Radiative Decays involving Scalar Mesons

Radiative Decays involving Scalar Mesons Masayasu Harada (Nagoya Univ.) based on • D.Black, M.H. and J.Schechter, Phys. Rev. Lett. 88, 181603 (2002) • D.Black, M.H. and J.Schechter, in preparation. @ Japan-US Workshop on“Electromagnetic Meson Production and Chiral Dynamics” (April 8, Osaka, Japan)

1. Introduction

◎ 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 ?

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

2. Quark Structure of Light Scalar Mesons

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

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

☆ Scalar nonet consistent with “experiment” !

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

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

☆ Relation to quark structure

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

c = d = 0 ; b < 0

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

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

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

☆ 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

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 )

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

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

・ 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

☆ f→p0hgthrough g f p0 h poor fit for

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

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

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.

☆ 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

Radiative Decays involving Scalar Mesons