Isospin Symmetry Breaking within the HLS Model: A Full (ρ,ω,ϕ\rho, \omega, \phi) Mixing Scheme

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from \rho-\omg mixing and one finds support for the Orsay phase modelling of the e^+e^- \ra \pi^+ \pi^- amplitude. We then examine an effective procedure which generates mixing in the whole $\rho$, \omg, $\phi$ sector of the HLS Model. The corresponding model allows us to account for all two body decays of light mesons accessible to the HLS model in modulus and phase, leaving aside the \rho \ra \pi \pi and K^* \ra K \pi modes only, which raise a specific problem. Comparison with experimental data is performed and covers modulus and phase information; this represents 26 physics quantities successfully described with very good fit quality within a constrained model which accounts for SU(3) breaking, nonet symmetry breaking in the pseudoscalar sector and, now, isospin symmetry breaking.Comment: 38 pages, version published in Eur. Phys. J.

B decays dominated by omega-phi mixing

Recently Belle has established the 90% confidence level (CL) upper limit \b < 9.4 \times 10^{-7} for the branching ratio for $B^0\to J/\psi \phi$, a process expected to be suppressed by the Okubo-Zweig-Iizuka (OZI) rule disfavoring disconnected quark diagrams. We use information on $\omega$--$\phi$ mixing to establish likely lower bounds on this and related processes. We find that the Belle result is about a factor of five above our limit, while other decays such as $B^0 \to \bar D^0 \phi$ and $B^+ \to \pi^+ \phi$, for which upper limits have been obtained by BaBar, could be observable with similar improvements in data. We argue that a significant enhancement of our predicted decay rates by rescattering is unlikely.Comment: paragraph added, submitted to Physics Letters

VMD, the WZW Lagrangian and ChPT: The Third Mixing Angle

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian ${\cal L}^{(0)}+{\cal L}^{(1)}$. This allows to rely on radiative decays of light mesons ($VP\gamma$ and $P \gamma\gamma$) in order to extract some numerical information of relevance to ChPT: a value for $\Lambda_1=0.20 \pm 0.04$, a quark mass ratio of $\simeq 21.2 \pm 2.4$, and a negligible departure from the Gell-Mann--Okubo mass formula. The mixing angles are $\theta_8=-20.40^\circ \pm 0.96^\circ$ and $\theta_0=-0.05^\circ \pm 0.99^\circ$. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle $\theta_P$ is actually quite appropriate and algebraically related to the $\eta/\eta'$ mixing pattern presently preferred by the ChPT community. For instance the traditional $\theta_P$ is functionally related to the ChPT $\theta_8$ and fulfills $\theta_P \simeq \theta_8/2$. The vanishing of $\theta_0$, supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) \ra SU(3)$\times$ U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.Comment: 31 pages, 1 figur

A Global Treatment Of VMD Physics Up To The ϕ\phi: I. e+e−e^+e^- Annihilations, Anomalies And Vector Meson Partial Widths

The HLS Model, equipped with a mechanism providing the breaking of U(3)/SU(3) symmetry and an isospin symmetry breaking leading naturally to vector meson mixing, has been recently shown to successfully account for e^+ e^- \ra \pi^+\pi^- cross section and for the dipion spectrum in $\tau$ decay. The present study shows that the full anomalous sector of the HLS model can be considered and is validated by the experimental data. Indeed, this extended model provides a successful simultaneous fit to the e^+ e^- \ra \pi^+\pi^- data together with the available data on e^+ e^- \ra \pi^0\gamma, e^+ e^- \ra \eta\gamma and e^+ e^- \ra \pi^0 \pi^+\pi^- cross sections. It is shown that the fit of these data sets also predicts an accurate description of the \eta/\eta^\prime \ra \pi^+ \pi^- \gamma decays fully consistent with the reported information on their branching fractions and spectra. Finally, one also derives from our global fits products of widths of the form \Gamma (V \ra f_1)\Gamma(V \ra e^+ e^-) and ratios of the form \Gamma (V \ra f_1)/\Gamma (V \ra f_2) describing decays of vector mesons to several non--leptonic final states.Comment: 58 pages, 10 figures Corrected a few misprints. Footnote 10 change

A Global Treatment Of VMD Physics Up To The ϕ\phi: I. e+e−e^+e^- Annihilations, Anomalies And Vector Meson Partial Widths

The HLS Model, equipped with a mechanism providing the breaking of U(3)/SU(3) symmetry and an isospin symmetry breaking leading naturally to vector meson mixing, has been recently shown to successfully account for e^+ e^- \ra \pi^+\pi^- cross section and for the dipion spectrum in $\tau$ decay. The present study shows that the full anomalous sector of the HLS model can be considered and is validated by the experimental data. Indeed, this extended model provides a successful simultaneous fit to the e^+ e^- \ra \pi^+\pi^- data together with the available data on e^+ e^- \ra \pi^0\gamma, e^+ e^- \ra \eta\gamma and e^+ e^- \ra \pi^0 \pi^+\pi^- cross sections. It is shown that the fit of these data sets also predicts an accurate description of the \eta/\eta^\prime \ra \pi^+ \pi^- \gamma decays fully consistent with the reported information on their branching fractions and spectra. Finally, one also derives from our global fits products of widths of the form \Gamma (V \ra f_1)\Gamma(V \ra e^+ e^-) and ratios of the form \Gamma (V \ra f_1)/\Gamma (V \ra f_2) describing decays of vector mesons to several non--leptonic final states.Comment: 58 pages, 10 figures Corrected a few misprints. Footnote 10 change

Pseudoscalar Meson Mixing in Effective Field Theory

We show that for any effective field theory of colorless meson fields, the mixing schemes of particle states and decay constants are not only related but also determined exclusively by the kinetic and mass Lagrangian densities. In the general case, these are bilinear in terms of the intrinsic fields and involve non-diagonal kinetic and mass matrices. By applying three consecutive steps this Lagrangian can be reduced into the standard quadratic form in terms of the physical fields. These steps are : (i) the diagonalization of the kinetic matrix, (ii) rescaling of the fields, and (iii) the diagonalization of the mass matrix. In case, where the dimensions of the non-diagonal kinetic and mass sub-matrices are respectively, $k\times k$ and $n\times n$, this procedure leads to mixing schemes which involve $[k(k-1)/2] + [n(n-1)/2]$ angles and $k$ field rescaling parameters. This observation holds true irrespective with the type of particle interactions presumed. The commonly used mixing schemes, correspond to a proper choice of the kinetic and mass matrices, and are derived as special cases. In particular, $\eta$-$\eta '$ mixing, requires one angle, if and only if, the kinetic term with the intrinsic fields has a quadratic form.Comment: REVTeX, 6 page

Can VMD improve the estimate of the muon g-2 ?

We show that a VMD based theoretical input allows for a significantly improved accuracy for the hadronic vacuum polarization of the photon which contributes to the theoretical estimate of the muon g-2. We also show that the only experimental piece of information in the $\tau$ decay which cannot be accounted for is the accepted value for {\rm Br}(\tau \ra \pi \pi \nu_\tau), while the spectum lineshape is in agreement with expectations from $e^+ e^-$ annihilations.Comment: 6 pages, 1 figure Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, Chin