Vector Meson Dominance Model Research Articles

Measurement of thee+e−→ηπ+π−cross section in the center-of-mass energy range 1.22–2.00 GeV with the SND detector at the VEPP-2000 collider

In the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider the cross section for the process $e^+e^-\to\eta\pi^+\pi^-$ has been measured in the center-of-mass energy range from 1.22 to 2.00 GeV. Obtained results are in agreement with previous measurements and have better accuracy. The energy dependence of the $e^+e^-\to\eta\pi^+\pi^-$ cross section has been fitted with the vector-meson dominance model. From this fit the product of the branching fractions $B(\rho(1450)\to\eta\pi^+\pi^-)B(\rho(1450)\to e^+e^-)$ has been extracted and compared with the same products for $\rho(1450)\to\omega\pi^0$ and $\rho(1450)\to\pi^+\pi^-$ decays. The obtained cross section data have been also used to test the conservation of vector current hypothesis.

Equivalence Between Vector Meson Dominance and Unitarised Chiral Perturbation Theory

It is explicitly shown that either the approximate solution of the integral equation for the inverse of the pion form facto,r or the result of the Pad\(\text{\'e}\) approximant method of resumming the one loop Chiral Perturbation Theory (CPTH) are equivalent to the standard vector meson dominance (VMD) models, using the vector meson coupling to two pseudoscalars given by the KSRF relation. Inconsistencies between the one loop CPTH and its unitarised version (or the VMD model) are pointed out. The situation is better for the CPTH calculation of the scalar form factor and the related S-wave $\pi \pi$ scattering. The branching ratios of \(\tau \to \pi^+ \pi^0 \nu \), \(\tau \to K \pi \nu \), \(\tau \to K^+ \eta \nu\) and $\tau \to K^+ \bar{K^0} \nu\) using only two inputs as the \(\rho\) and \(K^*\) masses, or the two corresponding rms radii, agree with the experimental data. Using the same number of parameters, the corresponding one loop CPTH calculation cannot explain the $\tau$ data.

Study of the η′→Ve+e− decay with hidden local symmetry model**Supported by National Natural Science Foundation of China (11147008, 11275057, U1332103, U1232101) and Program for Science and Technology Innovation Talents in Universities of Henan Province (2012HASTIT030)

Within the hidden local symmetry framework, the Dalitz decay η′→Ve+e− is studied with the vector meson dominance model. It is found that the partial width Γ(η′→ωe+e−) ≈ 40 eV and branching ratio β(η′→ωe+e−) ≈ 2×10−4, and Γ(η′→ρe+e−) ≈ 10Γ(η′→ωe+e−) and β(η′→ρe+e−) ≈ 10β(η′→ωe+e−). The maximum position of the dilepton distribution is me+e− ≈1.33 MeV. These decays are measurable with the advent of high statistic η′ experiments.

Axial anomaly and vector meson dominance model

A connection between the axial anomaly and the vector meson dominance model is revealed for the processes of pseudoscalar meson-photon transitions. The analytic continuation of the anomaly sum rules, which are exact QCD relations following follow from the dispersive representation of the axial anomaly, to the time-like region is performed. Using these sum rules, the transition form factors of π0, η, and η′ mesons in this region are calculated. A good agreement with the available experimental data is found.

Direct [formula omitted] production in [formula omitted] collisions

Direct production of the charmonium-like state X(3872) in e+e− collisions is considered in the framework of the vector meson dominance model. An order-of-magnitude estimate for the width Γ(X→e+e−) is found to be ≳0.03 eV. The same approach applied to the χc1 charmonium decay predicts the corresponding width of the order 0.1 eV in agreement with earlier estimates. Experimental perspectives for the direct production of the 1++ charmonia in e+e− collisions are briefly discussed.

