Mixing of scalar meson and glueball Charm 2006, Beijing, June 6, 2006 Mixing of scalar meson and glueball Qiang Zhao Institute of High Energy Physics, CAS, P.R. China “Scalar puzzles” from the recent exp. data Scalar glueball and QQ* mixing Mechanisms for scalar meson productions in (i) J/ V f0 V PP ( V= , ; P = , , , K), (ii) c0 PP, VV, f0 f0. Summary In collaboration with Frank Close and Bing-song Zou
M. Chanowitz 0 1 0 I=0 Mass Exotic type 1: Mesons have the same JPC as a QQ*, but cannot be accommodated into the SU(3) nonet: 3 3* = 8 1 3 4 1 1 M. Chanowitz f0(1810) Mass f0(1790) f0(1710) f0(1500) Glueball ? QQ*-glue mixing ? f0(1370) (1020) (958) f0(980) Multiquarks? Meson molecule ? (782) (547) /f0(600) 0 1 0 I=0
Experimental signals for scalar mesons Crystal Barrel, WA102, MARKIII, DM2 … Beijing Spectrometer (BES) J/ V f0; f0 PP, J/ f0; f0 PP, VV cj f0 f0, f0 f2 V=, , K*, ; PP=, , , KK^,
f0(1370) at BES f0(1370) is dominant over K K, , ; nonstrange nn* f0(1370) f0(1370) clearly seen in J/ , but not seen in J/ . NO f0(1370) S. Jin, Plenary talk at ICHEP04
f0(1710) at BES Clear f0(1710) peak in J/ KK. f0(1710) KK^ is dominant. ss* f0(1710) Clear f0(1710) peak in J/ KK. No f0(1710) observed in J/ ! NO f0(1710) S. Jin, Plenary talk at ICHEP04
= (uu+dd)/2 = ss c c c uudd c ss V= J/ J/ A flavour filter for OZI singly disconnected transitions: = (uu+dd)/2 = ss V= c c J/ J/ c uudd c ss f0(1370) f0(1710) Could the exp. puzzle imply correlations between the structure of scalars and their prod. mechanism in J/ V f0 ?
Glueball: q M c q* J/ q c* M q* Glue rich intermediate states f0 Mesons are made of colored gluons confined by strong interaction q M c glue q* J/ q c* M q* Glue rich intermediate states f0 Lattice 0++: 1.5 ~ 1.7 GeV Exp. Scalars: f0(1370) f0(1500) f0(1710) f0(1790) (?) f0(1810) (?) Lattice QCD prediction Morningstar and Peardon, PRD60, 034509 (1999)
Glueball and QQ* mixing in the scalar mesons In the basis of |G> = gg, |S> = ss*, and |N> = nn* = (uu*+dd*)/2, the glueball-quarkonia mixing can be expressed as: S G N where i=1,2,3, and f1,2,3 = f0(1710), f0(1500) and f0(1370), respectively. Amsler & Close, PLB353, 385(1995); PRD53, 295(1996); Close & Kirk, PLB483, 345(2000).
Parameterization of f0 PP r3 g0 g0 r2 g0 f0 P P Partial decay widths for f0 PP: Close & Zhao, PRD71, 094022(2005)
WA102 WA102+BES f0 states 1710 S 1500 G N 1370 Lattice QCD: MG ~ 1.5 – 1.7 GeV Strong QCD character.
Implications of the OZI-rule violation: gg ss* nn* 0.36 0.93 0.09 0.84 0.35 0.41 0.40 0.07 0.91 c KK^ c ss f0(1710) i) OZI rule on f0(1370): br(J/ f0(1370)KK^)<< br(J/ f0(1370)) Exp: br(J/ f0(1370)) is dominant ! ii) OZI rule on f0(1710): br(J/ f0(1710)KK^) > br(J/ f0(1710)KK^) Exp: br(J/ f0(1710)KK^) / br(J/ f0(1710)KK^) ~ 0.3 !
