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

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

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

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

The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach

We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in tau decays. For this purpose, we work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical rho, omega and phi fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the 4--momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (V P gamma and P gamma gamma couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (omega/ phi --> pi+ pi-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and tau dipion spectra. The expression for pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e+e- and switching on those for tau decays. Besides, the model also provides a good account of all decay modes of the form V P gamma, Pgamma gamma as well as the isospin breaking decay modes. It leads us to propose new reference values for the rho^0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our description of the pion form factor. Other topics (phi --> K anti K, the rho meson mass and width parameters) are briefly discussed. Therefore, we confirm the 3.3 sigma discrepancy between the theoretical estimate of a_mu based on e+e- and its direct BNL measurement.Comment: 71 pages, 8 figures. Accepted by EPJ C. Version 3: correct minor typos, minor changes spread out into the text. Extension of Sections 12.2 and 12.3.5 and introduction of the new Appendix

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

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