Could the quark electroweak and mass eigenstates coincide?

We conjecture that in the absence of new mixing effects at the weak scale the standard quark mass eigenstates and the quark weak eigenstates would coincide, and that for all three families a simple hierarchy would apply, with m_u^o > m_d^o. We further assume that the observed mass inequality m_d>m_u arises from mixing of d with a heavier quark D. This approach leads to a CKM matrix that is automatically expressed in terms of mass ratios and different from other ones that have been studied; it is consistent with experimental constraints. In addition to requiring the existence of D with a mass on the electroweak scale, in general an unambiguous prediction is that |V_td| = |V_ub|, which is soon testable. The approach can be implemented in E₆-based models.     

Hierarchical chiral symmetry breaking and quark mass matrices revisited

We demonstrate how the assumption of hierarchical chiral symmetry breaking can be systematically used to create phenomenologically satisfactory mass matrices. In place of postulating a particular set of mass matrices at the outset, we emphasize that once a particular basis for the first stage of chiral symmetry breaking is selected, the following steps are determined by the known information on quark masses and mixings. We illustrate this procedure for the basis originally chosen by Fritzsch and find a modified set of quark mass matrices, corresponding to equal final-stage nondiagonal radiative contributions, which fits the data much better in the minimal Higgs framework, providedm _t ?88 GeV and the mixing ratio |V _ub |/|V _cb |?0.15.     

Mass and mixing angle predictions from infra-red fixed points

It is argued that low energy parameters, such as masses and mixing angles, may be related by the infra-red fixed points of the underlying field theory. For the Kobayashi-Maskawa 6 quark model the infra-red fixed points predicts the top quark mass m_t = 135 GeV and the Higgs mass m_H = 72 GeV. The implications for the mixing angles and phase are discussed and we also show that grand unification predictions should not be significantly affected.     

Quark mixing in weak interactions

The status of the quark mixing in weak interaction is reviewed. The 3×3 quark mixing matrix for the three left-handed doublet model is analyzed using various experimental information involving strange, charmed, and b-flavored particles. Its interplay with nonleptonic decays, implication on neutral particle-antiparticle mixing and CP violation in heavy quark systems, and the possible origin of the quark mixing from quark mass matrix are discussed. Finally we briefly review the status of alternative sources for CP violation, and alternative models to the three left-hand quark doublet model.     

Mixing angles,mass matrix and CP violation in the Kobayashi-Maskawa model

We analyze the K_L ? K_S mass difference Δm and CP-violating parameters η_+? and η₀₀ in terms of the mixing angles of the six-quark Kobayashi-Maskawa model. In contrast to previous analyses, we include a parameter to allow for uncalculable contributions of low-mass intermediate states to the mass matrix. As a result, Δm provides only weak constraints on the mixing angles but stronger constraints may possibly be obtained using data on η₀₀.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

Leading logarithms of heavy quark masses in processes with light and heavy quarks

The matrix elements of operators containing both heavy quark (Q) and light quark (q) fields can contain large logarithms of the type ln(m_Q²/μ²), where μ is a typical QCD mass scale and m_Q is the heavy quark mass. We outline a method for summing leading logarithms of this type. We apply it to the decay constant f_M of a low lying pseudoscalar meson M with Q̄q flavor quantum numbers and predict the ratios of decay constants for mesons with different heavy flavors. We also apply it to a matrix element of a four-quark operator which is relevant for B⁰−B̄⁰ mixing.     

Flavour mixing and quark masses in sequential flavour dynamics

We discuss the mixing of quark flavours in sequential flavour dynamics in the case of an arbitrary number of quark generations. For n generations the dominant weak interaction mixing is described by n ? 1 mixing angles, which are computed in terms of the quark masses.     

Neutrino masses and mixings based on a special set of quark mass matrices (II)

In the framework of a 6×6 neutrino mass matrix with the standard seesaw mechanism, simple empirical forms are used for the leptonic Dirac mass submatrices which exhibit hierarchical chiral symmetry-breaking structure with just six parameters, as suggested by our previous work with quark mass matrices. Through a Monte Carlo analysis of Euler angle rotations applied to diagonal forms for the right-handed Majorana mass submatrix, we generate scatter plots in the δm ₂₃ ² vs sin²2θ ₂₃ and δm ₁₃ ² vs sin²2θ ₁₃ oscillation planes for a fixed point in the nonadiabatic MSW band. Only a small, statistically insignificant, segment of the 23 mixing plane exists corresponding to depletions of both the solarv _e and atmosphericv _μ fluxes; however, for such solutions the righthanded Majorana submatrix exhibits a hierarchical chiral symmetry-breaking form remarkably similar to that for the Dirac submatrices.     