Scalar mesons production in J/ V f0 I) Singly disconnected diagram II) Doubly disconnected diagram g (ss*) (ss*) c g c J/ J/ c* f0 (ss*) c* f0 (nn*) III) Glue configuration pQCD Okubo-Zweig-Iizuka (OZI) rule: I) ~III) ~ II) =g2/4 ~ 0.3 However, a glueball component implies significant OZI-rule violations. (ss*) c J/ c* f0 (gg)
Factorization of J/ V f0 V P P V (, ) Transition amplitudes via potential V J/ P f0 III) I) II) P Doubly OZI disconnected Project to the final physical states: Gluon-counting rule: I) ~ III)
Partial decay width for J/ V f0 V P P (ss*) (nn*) c c J/ J/ c* G(gg) c* G(gg) Flavor-blindness of quark-gluon interaction:
Step 1: Direct test of the OZI rule BES Experiment: br(J/ f0(1710)KK*) = (2.0 0.7) 104 br(J/ f0(1710)KK*) = (13.2 2.6) 104 a) OZI rule applies: r 0 PDG estimate: Rexp = 0.75 b) OZI rule violated: r ~ 1 where r = 2.2
Step 2: Normalize the G production Normalized glueball production b.r. ratios Scalar decay br. ratios
Step 3: Theoretical predictions for J/V f0 V KK*, V The “puzzle” can be explained in the glueball-QQ* mixing scheme, which implies large OZI violation effects in the scalar production. Puzzle Evidence for the presence of scalar glueball ?
+ iv) c0f0f0, f0f2 Further test of the gluon-QQ*mixings 1 billion J/ events from BESIII gg ss* nn* f0 probe the quark components of the scalars: f0(1370) : f0(1500) : f0(1710) ~ 12 : 2 : 1 ii) f0 V, (V= , 0) f0(1710) ( ) > ( 0) f0(1370) ( ) < ( 0) f0(1500) ( ) < ( 0) iii) J/ f0 f0(1710) > f0(1500) > f0(1370) iv) c0f0f0, f0f2 f0(1710) f0(1500) f0(1370) 0.36 0.93 0.09 0.84 0.35 0.41 0.40 0.07 0.91 gg ss* nn* f0(1710) f0(1500) f0(1370) +
2. c0,2 hadronic decays VV, PP, & SS (b) g0 r (c) (d) g0: basic gqq* coupling r: OZI-rule violation R: SU(3)f breaking t: glueball coupling strength Zhao, PRD72, 074001 (2005)
For a typical state: the transition amplitude is factorized to be: A commonly used form factor:
i) c0,2 V V c0 c2 BES data Predictions The OZI violation need to be constrained by data for channel.
ii) c0,2 P P Improved data for channel are required.
iii) c0,2 f0 f0 Branching ratio fractions a) If OZI-rule is respected, i.e. r0, will be the smallest decay channel. b) If OZI-rule is violated, i.e. r1, will be the largest decay channel. normalized Exp. Data from BES for c0 f0(1710) f0(1370) KK. (hep-ex/0508050)
Summary-1 I. The glueball contents are essentially important for interpreting the “puzzling” data from BES for the scalar meson production in J/ decays. II. The strong glueball-QQ* mixings within the scalar mesons imply large OZI violations in J/ V f0, and suggest the crucial role played by the doubly disconnected processes. A possible source for the OZI-rule violation is transitions via intermediate meson exchanges. K* K K Zhao, Zou & Ma, PLB631, 22(2005), hep-ph/0508088.
Summary-2 III. A normalization of the glueball production rate is obtained, which possesses predictive power for the study of the glueball mixing effects in the J/ radiative decay channel and c0 f0f0. Further experimental data will be useful for establishing these f0 states as glueball-QQ* mixing states: BES, CLEO-c, GSI (?)… Glue-X at JLab?
Thanks !