Vector meson dominance and deep inelastic scattering at low and mediumQ2

We argue that deep inelastic scattering (DIS) at small values of ${Q}^{2}$ is an essentially nonperturbative process and can be described, partially at least, by the vector meson dominance (VMD) model. We show this by the straightforward calculation that the VMD model alone can successfully explain data on structure functions of DIS in a broad interval of $x(5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\textdiv{}{10}^{\ensuremath{-}4})$ for the region ${Q}^{2}\ensuremath{\le}1\text{ }\text{ }{\text{GeV}}^{2}$. For a description of data at larger ${Q}^{2}$ we use the two-component ($\mathrm{VMD}+\text{perturbative}\text{ }\mathrm{QCD}$) approach. We show that these two components can be separated if VMD is used in the aligned jet version. We take into account, in calculations of the VMD component of structure functions, the excited states of the $\ensuremath{\rho}$-meson and nondiagonal transitions between different members of the $\ensuremath{\rho}$-meson family. Amplitudes of these transitions arre obtained using a formalism of the light-front Bethe-Salpeter equation and the method of diffraction-scattering eigenstates. The perturbative QCD component is calculated using a framework of the color dipole model with the dipole cross section having a Regge-type energy dependence. We present results of the detailed comparison of our predictions with experimental data for structure functions of the nucleon. We also obtain approximate predictions for the structure functions in the region of very small $x$, up to ${10}^{\ensuremath{-}8}\textdiv{}{10}^{\ensuremath{-}9}$, and show that the nonperturbative component at such values of $x$ is still relatively large and must be taken into account if ${Q}^{2}$ is about a few ${\mathrm{GeV}}^{2}$ or less.

DETERMINATION OF THE MAGNETIC DIPOLE MOMENT OF THE RHO MESON

We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the e+e- → π+π-2π0 process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the γ* → 4π vertex using a vector meson dominance model, including all intermediate resonance contributions. We find that μρ = 2.1 ± 0.5 [e/2mρ].

Production ofJ/Ψon the nucleon and on deuteron targets

A coupled-channel model with $\pi N$, $\rho N$ and $J/\Psi N$ channels is developed to predict the $\pi + N \rightarrow J/\Psi + N $ cross sections. The $J/\Psi$-$N$ interaction is parameterized in a form related to what has been predicted by the effective field theory approach and Lattice QCD. The other interactions within the model are constrained by the decay width of $J/\Psi \rightarrow \rho + \pi$ and the total cross section data of $\pi N$ reactions. The calculated meson-baryon amplitudes are then used to predict the cross sections of the $J/\Psi$ production on the deuteron target by including the contributions from the impulse term and the one-loop calculations of the final $NN$ and $J/\Psi N$ re-scattering effects. Predictions of the dependence of the cross sections of $\pi^- + p \rightarrow J/\Psi+ n$, $\gamma + d \rightarrow J/\Psi + n + p$, and $\pi^+ d \rightarrow J/\Psi +p +p$ on the $J/\Psi$-$N$ potentials are presented for experimental determinations of the $J/\Psi$-$N$ interaction. Within the vector meson dominance model, we have also applied the constructed coupled-channel model to predict the $\gamma + p\rightarrow J/\Psi + p$ cross sections near the $J/\Psi$ production threshold.

Non-contact Interactions and the Hadronic Light-by-light Contribution to the Muon $g-2$

We summarise recent results for the quark loop part of the light-by-light scattering contribution to the muons anomalous magnetic moment. In particular we focus on the impact of a momentum dependent quark and quark-photon vertex. We compare the Dyson-Schwinger description with that of the extended Nambu--Jona-Lasinio model (ENJL) and find important quantitative differences. In particular the transverse parts of the quark-photon-vertex, which serve as a dynamical extension of simple vector meson dominance models, do not yield the large suppression as found in the ENJL model.

The ωρπ coupling and the influence of heavier resonances

We determine the value of the ω − ρ − π mesons coupling (gωρπ), in the context of the vector meson dominance model, from radiative decays, the ω → 3π decay width and the e+e− → 3π cross section. For the last two observables we consider the effect of either a heavier resonance (ρ'(1450)) or a contact term . A weighted average of the results from the set of observables yields gωρπ = 13.9 ± 0.1 GeV−1 in absence of those contributions, and gωρπ = 11.9 ± 0.2 GeV−1 or gωρπ = 11.4 ± 0.1 GeV−1 when including the p' or contact term respectively. Improved measurements of these observables and the p'(1450) meson parameters are needed to give a definite answer on the pertinence of the inclusion of this last one in the considered processes.