Neutrino mass ordering and μ-τ reflection symmetry breaking

If the neutrino mass spectrum turns out to be m_3 m_1 m_2, it may be relabeled as m_1 m_2 m_3 such that all the masses of fundamental fermions with the same electrical charges are in order. In this case the columns of the 3×3 lepton flavor mixing matrix U should be reordered accordingly, and the resulting pattern U may involve one or two large mixing angles in the standard parametrization or its variations. Since the Majorana neutrino mass matrix remains unchanged in such a mass relabeling, a possible μ-τ reflection symmetry is respected in this connection and its breaking effects are model-independently constrained at the 3σ level by using current experimental data.     

Effective potential methods and the Higgs mass spectrum in the MSSM

We generalize the analytical expressions for the two-loop leading-log neutral Higgs boson masses and mixing angles to the case of general left- and right-handed soft supersymmetry breaking stop and sbottom masses and left-right mixing mass parameters (m_Q, m_U, m_D, A_t, A_b). This generalization is essential for the computation of Higgs masses and couplings in the presence of light stops. At high scales we use the minimal supersymmetric standard model effective potential, while at low scales we consider the two-Higgs doublet model (renormalization group improved) effective potential, with general matching conditions at the thresholds where the squarks decouple. We define physical (pole) masses for the top quark, by including QCD self-energies, and for the neutral Higgs bosons, by including the leading one-loop electroweak self-energies where the top/stop and bottom/sbottom sectors propagate. For m_Q = m_U = m_D and moderate left-right mixing mass parameters, for which the mass expansion in terms of renormalizable Higgs quartic couplings is reliable, we find excellent agreement with previously obtained results.     

Cabibbo angle,CP violation and quark masses

By adding suitable discrete flavor symmetries to SU(2)_L ? SU(2)_R ? U(1) left-right symmetric gauge models of weak and electromagnetic interactions, we are able to express all the mixing angles between the quark flavors (u, d, s,c) in terms of the quark masses. This enables us to compute the Cabibbo angle and the CP violating phases using plausible values for the quark masses. The CP violating K ar 2π decay amplitude η_+? (and η₀₀ in the model is then given purely in terms of the parity violating parameter of the model (m_WL⁺/m_WR⁺)².     

Neutrino masses and the scale of B-L violation

A systematic study of neutrino masses in models with local B-L symmetry is presented. The observed SU(4)_c violation in fermion masses, which is necessary to explain why m_e is not equal m_d, is related to the scale of B-L violation. An alternative approach uses renormalization group methods to determine this scale. The heaviest neutrino mass is predicted to be 0.1–50 eV in the case of four fermion generations. Two different generation patterns for neutrino masses are found, one predicting large mixing between ν_e and ν_μ (and eventually ν_τ) and the other predicting leptonic mixing angles of the same order as quark mixing angles.     

Spontaneous CP violating phase as the phase in PMNS matrix

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 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 Yukawa couplings are also constrained. Different ways of identifying the phases have different predictions for \(\mu\to e e\bar{e}\) and \(\tau\to l_{1} l_{2} \bar{l}_{3}\). Future experimental data can be used to distinguish different models.     

Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses

The meson spectrum of QCD is studied in the framework of nonperturbative QCD as a function of varying quark masses m _q . It is shown that the total spectrum consists of two branches: 1) the standard one, which may be called the flux-tube spectrum, depending approximately linearly on m _q , and 2) the chiral symmetry breaking (CSB) spectrum for pseudoscalar (PS) flavor nonsinglet mesons with mass dependence √m _q . The formalism for PS mesons is derived from the QCD Lagrangian with m _q corrections, and a unified form of the PS propagator was derived. It is shown that the CSB branch of PS mesons joins to the flux-tube branch at around m _q = 200 MeV. All these results are in close correspondence with recent numerical data on large lattices.     

Exclusive c → s,d Semileptonic Decays of Spin-1/2 and Spin-3/2 cb Baryons

We present results for exclusive semileptonic decay widths of ground state spin-1/2 and spin-3/2  cb baryons corresponding to a c → s, d transition at the quark level. The relevance of hyperfine mixing in spin-1/2 cb baryons is shown. Our form factors are compatible with heavy quark spin symmetry constraints obtained in the infinite heavy quark mass limit.     

The Magnetic Mass of Transverse Gluon, the B-Meson Weak Decay Vertex and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass m _mag becomes approximately equal to T _c at ${T=T_c\sim 1.14\Lambda_{\overline{MS}} \sim 260}$ MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.     

ρ0-ω mixing in U(3)L×U(3)R chiral theory of mesons}

In this paper, U(3)_L×U(3)_R chiral theory of mesons is extended to the leading order in quark mass expansion in order to evaluate the ρ⁰-ω mixing. It is shown that the use of path integral method to integrate out the quark fields naturally leads to the ρ⁰-ω mixing vertices, and this mixing is entirely from the quark loop in this theory. The off-shell behaviour of the mixing amplitude is analyzed. The on-shell mixing amplitude is obtained from the decay ω→π⁺π⁻. Furthermore, the constraints on the light quark mass parameters are extracted from the ρ⁰-ω mixing and the mesons masses, and the mass splitting of K^*(892)-mesons is predicted. Received: 30 January 1998 / Revised version: 3 June 1998