We make a theoretical study of the $\J$ decays into $\omega\pi\pi$,
$\phi\pi\pi$, $\omega K \bar{K}$ and $\phi K\bar{K}$ using the techniques of
the chiral unitary approach stressing the important role of the scalar
resonances dynamically generated through the final state interaction of the two
pseudoscalar mesons. We also discuss the importance of new mechanisms with
intermediate exchange of vector and axial-vector mesons and the role played by
the OZI rule in the $\J\phi\pi\pi$ vertex, quantifying its effects. The results
nicely reproduce the experimental data for the invariant mass distributions in
all the channels considered.Comment: Prepared for the 10th International Symposium on Meson-Nucleon
  Physics and the Structure of the Nucleo

Chiang, H. C.

Oset, E.

Palomar, J. E.

Roca, L.

English

arXiv

We make a theoretical study of the $\J$ decays into ωππ, ϕππ, ωKK¯ and ϕKK¯ using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the $\J\phi\pi\pi$ vertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels considered

Roca Zamora, Luis

Palomar Burdeus, Juan Esteban

Oset Báguena, Eulogio

Chiang, H.C.

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/0410405v1  29 Oct 2004Unitary chiral dynamics in J/Ψ decays into V PP and therole of the scalar mesonsL. Roca1, J. E. Palomar1, E. Oset1 and H. C. Chiang21Departamento de F´ısica Teo´rica and IFIC, Centro Mixto Universidad de Valencia-CSIC,Institutos de Investigacio´n de Paterna, Aptdo. 22085, 46071 Valencia, Spain2Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, ChinaAugust 8, 2013AbstractWe make a theoretical study of the J/Ψ decays into ωpipi, φpipi, ωKK¯ and φKK¯ using thetechniques of the chiral unitary approach stressing the important role of the scalar resonancesdynamically generated through the final state interaction of the two pseudoscalar mesons.We also discuss the importance of new mechanisms with intermediate exchange of vector andaxial-vector mesons and the role played by the OZI rule in the J/Ψφpipi vertex, quantifying itseffects. The results nicely reproduce the experimental data for the invariant mass distributionsin all the channels considered.The J/Ψ decay into a pseudoscalar meson pair and a vector meson has been claimed to be one ofthe most suited reactions to study the long controversial nature of the scalar mesons, on which theinterpretation as qq¯ mesons or as meson-meson molecules has mainly centered the discussion. In thelast years, a chiral unitary coupled channel approach [1] has proved to be successful in describingmeson-meson interactions in all channels up to energies ∼ 1.2 GeV, far beyond the natural limitof applicability of the standard Chiral Perturbation Theory (ChPT), which is ∼ 500 MeV wherethe pole of the lightest resonance, the σ meson, appears. In this approach the scalar mesons riseup naturally as dynamically generated resonances, in the sense that, without being included asexplicit degrees of freedom, they appear as poles in the s-wave meson-meson scattering amplitudes.The aim of the present work 1 is to make a consistent and comprehensive description of theJ/Ψ → V PP decays, including all the mechanisms able to influence the region of pseudoscalarpair invariant masses up to ∼ 1.1 GeV, addressing the role played by the scalar mesons and theOZI rule. Following the framework of the chiral unitary approach, we will implement the finalmeson-meson state interaction in order to generate dynamically the scalar resonances involved.The first mechanisms considered are those involving a direct coupling of the J/Ψ to the twopseudoscalars and the vector, implementing the final state interaction of the pseudoscalars pair,as is depicted in Fig. 1 for the J/Ψ → ωpi+pi− channel. The thick dot in Fig. 1 means that oneis considering the full pipi(KK¯) → pi+pi− t-matrix, involving the loop resummation of the Bethe-Salpeter equation and no just the lowest order pipi(KK¯) → pi+pi− amplitude. Actually this loopresummation is what dynamically generates the scalar resonances. The J/ΨV PP vertex can beconstructed using SU(3) arguments to relate the different isospin channels and parameterizing theamplitudes in a way which clearly manifest the role played by the OZI rule in this direct vertex,accounted for by means of a parameter λφ such that, if the OZI rule would be exact, then λφwould be zero.In analogy with the approach in Ref. [3] (and in some sense to [4]), we consider next themechanisms involving the sequential exchange of a vector or axial-vector meson as depicted in1All the details of the model can be found in [2], on which the present contribution is based1J/Ψpi+pi+pi−pi−J/Ψ, ,pi+pi−pi0, ,pi+pi0pi−K , K− 0K , K+ 0ω ω+a) b)Figure 1: Diagrams with direct J/ΨV PP vertex at tree level, a), and with the iterated mesonloops, b).pi+pi−J/Ψp1q* q *p2pi−pi+J/Ψp1p2ρ − ρ+ωq +P qωP’Figure 2: Diagrams for the tree level mechanisms with sequential vector meson exchange.Fig. 2 for the vector meson case for the ωpipi channel. The vertices needed are obtained fromsuitable phenomenological Lagrangians (see [2, 3, 5]). In Figs. 3 and 4 we show the mechanismswith the implementation of the FSI of the pseudoscalar mesons.The only two free parameters in our model are the coupling of the direct J/ΨV PP vertexand the OZI rule violation parameter, λφ. Fitting