Vector meson electroproduction in QCD

Based on the generalized QCD vector meson dominance model, we study the electroproduction of a vector meson off a proton in the QCD inspired eikonalized model. Numerical calculations for the total cross section σtot and differential cross section dσ/dt are performed for ρ, ω and φ meson electroproduction in this paper. Since gluons interact among themselves (self-interaction), two gluons can form a glueball with quantum numbers IG, JPC = 0+,2++, decay width Γt ≈ 100 MeV, and mass of mG = 2.23 GeV. The three gluons can form a three-gluon colorless bound state with charge conjugation quantum number C = −1, called the Odderon. The mediators of interactions between projectiles (the quark and antiquark pair fluctuated from the virtual photon) and the proton target (a three-quark system) are the tensor glueball and the Odderon. Our calculated results in the tensor glueball and Odderon exchange model fit to the existing data successfully, which evidently shows that our present QCD mechanism is a good description of meson electroproduction off a proton. It should be emphasized that our mechanism is different from the theoretical framework of Block et al. We also believe that the present study and its success are important for the investigation of other vector meson electro- and photoproduction at high energies, as well as for searching for new particles such as tensor glueballs and Odderons, which have been predicted by QCD and the color glass condensate model (CGC). Therefore, in return, it can test the validity of QCD and the CGC model.

THE ωρπ COUPLING IN THE VMD MODEL REVISITED

We determine the value of the ω-ρ-π mesons coupling (gωρπ), in the context of the vector meson dominance model, from radiative decays, the ω→3π decay width and the e+e-→3π cross-section. For the last two observables we consider the effect of either a heavier resonance (ρ′(1450)) or a contact term. A weighted average of the results from the set of observables yields gωρπ = 14.7±0.1 GeV -1 in absence of those contributions, and gωρπ = 11.9 ± 0.2 GeV -1 or gωρπ = 11.7 ± 0.1 GeV -1 when including the ρ′ 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 ρ′(1450) meson parameters are needed to give a definite answer on the pertinence of the inclusion of this last one in the considered processes.

RADIATIVE LEPTONIC DECAYS OF THE CHARGED B AND D MESONS INCLUDING LONG-DISTANCE CONTRIBUTION

In this work, we study the radiative leptonic decays of B-, D-and [Formula: see text], including both the short-distance and long-distance contributions. The short-distance contribution is calculated by using the relativistic quark model, where the bound state wave function we used is that obtained in the relativistic potential model. The long-distance contribution is estimated by using vector meson dominance model.

Axial anomaly and the interplay of quark loops with pseudoscalar and vector mesons in theγ*→π+π0π−process

Motivated by the ongoing measurements of the Primakoff process ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ by the COMPASS Collaboration at CERN, the transition form factor for the canonical anomalous process ${\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$ is calculated in a constituent quark-loop model. The simplest contribution to this process is the quark ``box'' amplitude. In the present paper we also explicitly include the vector meson degrees of freedom, i.e., the $\ensuremath{\rho}$ and the $\ensuremath{\omega}$, thus giving rise to additional, resonant contributions. We find that in order to satisfy the axial anomaly result, a further subtraction in the resonant part is needed. The results are then compared with the vector meson dominance model as well as the Dyson-Schwinger calculations, the chiral perturbation theory result, and the available data.

Absorption cross sections by nucleons

The cross sections of $B_{c}$\ absorption by nucleons are calculated in meson-baryon exchange model using hadronic Lagrangian based on SU(4)/SU(5) flavor symmetries. The values of different coupling constants used in the model are obtained from vector meson dominance model, QCD sum rule or SU(4)/SU(5) flavor symmetries. Calculated values of cross sections are found to be significantly different from the previous study in which b-flavored hadron exchange is neglected. These results could be useful in calculating production rate of $B_{c}$ meson in relativistic heavy ion collisions.

