energy transfers and found that they agree quite well. As our theoretical formalism provides robust predictions of some data and the experimental data are rather detailed and precise, we conclude that the recently discovered intriguing phenomenon of small heating of UCN in traps is due to their collisions with such levitating nanoparticles. Moreover, this new phenomenon might be relevant to the striking contradiction between the results of the neutron lifetime measurements and the smallest reported uncertainties, as it might cause major false effects in these experiments; thus, it affects fundamental conclusions concerning precision checks of unitarity of the Cabibbo–Kobayashi–Maskawa matrix, cosmology and astrophysics. Dedicated measurements of UCN inelastic scattering on specially prepared surfaces and nanoparticles/nano-droplets levitating above them might provide a unique method for studying surface potentials.

Study ofB¯→Xuℓν¯decays inBB¯events tagged by a fully reconstructedB-meson decay and determination of|Vub|

We report measurements of partial branching fractions for inclusive charmless semileptonic B decays B¯→Xuℓν¯ and the determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element |Vub|. The analysis is based on a sample of 467×106 Υ(4S)→BB¯ decays recorded with the BABAR detector at the PEP-II e+e− storage rings. We select events in which the decay of one of the B mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other B meson. We measure partial branching fractions ΔB in several restricted regions of phase space and determine the CKM element |Vub| based on different QCD predictions. For decays with a charged lepton momentum pℓ*>1.0 GeV in the B meson rest frame, we obtain ΔB=(1.80±0.13stat±0.15sys±0.02theo)×10−3 from a fit to the two-dimensional MX−q2 distribution. Here, MX refers to the invariant mass of the final state hadron X and q2 is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract |Vub|=(4.33±0.24exp±0.15theo)×10−3 as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for B¯0 and B− decays and derive a limit on the isospin breaking in B¯→Xuℓν¯ decays.2 MoreReceived 5 December 2011DOI:https://doi.org/10.1103/PhysRevD.86.032004© 2012 American Physical Society

Searching for new physics at the frontiers with lattice quantum chromodynamics

Numerical lattice-quantum chromodynamics (QCD) simulations, when combined with experimental measurements, allow the determination of fundamental parameters of the particle-physics Standard Model and enable searches for physics beyond-the-Standard Model. We present the current status of lattice-QCD weak matrix element calculations needed to obtain the elements and phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and to test the Standard Model in the quark-flavor sector. We then discuss evidence that may hint at the presence of new physics beyond the Standard Model CKM framework. Finally, we discuss two opportunities where we expect lattice QCD to play a pivotal role in searching for, and possibly discovery of, new physics at upcoming high-intensity experiments: rare decays and the muon anomalous magnetic moment. The next several years may witness the discovery of new elementary particles at the Large Hadron Collider (LHC). The interplay between lattice QCD, high-energy experiments at the LHC, and high-intensity experiments will be needed to determine the underlying structure of whatever physics beyond-the-Standard Model is realized in nature.

A prediction of neutrino mixing matrix with CP violating phase

The latest experimental progress has established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parameterizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi–Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase δCK=(85.48−1.80(−4.90)+4.67(+12.87))° within 1σ (3σ) range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP violation related measurements.

Kobayashi-Maskawa parametrization of lepton flavor mixing and its application to neutrino oscillations in matter

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 (\theta_1, \theta_2, \theta_3 and \delta_KM) to their effective counterparts in matter (\tilde{\theta}_1, \tilde{\theta}_2, \tilde{\theta}_3 and \tilde{\delta}_KM). We rediscover the Toshev-like relation sin \tilde{\delta}_KM sin 2\tilde{\theta}_2 = sin \delta_KM sin 2\theta_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matter-corrected flavor mixing parameters in two different experimental scenarios: (a) the neutrino beam energy E is above O(1) GeV and (b) E is below O(1) GeV. As an example, the probability of \nu_\mu -> \nu_e oscillations and CP-violating effects are calculated for the upcoming NOvA and Hyper-K experiments.

Introduction to flavour and CP violation in the Standard Model and beyond

Abstract We define the Cabibbo–Kobayashi–Maskawa matrix and briefly discuss its present determination. We recall the formalism for heavy-meson mixing and CP violation in meson decays. Finally we extend our discussion of flavour and CP violation beyond the Standard Model.

B → a0(1450)ρ(ω) Decays in Perturbative QCD Approach

In the two-quark model supposition for the meson a0(1450), which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct CP-violating asymmetries for decays B → a0(1450)ρ(ω) are studied by employing the perturbative QCD factorization approach. We find the following results: (a) For the decays B− → a00(1450)ρ− and B̄0 → a+0(1450)ρ−, their branching ratios have large difference between two scenarios. Although their branching ratios are larger than other considered decay modes, their direct CP-violating asymmetries in both scenarios are small. (b) For the decays B− → a−0(1450)ρ0 and B̄0 → a−0(1450)ρ+, a00(1450)ρ0, a00(1450)ω, their branching ratios are close to each other between two scenarios, respectively. (c) Comparing with the decays B̄0 → π0ρ0, π0π0, the decay B̄0 → a00(1450)ρ0 receives a larger branching ratio in each scenario, which is sensitive to the variation of the Cabibbo—Kobayashi—Maskawa angle α.