our model to the J/Ψ → ωpi+pi− and J/Ψ →φpi+pi− experimental data we obtain values of λφ clearly different from zero (λφ = 0.12, 0.20)and reasonably smaller than one, what manifests the OZI rule violation within reasonable values.In Fig. 5, left column, we show the results for ωpipi and φpipi channels including an estimationof the theoretical error band. The experimental data shown in the figures have been obtainedfrom [6–9]. Concerning the scalar mesons, it is important to stress first that the final shape andstrength of the bump appearing in the pipi invariant mass distribution in the ωpipi channel at∼ 500 MeV is determined by a subtle interference between the final state interaction in the directJ/ΨV PP mechanisms and the tree level direct J/ΨV PP decay. This means that the shape andposition of the bump does not directly represent the physical properties of the σ meson, since it isdistorted due to interferences with other terms not related to the σ meson. Therefore one has tobe extremely careful when using the experimental data to extract the physical σ meson propertiesby fitting Breit-Wigner-like shapes. On the other hand, the relative weights of the f0(980) and theσ meson are well reproduced in both the ωpipi and φpipi channels in spite of their large differencein these channels. This relative weight is mainly determined by the OZI rule violation parameterand the interferences of the ”direct” terms with the other mechanisms, specially in the f0(980)region. In our model, since the scalar mesons are dynamically generated through the resummedmeson-meson amplitude, the relative weight between the f0(980) and the σ mesons is related to therelative weight between the KK¯ → pipi and pipi → pipi, in I = 0, scattering amplitudes. Speciallyremarkable is the fair agreement in the f0(980) region of the ωpipi channel despite the smallness ofpi−pi+pi−pi+pi+pi−pi0pi+pi0pi−pi+pi−J/Ψ J/ΨJ/Ψ+ +ω ωωρ ρ ρ− + 0Figure 3: Sequential vector meson exchange diagrams with final state interaction of pions2pi−pi+pi−pi+J/ΨJ/Ψ−K +Kpi−J/Ψ0K+K −K 0Kpi+pi+pi−J/Ψ0K0K+ωω+ωK *K * K *++ωK *− 0 0Figure 4: Sequential vector meson exchange diagrams with final state interaction of kaons980 1000 1020 1040 1060 1080 1100 1120 1140MI (MeV)00.20.40.60.8107 × dΓ/dMIDM2J/Ψ     ωK+K- G_ > 0980 1000 1020 1040 1060 1080 1100 1120 1140MI (MeV)00.20.40.60.811.21.41.6107× dΓ/dMIDM2MARK-IIIJ/Ψ     φK+K- G_ > 0300 400 500 600 700 800 900 1000 1100MI (MeV)0123456107 × dΓ/dMIDM2BES300 400 500 600 700 800 900 1000 1100MI (MeV)00.511.522.533.544.55 107 × dΓ/dMIDM2MARK-IIIJ/Ψ     ωpi+pi−J/Ψ     φpi+pi−Figure 5:3the bump and the fact that many mechanisms contribute in this region.Finally, in Figs.5, right column, we apply our results to the ωKK¯ and φKK¯ decay channels,obtaining a fair agreement without introducing any extra freedom in the model. This is a nice testof the present model, both reproducing the absolute strength, and also the shape, which showsmuch strength close to threshold as a reflection of the proximity of the f0(980) resonance belowthreshold.In conclusion, we have obtained a good description of these interesting J/Ψ decays combiningphenomenological Lagrangians and the techniques of the chiral unitary approach to implementthe final state rescattering of the pseudoscalar pairs, quantifying the controversial non-trivial roleof the scalar mesons and the violation of the OZI rule. The fact that once more one is ableto reproduce the shape and strength of the f0(980) and the σ resonances without the need tointroduce them as explicit degrees of freedom provides an extra support to the idea of the natureof these resonances as dynamically generated from the interaction of the mesons.References[1] J. A. Oller, E. Oset and A. Ramos, Prog. Part. Nucl. Phys. 45 (2000) 157.[2] L. Roca, J. E. Palomar, E. Oset and H. C. Chiang, arXiv:hep-ph/0405228.[3] J. E. Palomar, L. Roca, E. Oset and M. J. Vicente Vacas, Nucl. Phys. A 729 (2003) 743[arXiv:hep-ph/0306249].[4] E. Oset, J. R. Pelaez and L. Roca, Phys. Rev. D 67 (2003) 073013 [arXiv:hep-ph/0210282].[5] L. Roca, J. E. Palomar and E. Oset, arXiv:hep-ph/0306188.[6] N. Wu, arXiv:hep-ex/0104050.[7] J. E. Augustin et al. [DM2 Collaboration], Nucl. Phys. B 320 (1989) 1.[8] A. Falvard et al. [DM2 Collaboration], Phys. Rev. D 38 (1988) 2706.[9] W. S. Lockman [MARK-III Collaboration], SLAC-PUB-5139 Presented at 3rd Int. Conf. onHadron Spectroscopy, Ajaccio, France, Sep 23-27, 19894

Unitary chiral dynamics in J/Psi decays into VPP and the role of the scalar mesons

L. ROCA

J. E. PALOMAR

E. OSET

H. C. CHIANG

Crossref

UNITARY CHIRAL DYNAMICS IN J/Ψ DECAYS INTO VPP AND THE ROLE OF THE SCALAR MESONS

http://dx.doi.org/10.1142/S0217751X0502358X

Unitary chiral dynamics in $J/\Psi$ decays into $VPP$ and the role of
  the scalar mesons

Unitary chiral dynamics in $J/\Psi$ decays into $VPP$ and the role of the scalar mesons

Abstract

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Unitary chiral dynamics in J/ΨJ/\PsiJ/Ψ decays into VPPVPPVPP and the role of the scalar mesons

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Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

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Unitary chiral dynamics in $J/\Psi$ decays into $VPP$ and the role of the scalar mesons