Study of sigma meson structure in D meson

Study of sigma meson structure in D meson decay Masayasu Harada (Nagoya Univ. ) at International Workshop on New Hadon Spectroscopy (November 21, 2012, Haeundae, Busan, Korea) Based on ・ M. H. , H. Hoshino and Y. L. Ma, Phys. Rev. D 85, 114027 (2012)

1. Introduction

☆ “σ” particle (“QCD Higgs” particle) ・・・ Quantum fluctuation of the quark condensate → Clue to understand the chiral symmetry breaking A candidate ・・・ f 0(500) : lightest I=0 scalar meson In this talk, I cal f 0(500) the s meson. However, f 0(500) may not be a qqbar meson ! PDG 2012

◎ Standard qqbar quark model assignment What is f 0(500) ? 2 quark ( qqbar ) state “σ” particle 4 quark ( qqqbar ) state Exotic hadron

Outline 1. Introduction 2. Quark Structure of Scalar Mesons 3. Linear sigma model for light quark sector including s meson 4. s meson in pp scattering 5. s meson in D 1 → Dpp decay 6. Summary

2. Quark Structure of Scalar Mesons

2 -quark picture of scalar mesons mass (Me. V) f 0(500) Contradiction ?

Scalar meson puzzle mass (Me. V) f 0(500) Consistent ?

3. Linear sigma model for light quark sector including s meson

2 and 4 quark states in linear sigma model Amir H. Fariborz, Renata Jora, and Joseph Schechter, PRD 72, 034001 (2005) 3× 3 matrix fields ＆ (Linear Sigma Model): ４ quark field ～ ２ quark field ～ Scalar Pseudo scalar These transform in the same way under SU(3)L×SU(3)R : SU（３）R× SU（３）L： Different transformations under U(1)A : U（1）A：

U(1)A Symmetry ? ◎ Anomaly is suppressed in the large Nc QCD Current is conserved. U(1)A is spontaneously broken by the quark condensate. ◎ Definition of the spontaneously broken charge Light-front axial charge is well-defined. see, e. g. , S. Weinberg, Phys. Rev. 177 (1969) 2604.

mixing When the U(1)A symmetry exists, 2 -quark state and 4 -quark state do not mix with each other. But, the U(1)A symmetry is broken by anomaly explicitly by spontaneous chiral symmetry breaking ⇒ mixing between 2 -quark state and 4 -quark state Lightest 2 nd 3 rd Heaviest

An effective Lagrangian Linear sigma model including 2 -nonet fields : SU(3)L×SU(3)R invariant, U(1)A invariant. : SU(3)L×SU(3)R invariant, U(1)A breaking (anomaly). constrained by anomaly matching with QCD : Explicit SU(3)L×SU(3)R×U(1)A breaking terms. (effects of current quark masses)

Phenomenological Analysis using a special form of the potential A. H. Fariborz, R. Jora, and J. Schechter, PRD 79, 074014 (2009) Note : A 2/A 1 = md/mu ; A 3/A 1 = ms/mu generate mixing between 2 -quark and 4 -quark states

Phenomenological Study of f 0(500) Inputs : fixed values mp = 137 Me. V ; Fp = 92. 6 Me. V m[ a 0(980) ] = 987. 4 Me. V, m[ a 0(1450) ] = 1474 Me. V; A 2/A 1 = md/mu = 1 variable values 1200 Me. V < m[ p(1300) ] < 1400 Me. V (exp: 1300 ± 100 Me. V) 20 < A 3/A 1 = ms/mu < 30 • masses of I=0 scalar mesons • Mass hierarchy is reasonably reproduced. • Note that the light sigma meson appears automatically in the present model.

Quark Contents of f 0(500) percentage of components fa fc fd fb fa = (uubar + ddbar)/√ 2 ; fb = ssbar ; fc = (usubarsbar + dsdbarsbar)/√ 2 ; fd = udubardbar • ex: for m[ p(1300) ] = 1215 Me. V, fa : fb : fc : fd = 0. 36 : 0. 04 : 0. 36 : 0. 24 → The f 0(500) includes about 40% 2 -quark and 60% 4 quark. • The lightest scalar is roughly about half 2 -quark and half 4 -quark state.

4. s meson in pp scattering

pp scattering in the linear s model Relations among coupling constants due to the chiral symmetry π π π pp scattering amplitude includes spp couping and sigma mass in the low energy region σ

Fit to pp scattering data

5. s meson in D 1 → Dpp decay

“chiral doubling” M. A. Nowak, M. Rho and I. Zahed, PRD 48, 4370 (1993) excited states heavy quark symmetry (heavy quark partner ) ground states chiral symmetry (chiral partner) MD(0+, 1+) – MD(0 -, 1 -) ~ 0. 43 Ge. V Chiral doubling seems to work.

U(1)A of D mesons ◎ Assume D(0 -, 1 -) and D(0+, 1+) ~ c qbar ⇒ U(1)A eigenstates : DL ~ D(0 -, 1 -) – D(0+, 1+) → DL e-in DR ~ D(0 -, 1 -) + D(0+, 1+) → DR e+in ⇒ Only 2 -quark light-mesons can couple to D mesons. This scalar meson is made of 2 -quarks. (Not a mass eigenstate) note : M(2 -quark) → M e+2 in ; M’(4 -quark) → M’ e-4 in

D 1 → Dpp decay We determine gspp and ms by fitting to pp scattering.

D 1 → Dpp decay width gspp > 0 gp. DD > 0 gspp < 0 gp. DD > 0 gspp > 0 gp. DD < 0 gspp < 0 gp. DD < 0 Constituent of sigma meson may be determined by future experiment

6. Summary ◎ We construct an effective model including the light scalar masons and the D mesons. • U(1)A symmetry plays an important role: • Heavy meson can couple only to 2 quark mesons. ◎ We study an effect of the sigma meson to D 1 → Dpp decay • Our result indicates that we can get some clues to understand the composition of the sigma meson from future experiments.