Wolfenstein parametrization at higher order: Seeming discrepancies and their resolution

The precise determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements is extremely important towards the understanding of CP violation. We explicitly study seeming discrepancies between the CKM matrix elements at the higher order of the expansion parameter λ in different Wolfenstein parametrizations derived from different exact parametrizations. A systematic way of resolving the seeming discrepancies is proposed. We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order λ) parameters. Our approach is further applied to the cases for the Wolfenstein-like parametrizations, such as the Qin–Ma parametrization.

Vacuum structure and chiral symmetry breaking in strong magnetic fields for hot and dense quark matter

We investigate chiral symmetry breaking in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio (NJL) model including the Kobayashi Maskawa t-Hooft (KMT) determinant term, using an explicit structure for the ground state in terms of quark antiquark condensates. The mass gap equations are solved self consistently and are used to compute the thermodynamic potential. We also derive the equation of state for strange quark matter in the presence of strong magnetic fields which could be relevant for proto-neutron stars. ~

NEW RESULT OF DIRECT CP VIOLATION IN B → π+π-π+π-

In the framework of factorization, based on the first-order of isospin violation, we study direct CP violation in the decay of [Formula: see text] including the effect of ρ–ω mixing. The CP violation depends strongly on Cabibbo–Kobayashi–Maskawa (CKM) matrix elements and the effective parameter, Nc. Recently, the experimental data for the branching ratios of [Formula: see text] are accurate and we can give the strong constraint on the range of Nc. We find that the CP violating asymmetry is large and ranges from -82% to -98% via ρ–ω mixing mechanism when the invariant mass of the π+π- pair is in the vicinity of the ω resonance. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.

Remarks on the Qin–Ma parametrization of quark mixing matrix

Recently, Qin and Ma (QM) have advocated a new Wolfenstein-like parametrization of the quark mixing matrix based on the triminimal expansion of the Cabibbo–Kobayashi–Maskawa (CKM) parametrization. The CP-odd phase in the QM parametrization is around 90° just as that in the CKM parametrization. We point out that the QM parametrization can be readily obtained from the Wolfenstein parametrization after appropriate phase redefinition for quark fields and that the phase δ in both QM and CKM parametrizations is related to the unitarity angles α, β and γ, namely, δ=β+γ or π−α. We show that both QM and Wolfenstein parametrizations can be deduced from the CKM and Chau–Keung–Maiani ones. By deriving the QM parametrization from the exact Fritzsch–Xing (FX) parametrization of the quark mixing matrix, we find that the phase of the FX form is in the vicinity of −270° and hence sinδ≈1. We discuss the seeming discrepancy between the Wolfenstein and QM parametrizations at the high order of λ≈|Vus|.

MASS HIERARCHY, MIXING, CP-VIOLATION AND HIGGS DECAY — OR WHY ROTATION IS GOOD FOR US

The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution to the strong CP problem in QCD by linking the theta-angle there to the Kobayashi–Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α ≈ 90 ° . The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU ( 5 ) , a discrete family symmetry such as A 4 or S 4 , a shaping symmetry including products of Z 2 and Z 4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α ≈ 90 ° by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.

UNIVERSAL MASS MATRIX AND LEPTONIC θ13 ANGLE

We propose a universal mixing hypothesis between quark and lepton sectors at high energy scale (probably GUT scale) where quark–lepton universality holds. Namely in the charged lepton diagonal base, all the other mass matrices for up and down quarks and neutrinos are diagonalized by the same unitary matrix except for the phase elements. Thanks to this hypothesis, the observed values of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix and the mixing angles θ12 and θ23 in the Maki–Nakagawa–Sakata (MNS) lepton mixing matrix can predict the unknown magnitudes of the mixing angle θ13 and of the CP violating Dirac phase δ in the MNS matrix. Their allowed regions are rather narrow, 0.036 &lt; sin θ13 &lt; 0.048 and 6° &lt; δ &lt; 12°.

Parametrization of fermion mixing matrices in Kobayashi-Maskawa form

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 mixing in a unified way.

ISOSPIN MIXING IN THE VICINITY OF THE N = Z LINE

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed β-decay rates in the vicinity of the N = Z line. A preliminary value obtained for the Cabibbo–Kobayashi–Maskawa matrix element, |Vud| = 0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev.C77, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.

A new simple form of quark mixing matrix

Although different parametrizations of quark mixing matrix are mathematically equivalent, the consequences of experimental analysis may be distinct. Based on the triminimal expansion of Kobayashi–Maskawa matrix around the unit matrix, we propose a new simple parametrization. Compared with the Wolfenstein parametrization, we find that the new form is not only consistent with the original one in the hierarchical structure, but also more convenient for numerical analysis and measurement of the CP-violating phase. By discussing the relation between our new form and the unitarity boomerang, we point out that along with the unitarity boomerang, this new parametrization is useful in hunting for new physics.