Scalar Glueball, Scalar Quarkonia, and their Mixing Hai-Yang Cheng Academia Sinica, Taipei in collaboration with Chun-Khiang Chua & Keh-Fei Liu NTHU, October 26, 2006 1 ¾ Each quark has one of three different color charges and antiquark carries an anti-color charge q q q ¾ Quarks exchange gluons and create a very strong color force ¾ Gluons carry a color and an anti-color and hence can have a self-coupling ¾ Single quark has not been observed yet. QCD tells it cannot be observed (quark confinement). All naturally occurring particles are colorless. 2 Glueball: color-singlet bound state of gluons as gluons have a self coupling Lighest glueballs: JPG=0++ 1710±50±80 MeV JPG=2++ 2390±30±120 MeV Y. Chen et al. hep-lat/0510074 z ι(1440) [now η(1405)] as 0-+ glueball z Amsler & Close (1995) claimed f0(1500) discovered at LEAR as an evidence for a scalar glueball because its decay to ππ,KK,ηη,ηη’ is not compatible with a simple qq picture. z V.V. Anisovich et al. (2005) claimed evidence of a tensor glueball, namely, f2(2000) 3 Scalar Mesons (JP=0+) K 0* (1430) * 0 K (1430) qq a0− (1470) 0 0 a (1470) f 0 (1500) K (1430) K 0* (800) 2 q q 2 a (980) K 0* (800) + + σ (600) f 0 (1710) K 0* (1430) * 0 − 0 a0+ (1470) f 0 (1370) K 0* (800) a00 (980) f 0 (980) a0+ (980) K 0* (800) 4 f0(1500): dominant scalar glueball ∼ 1550 MeV [Bali et al. ’93, Amsler et al. ’95] KK/ππ ∼ 0.25 ⇒ small ss content f0(1710): ππ is suppressed relative to KK ⇒ primarily ss dominated f0(1370): KK is suppressed relative to ππ ⇒ dominated by nn states G ss ⎛ MG ⎜ ⎜ y ⎜⎜ ⎝ 2y y MS 0 nn = uu + dd 2 nn 2y ⎞ ⎟ 0 ⎟ ⎟⎟ MN ⎠ f 0 (1710) = 0.36 G + 0.09 N + 0.93 S f 0 (1500) = −0.84 G − 0.41 N + 0.35 S f 0 (1370) = 0.40 G − 0.91 N − 0.07 S Amsler, Close, Kirk, Zhao, He, Li… MS>MG>MN MG∼ 1500 MeV, MS-MN ∼ 200-300 MeV Further support: f0(1710) is not seen in pp→ π0 f0 ⇒ f0(1710) dominated by ss While f0(1710) is observed in γγ→KK, f0(1500) has not been seen in γγ→KK or π+π- ⇒ ⇒ absence of f0(1500) coupling to 2γ glueball structure of f0(1500) 5 Other scenarios: Lee, Weingarten (lattice): f0(1710) glueball ; f0(1500) nn ; f0(1370) ss Giacosa et al. (χ Lagrangian): 4 allowed sloutions PDG (2006): p.168 Experimental evidence is mounting that f0(1500) has considerable affinity for glue and that the f0(1370) and f0(1710) have large uu+dd and ss components, respectively. F.E. Close (Oxford): a leading figure in hadron spectroscopy C. Amsler (Zurich): a dominant figure in searching for (exotic) non-qq mesons author of “Non-qq mesons”, Particle Data Group 6 7 Problems: Near degeneracy of a0(1450) and K0*(1430) cannot be explained due to the mass difference between MS and Mn Improved LQCD ⇒ MG ∼ 1700 MeV rather than ∼ 1500 MeV If f0(1710) is ss dominated, J/ψ→φf0(1710) >> J/ψ→ωf0(1710) BES ⇒ Γ(J/ψ→ωf0(1710)) = (6.6±2.7) Γ( J/ψ →φf0(1710)) J/ψ→γgg