Electroproduction of the Roper resonance on the proton: The role of the three-quark core and the molecularNσcomponent

The Roper resonance is considered as a mixed state of a three-quark core configuration and a hadron-molecular component $N+\ensuremath{\sigma}$. Based on this ansatz we study electroproduction of the Roper resonance. The strong and electromagnetic couplings induced by the quark core are calculated in the $^{3}P_{0}$ model. The contribution of the vector-meson cloud to the electromagnetic transition is given in the framework of the vector-meson dominance model. Results are compared with the recent JLab electroproduction data.

Production ofωπ0pairs in electron-positron annihilation

The process of electron-positron annihilation into a pair of ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\omega}$ mesons is considered in the framework of the SU(2)$\ifmmode\times\else\texttimes\fi{}$SU(2) Nambu--Jona-Lasinio model. Contributions of intermediate photons, $\ensuremath{\rho}(770)$ and ${\ensuremath{\rho}}^{'}(1450)$ vector mesons are taken into account. It is shown that the bulk of the cross section at energies below 2 GeV is provided by the process with intermediate ${\ensuremath{\rho}}^{'}(1450)$ state. The contribution due to single photon and $\ensuremath{\rho}(770)$ exchange is in agreement with the vector meson dominance model. Numerical results are compared with experimental data.

Low mass dimuon production in proton-nucleus collisions at 400 GeV/ c

The NA60 experiment has studied low-mass muon pair production in proton-nucleus collisions with a system of Be, Cu, In, W, Pb and U targets using a 400 GeV/ c proton beam at the CERN SPS. The mass spectrum is well described by the superposition of the two-body and Dalitz decays of the light neutral mesons η, ρ, ω, η ′ and ϕ new measurement of the electromagnetic transition form factors of the η and ω was performed. The values found are Λ η − 2 = 1.950 ± 0.059 (stat.) ± 0.042 (syst.) ( GeV / c 2 ) − 2 and Λ ω − 2 = 2.241 ± 0.025 (stat.) ± 0.028 (syst.) ( GeV / c 2 ) − 2 . They agree with the previous available measurements, improving their uncertainty thanks to the higher statistics, and confirm the discrepancy with the prediction of the Vector Meson Dominance model in the case of the electromagnetic form factor of the ω meson. The comparison of the data to an improved calculation including also a direct point-like term is discussed. The nuclear dependence of the production cross sections of the ω, ρ and ϕ mesons was also studied. An increase of the ϕ production with respect to the ω is observed from p-Be to p-U collisions. Parameterizing the nuclear dependence of the production cross sections with the power law σ pA ∝ A α , one finds α ω = 0.841 ± 0.014 (stat.) ± 0.030 (syst.) and α ϕ = 0.906 ± 0.011 (stat.) ± 0.025 (syst.) . A possible bias induced by the use of the light Be target is found. If it is excluded, the results are α ω = 0.801 ± 0.037 (stat.) ± 0.041 (syst.) and α ϕ = 0.963 ± 0.026 (stat.) ± 0.017 (syst.) , showing an increase of α ϕ and a decrease of α ω .

Measurement of the η and ω Dalitz decays transition form factors in p-A collisions at 400 GeV/c with the NA60 apparatus

The NA60 experiment has studied low-mass muon pairs production in proton-nucleus collisions at 400 GeV/c at the CERN SPS. The mass spectrum is well described by the superposition of the two-body and Dalitz decays of the light neutral mesons η, ρ, ω, ή and ϕ. The large collected statistics allows to isolate the contributions due to the Dalitz decays of the η and ω mesons, from which the electromagnetic transition form factors of the two mesons have been extracted. The found values agree with the previous available measurements, improving their uncertainty thanks to the higher statistics. The results thus confirm the discrepancy with the prediction of the Vector Meson Dominance model in the case of the electromagnetic form factor of the ω meson.

Electromagnetic form factors of nucleons in the extended vector meson dominance model

Extended vector meson dominance model, that allows to describe the electromagnetic form factors of nucleons obeying the asymptotic quark counting rule prescriptions and contains the minimal number of free parameters, is presented. We get a reasonable fit of form factors over experimentally available space-like region of momentum transfer and get also reasonable results in the time-like region.