Radiative Decays Of Vector Mesons Research Articles

Decays of light mesons in the relativistic quark model

In the framework of the relativistic quark model based on the point form of the Poincaré-invariant quantum mechanics, the parameters were fixed using the integral representations of the lepton decay constants of pseudoscalar and vector mesons containing u-, d- and s-quarks. As a result of numerical calculations using the oscillator wave function, the basic parameters of the model are obtained using the pseudoscalar density constant and current quark masses. The analysis showed that the obtained calculation results in the framework of the model and the experimental data on the lepton decays of hadrons agree well with each other. As a result, the calculation method is generalized to the case of hadronic transitions with γ-quantum emission and a subsequent calculation of the integral representations of radiative decay constants of pseudoscalar and vector mesons. The obtained values of the anomalous magnetic moments are compared with the baryon data. As a test of the model, the authors studied the behavior of the form-factors of radiative decays of vector mesons with a subsequent comparison to the modern experimental data in the q < 0.5 GeV range where the resonance effects are insignificant. As a result, self-consistent descriptions of lepton and radiative transitions were obtained within the framework of the model proposed by the authors.

η–η′ Mixing Angle from Vector Meson Radiative Decays

The η–η′ mixing from the derivative coupling SU(3)×SU(3) symmetry breaking term, produces an additional momentum-dependent pole term for processes with η′, but is suppressed in the η amplitude by a factor mη2/mη′2. Thus processes with η meson could then be described, to first order in SU(3) breaking, by the usual η–η′ mixing angle, while processes with η′ could be effectively described by a new mixing angle as in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature. In this talk, I would like to present a recent work in which we show that, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, the η–η′ system could be described by a meson field renormalization and a new mixing angle θ. From the sum rules relating θ and d to the measured vector meson radiative decays amplitudes, we obtain θ=−(13.99±3.1)°, d=0.12±0.03 from ρ→ηγ and η′→ργ decays, for ω, θ=−(15.47±3.1)°, d=0.11±0.03, and for ϕ, θ=−(12.66±2.1)°, d=0.10±0.03. It seems that vector meson radiative decays would favor a small η−η′ mixing angle as found in previous analysis.

η−η′mixing

The $\eta -\eta^{\prime}$ mixing mass term due to the derivative coupling $SU(3)\times SU(3)$ symmetry breaking term, produces an additional momentum-dependent pole term for processes with $\eta^{\prime}$, but is suppressed in the $\eta$ amplitude by a factor $m_{\eta}^{2}/m_{\eta^{\prime}}^{2}$. This seems to be the origin of the two-angle description of the pseudo-scalar decay constants used in the literature. In this paper, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, we show that the $\eta -\eta^{\prime}$ system could be described by a meson field renormalization and a new mixing angle $\theta$ which differs from the usual mixing angle $\theta_{P}$ by a small momentum-dependent mixing $d$ term. This new mixing scheme with exact treatment of the momentum-dependent mixing term, is actually simpler than the perturbation treatment and should be used in any determination of the $\eta -\eta^{\prime}$ mixing angle and the momentum-dependent mixing term. Assuming nonet symmetry for the $\eta_{0}$ singlet amplitude, from the sum rules relating $\theta$ and $d$ to the measured vector meson radiative decays amplitudes, we obtain consistent solutions with $\theta=-(13.99\pm 3.1)^{\circ}$, $d=0.12\pm 0.03$ from $\rho\to\eta\gamma$ and $\eta^{\prime}\to\rho\gamma$ decays, for $\omega$ , $\theta=-(15.47\pm 3.1)^{\circ}$, $d=0.11\pm 0.03$, and for $\phi$, $\theta=-(12.66\pm 2.1)^{\circ}$, $d=0.10\pm 0.03$. It seems that vector meson radiative decays would favor a small $\eta-\eta^{\prime}$ mixing angle and a small momentum-dependent mixing term.

