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Chiral Approach to the Phi Radiative Decays and the Quark Structure of the Scalar Meson

Chiral Approach to the Phi Radiative Decays and the Quark Structure of the Scalar Meson. Masayasu Harada (Nagoya Univ.). @ HEP-Nuclear Physics Cross Over Meeting (May 27, Nara Women's University, Nara, Japan). based on.

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Chiral Approach to the Phi Radiative Decays and the Quark Structure of the Scalar Meson

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  1. Chiral Approach to the Phi Radiative Decays and the Quark Structure of the Scalar Meson Masayasu Harada (Nagoya Univ.) @ HEP-Nuclear Physics Cross Over Meeting (May 27, Nara Women's University, Nara, Japan) based on • D.Black, M.H. and J.Schechter, Phys. Rev. Lett. 88, 181603 (2002) • D.Black, M.H. and J.Schechter, in preparation.

  2. 1. Introduction

  3. q q s q u d u d ☆ A possible structure of Pentaquarks Jaffe-Wilczek, PRL 91, 232003; Shuryak-Zahed, hep-ph/0310270 Θ+～ diquarks ・・・ play an important role Diquarks give a new information on forces between 2 quarks in QCD. 3 × 3 → 1 Most Atractive Channel Next MAC q 3 × 3 → 3 ⇒ Important for Color SuperConductivity It is interesting to study other bound states including diquarks.

  4. q q q q q q q q q q q q q ☆ Possible bound states including diquarks other than pentaquarks baryons ? ordinary mesons ? ordinary mesons X(3872) ? dibaryons ?

  5. ◎ Effective Lagrangian study of the properties of the scalar mesons ・ Radiative decays involving scalar mesons ☆ Light Scalar mesons scalar nonet ◎ Properties • interactions with other mesons • ・・・ • quark structure ・・・ 2-quark or 4-quark ? Exotic hadron ?

  6. Outline • Introduction • 2. Quark Structure of Light Scalar Mesons • 3. Effective Lagrangian for Scalar Mesons • - Masses of scalar mesons • and thier couplings to pseudoscalar mesons - • 4. Radiative Decays Involving Scalar Mesons • 5. Summary

  7. 2. Quark Structure of Light Scalar Mesons

  8. ☆ 2-quark picture ⇔ φ ⇔ K* ⇔ ρ, ω contradict ? ◎ “experiment”

  9. ☆ 4-quark picture ☆ diquark one-gluon exchange gives atraction in ◎ scalar diquarks ◎ scalar anti-diquarks

  10. ☆ Scalar nonet consistent with “experiment” !

  11. 3. Effective Lagrangian for Scalar Mesons - Masses of scalar mesons and their couplings to pseudoscalar mesons -

  12. ☆ Scalar meson nonet field D.Black, A.H.Fariborz, F.Sannino and J.Schechter, PRD 59, 074026 (1999) cf: vector meson nonet field

  13. ☆ Relation to quark structure

  14. - ms d = 2 ms b = 2 c < 0 ☆ Mass terms for scalar nonet quark mass

  15. c = d = 0 ; b < 0

  16. D.Black, A.H.Fariborz, F.Sannino and J.Schechter, PRD 59, 074026 (1999)

  17. from hadronic decays ◎ Fit π-π scattering D.Black, A.H.Fariborz, F.Sannino and J.Schechter, PRD 59, 074026 (1999) A.H.Fariborz and J.Schechter, PRD 60, 034002 (1999) ☆ An effective Lagrangian for the interactions among one scalar meson and two pseudoscalar mesons ◎ light pseudoscalar mesons (p, K, h) ・・・ approximate Nambu-Goldstone bosons ☆ Pseudoscalar mesons couple to other mesons with derivative interaction

  18. 4. Radiative Decays Involving Scalar Mesons • D.Black, M.H. and J.Schechter, Phys. Rev. Lett. 88, 181603 (2002) • D.Black, M.H. and J.Schechter, in preparation

  19. ☆ Radiative decays involving light scalar mesons scalar → g+g vector → scalar + g scalar →vector + g ◎ Effective Lagrangian ← SU(3)L×SU(3)R chiral symmetry + vector meson dominance

  20. g N V V = r, w, f V N N V V g g g ☆ Vector Meson Dominance (VMD) in (N→gg), (V→Ng) and (N→Vg ) N →γγ V → Nγ N → Vγ VMD → NVVvertex determines (N→gg), (V→Ng) and (N→Vg )

  21. ・・・ not contribute ☆ Effective Lagrangian for NVV vertices ☆ SU(3)L×SU(3)R chiral symmetry + VMD

  22. ☆ Predictions (GeV-1) (keV) ◎ Inputs ・・・ It may be difficult to distinguish two pictures from radiative decays !?

  23. ・ K-loop effect gives an important contribution N.N.Achasov and V.N.Ivanchenko, NPB315, 465 (1989) F.E.Close, N.Isgur and S.Kumano, NPB389, 513 (1993) ・・・ ☆ f→ f0 g decay ◎ prediction from present analysis 1.87±0.11 keV ◎ Inclusion of mixing to f0(1370), f0(1500), f0(1700) helps but not enough (Teshima-Kitamura-Morisita, hep-ph/0501073) ◎ Similar contribution for derivative coupling ? → Let us study φ→π0ηγ decay

  24. ☆ f→p0hgthrough g f p0 h poor fit for

  25. ☆ f→p0hgthrough with K-loop ・ good fit for ・poor fit for K K Note : Exact Cancellation of divergences

  26. ☆ f→p0hgthrough with and without K-loop g f p0 h K K Good agreement with experiment !

  27. hadronic processes ⇒ 5. Summary ☆ Analysis on the quark structure of the scalar mesons based on the effective Lagrangian approach • mass hierarchy ☆ Radiative decays involving scalar mesons Both pictures predict similar values for several radiative decays. ⇒ It may be difficult to distinguish two pictures from radiative decays !? Problems in φ→π0π0γand φ→ηπ0γ decays ⇒ Inclusion of K-loop effects gives a good fit to experimental data.

  28. ☆ Future directions • Study the φ→π0π0γ decay • Include K-loop into a0, f0 propagators • Include non-resonant background • Study several radiative decays • ・・・ Explore the structure of the light scalar nonet

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