and glueballs couple strongly to gluons ⇒ If f0(1500) is primarily a glueball, J/ψ →γf0(1500) >> J/ψ→γf0(1710) Expt ⇒ Γ(J/ψ →γf0(1710)) ∼ 5 Γ(J/ψ→γf0(1500)) 8 In this work we consider two recent lattice inputs for mass matrix: glueball spectrum from quenched LQCD approximate SU(3) symmetry in scalar meson sector (> 1GeV) Y. Chen et al. hep-lat/0510074 z improved quenched LQCD calculations based on much larger & finer lattices z infinite quark mass ⇒ no qq loops M(0++)=1710 ± 50 ± 80 MeV MG before mixing should be close to 1700 MeV 1650 MeV by Lee, Weingarten 1550 Mev by Bali 9 ψψ IG (JPC) ≡ 1− (0+ + ), 1− (1+ + ) Mathur et al. hep-ph/0607110 qq nature of a0(1450) 1.42±0.13 GeV a0(980) is not seen ⇒ not a qq state ! a0(1450) mass is independent of quark mass when mq≤ ms 10 ⇒ Flavor SU(3) is a good symmetry for scalar meson sector > 1 GeV ⇒ MS should be close to MN LQCD ⇒ ⇒ K0*(1430)=1.41±0.12 GeV near degeneracy of K0*(1430) and a0(1450) This unusual behavior is not understood and it serves as a challenge to the existing QM Near degeneracy also occurs in charm sector, Ds0*(2317) & D0*(2308). This is the place where the conventional QM seems not to work. Belle: 2308±17±32 MeV for D0* FOCUS: 2407±21±35 MeV 11 Lattice calculations of a0 Bardeen et al Wilson fermion ma0=1.326±0.086 GeV RBC domain wall fermion ma0=1.43±0.10 GeV ma0=1.58±0.34 GeV SCALAR Kunihiro et al dynamical fermion ma0∼ 1.8GeV for mπ/mρ∼ 0.7 UKQCD(03’) UKQCD(06’) dynamical fermion ma0=1.0±0.2 GeV ma0=1.01±0.04 GeV ma0 ∼ 1.45 GeV BGR MILC Alford & Jaffe stagged fermion indication for a0 indication of bound qqqq states 12 Prelovsek, Dawson, Izubuchi, Orginos, Soni PR, D70, 094503 (2004); hep-ph/0511110: domain wall fermions Mass for lightest nonsinglet two-quark a0 = 1.58 ± 0.34 GeV, which can be identified with a0(1450) 13 ψ γ 5ψ ψ γ 5ψ [ππ , I (J G PC + ) ≡ 0 (0 ++ )] Four quark spectrum (GeV) 2 1.8 1.6 Scattering states 1.4 m2 1.2 1 p=1 0.8 0.6 Eπ ( p = 1) + Eπ ( p = 1) m1 p=0 0.4 m0 0.2 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 2 mπ (GeV2) Possible BOUND state σ(600)? Eπ ( p = 0) + Eπ ( p = 0) Scattering states (Negative scattering length) In chiral limit, mσ=540±170 MeV Need to check the volume dependence of the observed states 14 Two lattice sizes : 123x28, 163x28 For two-particle state, W12/W16=V3(16)/V3(12)=163/123=2.37 For one-particle state, W12/W16=1 scattering states σ state 15 ♦ Scalar qq meson has a unit of orbital angular momentum ) a higher mass above 1 GeV f0(1370), a0(1450), K*0(1430) and f0(1500)/f0(1710) form a P-wave qq nonet with some possible mixing with glueballs, supported by lattice. ♦ Four-quark qqq q scalar meson can be lighter due to (i) absence of the orbital angular momentum barrier in S-wave 4-quark state. (ii) a strong attraction between (qq ) 3 and (q q ) 3 ) a mass