Narrow Results

Quarks come in three colors and have electric charges in multiples of one-third. There are also three families of quarks and leptons. Though the first two properties can be understood in terms of unification symmetries such as SU(5), SO(10), or E₆, why should there only be three families remains a mystery. We propose how all three properties involving the number three are connected in a fivefold application of the gauge symmetry SU(3).

The spin structure of lambda has its special importance in analyzing the spin content of other hadrons. Assuming hadrons as a cluster of quarks and gluons (generally referred as valence and sea), statistical approach has been applied to study spin distribution of lambda among quarks. We apply the principle of detailed balance to calculate the probability of various quark–gluon Fock states and check the impact of SU(3) breaking on these probabilities particularly in sea for the Fock states containing strange quark. The flavor probability when multiplied by spin and color multiplicities of these quark–gluon Fock states results in estimating the individual contributions from valence and sea. We conclude that breaking in symmetry significantly affects the polarization of quarks inside the hyperons.

The LHCb collaboration has recently reported evidence for nonzero CP asymmetries in B⁺ decays into π⁺K⁺K^-, π⁺π⁺π^-, K⁺K⁺K^- and K⁺π⁺π^-. The branching ratios for these decays have also been measured with different values ranging from 5×10^-6 to 51×10^-6. If flavor SU(3) symmetry is a good symmetry for B decays, in the case that the dominant amplitude is momentum independent it is expected that branching ratios Br and CP violating rate differences satisfy, Br(π⁺π⁺π^-) = 2 Br(π⁺K⁺K^-), Br(K⁺K⁺K^-) = 2 Br(K⁺π⁺π^-) and Δ_CP(π⁺π⁺π^-) = 2Δ_CP(π⁺K⁺K^-) = -Δ_CP(K⁺K⁺K^-) = -2Δ_CP(K⁺π⁺π^-). The experimental data do not exhibit the expected pattern for the branching ratios. The rate differences for B⁺→π⁺π⁺π^- and B⁺→K⁺ K⁺ K^- satisfy the relation between ΔS = 0 and ΔS = 1 as well, but the other two do not, with the CP asymmetries having different signs than expected. In this paper, we study how to include momentum dependent and also SU(3) breaking effects on these decays to explain experimental data. We find that by including only the lowest order derivative terms, in the SU(3) limit, the decay patterns cannot be explained. Large SU(3) breaking effects are needed to explain the data.

A detailed study of fragmentation of vector mesons at the next-to-leading order (NLO) in QCD is given for e⁺e^- scattering. A model with broken SU(3) symmetry using three input fragmentation functions α(x, Q²), β(x, Q²) and γ(x, Q²) and a strangeness suppression parameter λ describes all the light quark fragmentation functions for the entire vector meson octet. At a starting low energy scale of for three light quarks (u, d, s) along with initial parametrization, the fragmentation functions are evolved through DGLAP evolution equations at NLO and the cross-section is calculated. The heavy quarks contribution are added in appropriate thresholds during evolution. The results obtained are fitted at the momentum scale of for LEP and SLD data. Good-quality fits are obtained for ρ, K*, ω and ϕ mesons, implying the consistency and efficiency of this model. Strangeness suppression in this model is understood both in terms of ratios of quark fragmentation functions alone as well as in terms of observables; the latter yield a suppression through the K*/ρ multiplicity ratio of about 0.23 while the x dependence of this suppression is also parametrized through the cross-section ratios.

We present a model-independent analysis of CP violation, inspired by recent experimental observations, in charmed meson decays. The topological diagram approach is used to study direct CP asymmetries for singly Cabibbo-suppressed two-body hadronic decays of charmed mesons. We extract the magnitudes and relative phases of the corresponding topological amplitudes from available experimental information. In order to get more precise and reliable estimates of direct CP asymmetries, we take into account contributions from all possible strong penguin amplitudes, including the internal $b$-quark penguin contributions. We also study flavor SU(3) symmetry breaking effects in these decay modes and consequently predict direct CP asymmetries of unmeasured modes.

The relation between strong isospin I and weak isospin i is discussed. In particular an equation between the third components I₃ and i₃ is given. This relation indicates that the strong isospin and weak isospin symmetries are both SU(2) subgroups of a new SU(3) symmetry underlying the structure of leptons and quarks.

A new composite model for leptons and quarks is presented. The model treats leptons and quarks as composites of three kinds of spin-½ particles (rishons), which belong to a fundamental triplet representation of a flavor SU(3) symmetry. A super-strong color-type force binds rishons together to form colorless leptons or quarks. Quarks display a valence property, which corresponds to the quark color of the Standard Model. Leptons have no valence property and are inert with respect to the super-strong color interaction. Both the strong color force and the weak interaction of the Standard Model are residual interactions of the super-strong color force in the new model.

We show that pseudospin symmetry is a symmetry of the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. We also show that pseudospin for nuclei implies spin symmetry for anti-nucleons moving in a nuclear environment.