Meson decays in an extended Nambu—Jona-Lasinio model with heavy quark flavors

In a previous work, we proposed an extended Nambu-Jona-Lasinio (NJL) model including heavy quark flavors. In this work, we will calculate strong and radiative decays of vector mesons in this extended NJL model, including light ρ, ω, K*, Φ and heavy D*, Ds*, B*, Bs*.

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $\pi\pi$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $\sigma\gamma$ electromagnetic form factor. Finally, and evaluation of the contribution of $\gamma\pi\pi$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.

η–[formula omitted] mixing angle from vector meson radiative decays

The octet–singlet η–η′ mixing mass term could have a derivative O(p2) term as found in recent analysis of the η–η′ system. This term gives rise to an additional momentum-dependent pole contribution which is suppressed by a factor mη2/mη′2 for η relative to the η′ amplitude. The processes with η meson can then be described, to a good approximation, by the momentum-independent mixing mass term which gives rise to a new η–η′ mixing angle θP, like the old η–η′ mixing angle used in the past, but a momentum-dependent mixing term d, like sin(θ0−θ8) in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature, is needed to describe the amplitudes with η′. In this Letter, we obtain sum rules relating θP and d to the physical vector meson radiative decays with η and η′, as done in our previous work for η meson two-photon decay, and with nonet symmetry for the η′ amplitude, we obtain a mixing angle θP=−(18.76±3.4)°, d=0.10±0.03 from ρ→ηγ and η′→ργ decays, for ω, θP=−(15.81±3.1)°, d=0.02±0.03, and for ϕ, θP=−(13.83±2.1)°, d=0.08±0.03. A larger value of 0.06±0.02 for d is obtained directly from the nonet symmetry expression for the η′→ωγ amplitude. This indicates that more precise vector meson radiative decay measured branching ratios and higher order SU(3) breaking effects could bring these values for θP closer and allows a better determination of d.

Magnetic moments of octet baryons, angular momenta of quarks, and sea antiquark polarizations

One can determine antiquark polarizations in proton using the information from deep inelastic scattering, $\beta$ decays of baryons, orbital angular momenta of quarks, as well as their integrated magnetic distributions. The last quantities were determined previously by us performing a fit to magnetic moments of baryon octet. However, because of the SU(3) symmetry our results depend on two parameters. The quantity $\Gamma_{V}$, measured recently in a COMPASS experiment, gives the relation between these parameters. We can fix the last unknown parameter using the ratio of up and down quark magnetic moments which one can get from the fit to radiative vector meson decays. We calculate antiquark polarizations with the orbital momenta of valence quarks that follow from lattice calculations. The value of difference for up and down antiquark polarizations obtained in our calculations is consistent with the result obtained in a HERMES experiment.

A global fit to determine the pseudoscalar mixing angle and the gluonium content of the η' meson

We update the values of the η-η' mixing angle and of the η' gluonium content by fitting our measurement R = BR( → η'γ)/BR( → ηγ) together with several vector meson radiative decays to pseudoscalars (V → Pγ), pseudoscalar mesons radiative decays to vectors (P → Vγ) and the η' → γγ, π0 → γγ widths. From the fit we extract a gluonium fraction of ZG2 = 0.12±0.04, the pseudoscalar mixing angle ψP = (40.4±0.6)° and the −ω mixing angle ψV = (3.32±0.09)°. ZG2 and ψP are fairly consistent with those previously published. We also evaluate the impact on the η' gluonium content determination of future experimental improvements of the η' branching ratios and decay width.

Erratum: Glue content and mixing angle of theη−η′system: The effect of the isoscalar0−continuum [Phys. Rev. D70, 116001 (2004)

Masses and topological charges of the eta and eta' mesons are expressed in terms of the singlet-octet mixing angle theta. Contributions of the pseudoscalar 0- continuum are evaluated in a model independant way. Applications to the decay eta --> 3pi and to the radiative decay of vector mesons involving eta and eta' are considered. Agreement with experiment is in general good and the results quite stable for -30.5 <= theta <= -18.5

Glue content and mixing angle of theη−η′system: The effect of the isoscalar0−continuum

Masses and topological charges of the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons are expressed in terms of the singlet-octet mixing angle $\ensuremath{\theta}$. Contributions of the pseudoscalar ${0}^{\ensuremath{-}}$ continuum are evaluated in a model independent way. Applications to the decay $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ and to the radiative decay of vector mesons involving $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ are considered. Agreement with experiment is, in general, good and the results quite stable for $\ensuremath{-}30.5\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}\ensuremath{-}18.5\ifmmode^\circ\else\textdegree\fi{}$.

