We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the $e^+ e^- to pi^+ pi^- 2 pi^0$ process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the $gamma^* to 4pi$ verte
x using a vector meson dominance model, including the intermediate resonance contributions relevant at these energies. We find that $mu_rho = 2.1 pm 0.5$ in $e/2 m_rho$ units.
The extracted value for the $g^{eff}_{omega rhopi}$ effective coupling from experimental data, considering only the $rho$ meson, resumes not only the $rho$ meson effect but also all its additional radial excitation modes. By explicitly adding the rad
ial excitations of the $rho$ meson, considering a particular form of the spectrum and relations among the couplings, we identify the single $g_{omega rho pi}$ and the $rho$ radial excitations effect in the $omega rightarrow pi^0 gamma$ decay. We obtain that the individual coupling is in the range $g_{omegarhopi}= 8.2 - 8.6 {text GeV}^{-1}$, which is about 40% smaller than the effective $g^{eff}_{omegarhopi}$. We verify the consistency with the chiral approach in the $pi^0 rightarrow gammagamma$ and $gamma^* rightarrow 3pi$ processes. Besides the model dependence, our description succeeds in exhibiting how each contribution came into the game. In particular, we show that for the $gamma^* rightarrow 3 pi$ decay, the usual relation $mathcal{A}^{VMD}_{gamma3pi}=(3/2)mathcal{A}^{WZW}_{gamma3pi}$, encodes all the vector contributions and not only the $rho$ meson one. In addition, we find that there is an almost exact (accidental) cancelation between the radial excitations and the contact term contributions.
We determine the value of the omega -rho- pi mesons coupling (g_{omegarhopi}), in the context of the vector meson dominance model, from radiative decays, the omega rightarrow 3pi decay width and the e^+e^- rightarrow 3pi cross section. For the last t
wo observables we consider the effect of either a heavier resonance (rho(1450)) or a contact term. A weighted average of the results from the set of observables yields g_{omegarhopi} =14.7 pm 0.1 GeV^{-1} in absence of those contributions, and g_{omegarhopi} =11.9 pm 0.2 GeV^{-1} or g_{omegarhopi} =11.7 pm 0.1 GeV^{-1} when including the rho or contact term respectively. The inclusion of these additional terms makes the estimates from the different observables to lay in a more reduced range. Improved measurements of these observables and the rho(1450) meson parameters are needed to give a definite answer on the pertinence of the inclusion of this last one in the considered processes.
The inclusion of the unstable features of a spin-1 particle, without breaking the electromagnetic gauge invariance, can be properly accomplished by including higher order contributions as done in the so-called fermion loop scheme (for the W gauge bos
on), and the boson loop scheme (for vector mesons). This induces a non trivial modification to the electromagnetic vertex of the particle, which must be considered in addition to any other contribution computed as stable particles. Considering the modified electromagnetic vertex, we obtain general expressions for the corresponding corrections to the multipoles as a function of the mass of the particles in the loop. For the W gauge boson no substantial deviations from the stable case is observed. For the rho and K* mesons the mass of the particles in the loop makes a significant effect, and can be comparable with corrections of different nature .
We provide a non-perturbative expression for the hadron production in electron-positron annihilation at zero temperature in a strongly coupled, large-Nc SU(Nc) field theory with Nf << Nc quark flavors. The resulting expressions are valid to leading o
rder in the electromagnetic coupling constant but non-perturbatively in the SU(Nc) interactions and the mass of the quark. We obtain this quantity by computing the imaginary part of the hadronic vacuum polarization function Pi_q using holographic techniques, providing an alternative to the known method that uses the spectrum of infinitely stable mesons determined by the normalizable modes of the appropriated fields in the bulk. Our result exhibits a structure of poles localized at specific real values of q^2, which coincide with the ones found using the normalizable modes, and extends it offering the unique analytic continuation of this distribution to a function defined for values of q^2 over the complex plane. This analytic continuation permits to include a finite decay width for the mesons. By comparison with experimental data we find qualitatively good agreement on the shape of the first pole, when using the rho meson parameters and choosing a proper normalization factor. We then estimate the contribution to the anomalous magnetic moment of the muon finding an agreement within 25%, for this choice of parameters.
We compute the difference in decay widths of charged and neutral rho(770) vector mesons. The isospin breaking arising from mass differences of neutral and charged pi and rho mesons, radiative corrections to rho -> pipi, and the rho -> pipigamma decay
s are taken into account. It is found that the width difference Delta Gamma_rho is very sensitive ot the isospin breaking in the $rho$ meson mass Delta m_rho. This result can be useful to test the correlations observed between the values of these parameters extracted from experimental data.
We study the effect of the sigma(600) and a_1(1260) resonances in the rho^0 -> pi^+ pi^- gamma decay, within the meson dominance model. Major effects are driven by the mass and width parameters of the sigma(600), and the usually neglected contributio
n of the a_1(1260), although small by itself, may become sizable through its interference with pion bremsstrahlung, and the proper relative sign can favor the central value of the experimental branching ratio. We present a procedure, using the gauge invariant structure of the resonant amplitudes, to kinematically enhance the resonant effects in the angular and energy distribution of the photon. We also elaborate on the coupling constants involved.
