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.

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

New results in rho^0 meson physics

We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e^+ e^- -> pi^+ pi^$ and e^+ e^- -> mu^+ mu^- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We find that, of the models considered, only that proposed by Bando et al. is able to consistently account for all information, provided one allows its parameter "a" to vary from the usual value of 2 to 2.4. Our fit with this model gives a point-like coupling (gamma pi^+ \pi^-) of magnitude ~ -e/6, while the common formulation of VMD excludes such a term. The resulting values for the rho mass and pi^+ pi^- and e^+e^- partial widths as well as the branching ratio for the decay omega -> pi^+ pi^- obtained within the context of this model are consistent with previous results.Comment: 34 pages with 7 figures. Published version also available at http://link.springer.de/link/service/journals/10052/tocs/t8002002.ht

Corrections to Fermi's Golden Rule in ϕ→KKˉ\phi \to K\bar{K} Decays

We analyze the decays $\phi \to K\bar{K}$ utilizing a formulation of transition rates which explicitly exhibits corrections to Fermi's Golden Rule. These corrections arise in systems in which the phase space and/or matrix element varies rapidly with energy, as happens in $\phi \to K\bar{K}$, which is just above threshold. We show that the theoretical corrections resolve a puzzling $5\sigma$ discrepancy between theory and experiment for the branching ratio $R = \Gamma (\phi \to K^+K^-)/\Gamma(\phi \to K^0\bar{K}^0)$

SU(3) breaking and Hidden Local Symmetry

We study the various existing implementations of SU(3) breaking in the Hidden Local Symmetry model for the low energy hadronic sector following a mechanism originally proposed by Bando, Kugo and Yamawaki (BKY). We pay particular attention to hermiticity and current conservation. Following this, we present a new method for including symmetry breaking effects which preserves the BKY mas s relation among vector mesons. Symmetry breaking (SB) necessarily requires a transformation of the pseudoscalar fields, which, following BKY, we refer to a s field renormalization. We examine the consequences of propagating this throug h all Lagrangian terms including the anomalous ones. We thus explore the consequences of these various SB schemes for both charged and neutral pseudoscalar decay constants as measured in weak and anomalous decays respectively.Comment: 18 pages, REVTEX. Publication details added to title page. Published version available at http://publish.aps.org/ejnls/prdfetch/abstract/PRD/V58/E074006

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

Anomalous η/η′\eta/\eta^\prime Decays: The Triangle and Box Anomalies

We examine the decay modes \eta/\etp\ra \pi^+ \pi^- \gamma within the context of the Hidden Local Symmetry (HLS) Model. Using numerical information derived in previous fits to $VP\gamma$ and $Ve^+e^-$ decay modes in isolation and the $\rho$ lineshape determined in a previous fit to the pion form factor, we show that all aspects of these decays can be predicted with fair accuracy. Freeing some parameters does not improve the picture. This is interpreted as a strong evidence in favor of the box anomaly in the \eta/\etp decays, which occurs at precisely the level expected. We also construct the set of equations defining the amplitudes for \eta/\etp\ra \pi^+ \pi^- \gamma and \eta/\etp \ra \ggam at the chiral limit, as predicted from the anomalous HLS Lagrangian appropriately broken. This provides a set of four equations depending on only one parameter, instead of three for the traditional set. This is also shown to match the (two--angle, two--decay--constant) \eta-\etp mixing scheme recently proposed and is also fairly well fulfilled by the data. The information returned from fits also matches expectations from previously published fits to the $VP\gamma$ decay modes in isolation.Comment: 47 page

Vector meson dominance and the rho meson

We discuss the properties of vector mesons, in particular the rho^0, in the context of the Hidden Local Symmetry (HLS) model. This provides a unified framework to study several aspects of the low energy QCD sector. Firstly, we show that in the HLS model the physical photon is massless, without requiring off field diagonalization. We then demonstrate the equivalence of HLS and the two existing representations of vector meson dominance, VMD1 and VMD2, at both tree level and one loop order. Finally the S matrix pole position is shown to provide a model and process independent means of specifying the rho mass and width, in contrast to the real axis prescription currently used in the Particle Data Group tables.Comment: 18 pages, REVTE

Tri-meson-mixing of π\pi-η\eta-η′\eta' and ρ\rho-ω\omega-ϕ\phi in the light-cone quark model

The radiative transition form factors of the pseudoscalar mesons {$\pi$, $\eta$, $\eta'$} and the vector mesons {$\rho$, $\omega$, $\phi$} are restudied with $\pi$-$\eta$-$\eta'$ and $\rho$-$\omega$-$\phi$ in tri-meson-mixing pattern, which is described by tri-mixing matrices in the light-cone constituent quark model. The experimental transition decay widths are better reproduced with tri-meson-mixing than previous results in a two-mixing-angle scenario of only two-meson $\eta$-$\eta'$ mixing and $\omega$-$\phi$ mixing.Comment: 8 pages, 6 figures, final version to appear in EPJ

Chiral Anomaly and Eta-Eta' Mixing

We determine the $\eta-\eta'$ mixing angle via a procedure relatively independent of theoretical assumptions by simultaneously fitting $\eta- eta'$ reactions involving the anomaly--$\eta,\eta'\to\gamma\gamma, \pi^+\pi^-\gamma$. We extract reasonably precise renormalized values of the octet and singlet pseudoscalar decay constants $F_8,F_0$ as well as the mixing angle $\theta$.Comment: 12 page standard Latex file, three figures, added comment