Meson form factors and the quark-level linear σ model

The quark-level linear σ model (L σM) is employed to compute a variety of electromagnetic and weak observables of light mesons, including pion and kaon form factors and charge radii, charged-pion polarizabilities, semileptonic weak K ℓ3 decays, semileptonic weak radiative pion and kaon form factors, radiative decays of vector mesons, and nonleptonic weak K 2 π decay. The agreement of all these predicted observables with experiment is striking. In passing, the tight link between the L σM and vector-meson dominance is shown.

η→π0γγdecay within a chiral unitary approach

We improve the calculations of the $\eta \to \pi^0 \gamma \gamma$ decay within the context of meson chiral lagrangians. We use a chiral unitary approach for the meson-meson interaction, thus generating the $a_0(980)$ resonance and fixing the longstanding sign ambiguity on its contribution. This also allows us to calculate the loops with one vector meson exchange, thus removing a former source of uncertainty. In addition we ensure the consistency of the approach with other processes. First, by using vector meson dominance couplings normalized to agree with radiative vector meson decays. And, second, by checking the consistency of the calculations with the related $\gamma \gamma \to \pi^0 \eta$ reaction. We find an $\eta \to \pi^0 \gamma \gamma$ decay width of $0.47\pm 0.10$ eV, in clear disagreement with published data but in remarkable agreement with the most recent measurement.

Structure of radiative interferences andg=2for vector mesons

The result of Burnett and Kroll (BK) states that for radiative decays, the interference of $O({\ensuremath{\omega}}^{\ensuremath{-}1})$ in the photon energy $\ensuremath{\omega}$ vanishes after the sum over polarizations of the involved particles. Using radiative decays of vector mesons, we show that if the vector meson is polarized, the $O({\ensuremath{\omega}}^{\ensuremath{-}1})$ terms are null only for the canonical value of the magnetic dipole moment of the vector meson, namely, $\mathbf{g}=2$ in Bohr magneton units. A subtle cancellation of all $O({\ensuremath{\omega}}^{\ensuremath{-}1})$ terms happens when summing over all polarizations to recover the Burnett-Kroll result. We also show the source of these terms and the corresponding cancellation for the unpolarized case and exhibit a global structure that can make them individually vanish in a particular kinematical region.

Mixing of Pseudoscalar Mesons

η-η' mixing is discussed in the quark-flavor basis with the hypothesis that the decay constants follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents – which embody the axial vector anomaly – all mixing parameters are fixed to first order of flavor symmetry breaking. An alternative set of parameters is obtained from a phenomenological analysis. We also discuss mixing in the octet-singlet basis and show how the relevant mixing parameters are related to those in the quark-flavor basis. The dependence of the mixing parameters on the strength of the anomaly and the amount of flavor symmetry breaking is investigated. Finally, we present a few applications of the quark-flavor mixing scheme, such as radiative decays of vector mesons, the photon-pseudoscalar meson transition form factors, the coupling constants of η and η' to nucleons, and the isospin-singlet admixtures to the π0 meson.

ω-ρ mixing and theω→ππγdecay

We reexamine the $\omega \to \pi^{0} \pi^{0} \gamma $ decay, adding the effect of $\omega-\rho$ mixing to the amplitude calculated with the aid of chiral perturbation theory and vector meson dominance. We predict the neutral decay to occur with a width of $\Gamma($\omega \to \pi^{0} \pi^{0} \gamma $) =(390\pm96) {\rm eV}$ and also analyze the effect of the $\omega-\rho$ mixing on the $\Gamma($\omega \to \pi^{0} \pi^{0} \gamma $)/ \Gamma($\omega \to \pi^{+} \pi^{-} \gamma $)$ ratio. Several remarks on the effect of $\omega-\rho$ mixing on certain radiative decays of vector mesons are presented.

