Radiative Decays involving Scalar Mesons Masayasu Harada (Nagoya Univ.) based Japan-US Workshop on “Electromagnetic Meson Production and Chiral Dynamics” (April 8, Osaka, Japan) D.Black, M.H. and J.Schechter, Phys. Rev. Lett. 88, (2002) D.Black, M.H. and J.Schechter, in preparation.

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

Outline 1. 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

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

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

☆ Scalar nonet consistent with “experiment” !

- Masses of scalar mesons and their couplings to pseudoscalar mesons -

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

☆ Relation to quark structure

☆ Mass terms for scalar nonet - m s d = 2 m s b = 2 c < 0 quark mass

c = d = 0 ; b < 0

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

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

D.Black, M.H. and J.Schechter, Phys. Rev. Lett. 88, (2002) D.Black, M.H. and J.Schechter, in preparation

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

☆ Vector Meson Dominance (VMD) in (N→  ), (V→N  ) and (N→V  ) N V =    V V  N N V  V N →γγV → Nγ N → Vγ VMD → NVV vertex determines (N→  ), (V→N  ) and (N→V  )

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

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

☆  → f 0  decay ◎ prediction from present analysis ・ 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) ・・・ 1.87±0.11 keV ◎ Inclusion of mixing to f 0 (1370), f 0 (1500), f 0 (1700) helps but not enough (Teshima-Kitamura-Morisita, hep-ph/ ) ◎ Similar contribution for derivative coupling ? → Let us study φ→π 0 ηγ decay

☆  →  0  through   00  poor fit for

☆  →  0  through with K-loop K K Note : Exact Cancellation of divergences ・ good fit for ・ poor fit for

  00  K K ☆  →  0  through with and without K-loop Good agreement with experiment !

☆ Analysis on the quark structure of the scalar mesons based on the effective Lagrangian approach hadronic processes ⇒ mass hierarchy ☆ Radiative decays involving scalar mesons Problems in φ→π 0 π 0 γand φ→ηπ 0 γ decays ⇒ Inclusion of K-loop effects gives a good fit to experimental data. Both pictures predict similar values for several radiative decays. ⇒ It may be difficult to distinguish two pictures from radiative decays !?

☆ Future directions Study the φ→π 0 π 0 γ decay Include K-loop into a 0, f 0 propagators Include non-resonant background Study several radiative decays ・・・ Explore the structure of the light scalar nonet