Hierarchical chiral symmetries and the quark mass matrix

A hierarchical pattern of chiral symmetries is introduced, whose breaking is supposed to lead to the observed hierarchical pattern of the quark mass spectrum. Specific consequences for the interplay between the quark masses and the weak interaction mixing parameters are derived, in accordance with the observational constraints. They can be regarded as stringent constraints for any realistic dynamical theory of the quark mass spectrum. CP violation is absent in the limit m_u=m_d=0. A specific way to describe the weak interaction mixing emerges.     

A model of flavor mixing

A model of quark mass matrices is presented where flavor mixings can be expanded in powers of small parameters. These parameters characterize the observed quark mass pattern. The weak mixing matrix has a very simple form. The correlation of the weak mixing angles and CP-violating phases with the main features of the quark spectrum may be easily studied. An upper bound is predicted on the top-quark mass, m_t^p⩽45 GeV, and a rate for the b→u transition close to its experimental limit.     

Chiral SU(2)×SU(2) model with infrared quark confinement

An SU(2)×SU(2) chiral quark model describing the properties and interaction of pions and scalar and vector mesons is considered. The confinement of quarks is introduced in the model by means of an infrared cut-off in the one-loop quark diagrams. This cutoff gives rise to the elimination of the unphysical thresholds of the quark-antiquark pair production. The π-a ₁ transitions are taken into account. The model conserves all low-energy theorems. The masses of mesons and the widths of the decays ρ → 2π and σ → 2π are calculated.     

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.     

Bound states in gauge theories as the Poincaré group representations

The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincaré group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of γ + γ → π ₀ +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.     

On the addition of vector-like quarks to the standard model

We analyze some of the implications of adding vector-like isosinglet quarks to the standard model and its simplest extension based on the low-energy gauge group SU(3)_c × SU(2) × U(1)^m, which naturally arises in some grand unified theories as well as in some versions of superstring theories. Some of the novel features of this class of models are pointed out: non-unitarity of the Cabibbo-Koyabashi-Maskawa matrix, new CP-violating phases, flavour-changing neutral currents. We derive the CP invariance restrictions on the various quark mass terms and propose a parametrization of the quark mixing matrix which is particularly suitable for models with vector-like quarks. Constraints on these models are derived from rare kaon decays and the value of the K_L − K_S mass difference.     

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.     

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.     

Effective field theories for the heavy quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and α _s ) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.     

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one-loop order only depend on the remaining four dimension-two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to Δ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes P₁⁻ and P₂⁺ as well as the isovector S-wave effective range parameter b⁻. The one-loop calculation is in good agreement with the data. The difference P₁⁻ − P₂⁺ signals chiral loop effects in the πN P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.     

(Non)-Abelian gauge field theories of the Fermi gas. Neutron-quark stars

It is indicated that the ground state of Fermi systems with (non)-Abelian gauge interactions has a well defined quantum theory devoid of infrared divergences and mass singularities. This is exploited to develop a systematic quantum theory of the quark gas. The equation of state of the quark gas is evaluated up to second order in the Gell-Mann-Low charge α_S(μ). The analysis based on neutron matter models suggests that the matter in the neutron stars can be in the quark phase provided the color interaction is “moderately” strong i.e. α_S (3 GeV) ? 0.3.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

Light-front quark model and analysis of the spectrum of photons from inclusive B → X s γ decays

The electroweak-decay width Γ(B → X _s γ) is investigated in a light-front (LF) constituent quark model. A new partonlike formula is derived that establishes a simple relation between Γ(B → X _s γ) and the b → sγ decay width. A treatment of the b quark as an on-mass-shell particle and the inclusion of effects that arise from the transverse motion of the b quark in the B meson are basic features of this approach. Adopting different b-quark LF distribution functions, both phenomenological ones and those that are derived from constituent quark models, and neglecting perturbative corrections, we compute the photon energy spectra and the moments of the shape function. It is shown that the LF approach can be matched completely with a heavy-quark expansion (HQE), provided that the constituent b-quark mass is redefined in a way similar to that used in HQE to define the pole mass of the b quark. In this way, the correction to first order in 1/m _b can be eliminated from the total width in agreement with the general statement of HQE. We also show that the photon energy spectra calculated in the LF approach agree well with those obtained in the model of Altarelli et al., provided that the same distribution function is used as an input in both cases. Despite the simplicity of the model, our results are in fairly good agreement both with HQE predictions and with available experimental data.     

Quark condensates in nuclear matter with vacuum effects

On the basis of a bosonized Nambu- Jona-Lasinio (NJL) model with derivative expansions, quark condensates in nuclear matter are studied at one-quark loop level and the dependence of meson masses and couplings on the constituent quark mass is investigated. The condensate ratio obtained here < q?q > _ρB / < q?q > _vac is roughly 0.66 with constituent quark mass of 313 MeV, which yields a corresponding σ _N value to be roughly 42.2 MeV at the mean field level and σ _N =31.4 MeV with the vacuum dependence, where the model parameters describing a Lorentz scalar and a vector field are self-determined.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

P-Matrix approach and parameters of low-energy scattering in the presence of a Coulomb potential

The scattering of two charged strongly interacting particles is described on the basis of the P-matrix approach. In the P matrix, it is proposed to isolate explicitly the background term corresponding to purely Coulomb interaction, whereby it becomes possible to improve convergence of the expansions used and to obtain a correct asymptotic behavior of observables at high energies. The expressions for the purely Coulomb background P matrix, its poles and residues, and purely Coulomb eigenfunctions in the P-matrix approach are obtained. The nuclear-Coulomb parameters of the low-energy scattering of two charged hadrons are investigated on the basis of this approach combined with the method for isolating the background P matrix. Simple explicit expressions for the nuclear-Coulomb scattering length and effective range in terms of the residual P matrix are derived. For models of short-range strong interaction, these expressions give a general form of nuclear-Coulomb parameters for low-energy scattering. Specific applications of the general expressions derived in this study are exemplified by considering, on the basis of these expressions, some exactly solvable models of strong interaction, including the hard-core model, and, for these models, the nuclear-Coulomb parameters for low-energy scattering at arbitrary values of the orbital angular momentum are found explicitly for the first time. In particular, the nuclear-Coulomb scattering length and effective range are obtained explicitly for the boundary-condition model, the model of a hard-core delta-shell potential, the Margenau model, and the model of square-well hard-core potential.     

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.     

Electromagnetic low-energy constants in χPT

We investigate three-flavour chiral perturbation theory including virtual photons in the limit in which the strange quark mass is much larger than the external momenta and the up and down quark masses, and where the external fields are those of two-flavour chiral perturbation theory. In particular, we work out the strange quark mass dependence of the electromagnetic two-flavour low-energy constants C and k_i. We expect that these relations will be useful for a more precise determination of the electromagnetic low-energy constants. PACS 11.30.Rd; 12.39.Fe; 13.40.Dk; 13.40.Ks