Radiative decay of vector mesons

In this paper, radiative decays $\rho^0 \to \pi^+\pi^-\gamma, \pi^0\pi^0\gamma$ ,$\phi \to K^+K^-\gamma, K^0 \bar{K^0}\gamma$ are studied systematically in the U(3)$_L\timesU(3)_R$ chiral theory of mesons. The theoretical differential spectrum with respect to photon energy and branch ratio for $\rho^0 \to \pi^+\pi^-\gamma$ agree well with the experimental data. Differential spectrums and branch ratios for $\rho^0 \to \pi^0\pi^0\gamma, \phi \to K^+ K^-\gamma,\phi \to K^0\bar{K^0}\gamma$ are predicted. The process $\phi \to K^0 \bar{K^0} \gamma$ is relevant to precision measurment of CP-violation parameters in the kaon systerm at a $\phi$-factory. We give a complete estimate of the branch ratio for this decay process by including scalar resonance $f_0, a_0$ poles, nonresonant smooth amplitude and an abnormal parity process with $K^*$ pole which hasn't been considered before. We conclude that processes with intermediate $K^*$ do not pose a potential background problem for $\phi\to K^0\bar{K}^0$ CP violation experiments.

Vacuum Structure, Chiral Symmetry Breaking and Radiative Decays of Vector Mesons

The radiative decay widths of vector mesons were considered in a model involving chiral symmetry breaking through a nontrivial vacuum structure where the pion and kaon being treating consistently yield the constituent quark wave functions, approximately the same as that obtained from the gap equations and thus in a way determine the constituent quark field operators. Like its earlier success to some low energy hadronic phenomena, here also the model calculations of radiative decay widths of mesons are in reasonable agreements with other theoretical estimations as well as experimental measurements.

Hidden local symmetry for anomalous processes with isospin- and SU(3)-breaking effects.

We show that isospin/SU(3) breaking terms can be introduced to the anomalous VVP coupling in the hidden local symmetry scheme without changing Wess-Zumino-Witten term in the low-energy limit. We make the analysis for anomalous processes of 2-body and 3-body decays; radiative vector meson decays(V \to P\gamma), conversion decays of photon into a lepton pair(V \to P l^+ l^-) and hadronic anomalous decays(V \to PPP). The predictions successfully reproduce all experimental data of anomalous decays. In particular, we predict the decay widths of \rho^0 \to \pi^0 \gamma and \phi \to \eta' \gamma as 101 \pm 9 keV and 0.508 \pm 0.035 keV, respectively, which will be tested in the DAFNE \phi-factory. Moreover, prediction is also made for \phi \to \pi^0 e^+ e^-, \rho \to 3\pi, K^* \to K \pi \pi and so on, for which only the experimental upper bounds are available now.

Strange mesonic transition form factor.

The strange-quark vector current {rho}-to-{pi} meson transition form factor is computed at one-loop order using strange meson intermediate states. A comparison is made with a {phi}-meson dominance model estimate. They find that one-loop contributions are comparable in magnitude to those predicted by {phi}-meson dominance. It is possible that the one-loop contribution can make the matrix element as large as those of the electromagnetic current mediating vector meson radiative decays. However, due to the quadratic dependence of the one-loop results on the hadronic form factor cut-off mass, a large uncertainty in the estimate of the loops is unavoidable. These results indicate that non-nucleonic strange quarks could contribute appreciably in moderate-{vert_bar}Q{sup 2}{vert_bar} parity-violating electron-nucleus scattering measurements aimed at probing the strange-quark content of the nucleon.

Radiative vector-meson decays in SU (3) broken effective chiral lagrangians

Conventional SU (3)-breaking effects are shown to be easily introduced in the sector of effective chiral Lagrangians incorporating vector mesons and containing the VVP vertices related to the anomaly. An improved description of VP γ and P γγ transitions is obtained.