near or below 1 GeV Light scalar mesons σ, κ, f0(980), a0(980), form an S-wave nonet 16 Scalar Mesons and Glueball f 0 (1710) glueball K 0* (1430) * 0 K (1430) qq − 0 a (1470) a00 (1470) f 0 (1500) K (1430) K 0* (800) 2 q q 2 a (980) K 0* (800) + f 0 (1370) + σ (600) K 0* (1430) * 0 − 0 a0+ (1470) K 0* (800) a00 (980) f 0 (980) a0+ (980) K 0* (800) 17 uu dd ⎛ MU ⎜ ⎜ 0 M =⎜ 0 ⎜⎜ ⎝ 0 0 MD 0 0 ss 0 0 MS 0 G 0 ⎞ ⎛x ⎟ ⎜ 0 ⎟ ⎜x + 0 ⎟ ⎜ xs ⎟⎟ ⎜⎜ MG ⎠ ⎝ y x x xs y xs xs xss ys y⎞ ⎟ y⎟ ys ⎟ ⎟⎟ 0⎠ x: quark-antiquark annihilation y: glueball-quarkonia mixing first order approximation: exact SU(3) ⇒ MU=MD=MS=M, x=xs=xss, ys=y a0 octet singlet ⎛M ⎜ ⎜0 ⎜0 ⎜ ⎜0 ⎝ 0 M 0 0 0 0 M + 3x 3y G 0 ⎞ ⎧a0 = (uu − dd ) / 2 = 1474, M U = M D = 1474 ± 19 MeV ⎟ ⎪⎪ 0 ⎟ ⇒ ⎨ f 0 (1500) = (uu + dd − 2 ss ) / 6 = 1474 3y ⎟ ⎪ f (1370) and glueball are slightly mixed ⎟ ⎟ ⎪⎩ 0 MG ⎠ y=0, f0(1710) is a pure glueball, f0(1370) is a pure SU(3) singlet with mass = M+3x ⇒ x = -33 MeV y≠ 0, slight mixing between glueball & SU(3)-singlet qq. For |y| ∼| x|, mass shift of f0(1370) & f0(1710) due to mixing is only ∼ 10 MeV ⇒ In SU(3) limit, MG is close to 1700 MeV 18 SU(3) Breaking Need SU(3) breaking in mass matrix to lift degeneracy of a0(1450) and f0(1500) Need SU(3) breaking in decay amplitudes to accommodate observed strong decays e.g. f 0 (1500) = α (| uu 〉+ | dd 〉 ) + β | ss 〉 2 Γ( f 0 (1500) → KK ) 1 ⎛ β ⎞ p K , R1 = = ⎜1 + ⎟ Γ( f 0 (1500) → ππ ) 3 ⎝ α ⎠ pπ 2 β ⎞ pη Γ( f 0 (1500) → ηη ) 1 ⎛ R2 = = ⎜2 + ⎟ α ⎠ pπ Γ( f 0 (1500) → ππ ) 27 ⎝ For SU(3) octet f0(1500), β = -2α ⇒ R1=0.21 vs. 0.246±0.026 (expt) R2=0 LQCD [Lee, Weingarten] ⇒ y= 43±31 MeV, vs. 0.145±0.027 (expt) y/ys=1.198±0.072 y and x are of the same order of magnitude ! SU(3) breaking effect is treated perturbatively 19 Chiral suppression in scalar glueball decay If f0(1710) is primarily a glueball, how to understand its decay to PP ? If G→PP coupling is flavor blind, Γ(G → ππ ) / Γ(G → KK ) = 0.91 ⎧0.20 ± 0.04 WA102 Γ( f 0 (1710) → ππ ) ⎪ = ⎨< 0.13 BES from J /ψ → ω ( KK , ππ ) Γ( f 0 (1710) → KK ) ⎪ + 0.11 BES from J /ψ → γ ( KK , ππ ) ⎩0.41-0.17 chiral suppression: A(G→qq) ∝ mq/mG in chiral limit [Chanowitz] Γ(G → ππ ) / Γ(G → KK ) ∝ mu2 / ms2 ? Chiral suppression at hadron level is probably not so strong due to nonperturbative chiral symmetry breaking and hadronization [Chao, He, Ma] : mq is interpreted as chiral symmetry breaking scale [Zhang, Jin]: instanton effects may lift chiral suppression LQCD [Sexton, Vaccarino, Weingarten] ⇒ +0.372 +0.364 g ππ : g KK : gηη = 0.834 +−00..603 : 2 . 654 : 3 . 099 579 −0.402 −0.423 20 In absence of chiral suppression (i.e. gππ=gKK=gηη), the predicted f0(1710) width is too small (< 1 MeV) ⇒ importance of chiral suppression in G→PP decay Consider two different cases of chiral suppression in G→PP: (i) g ππ : g KK : gηη = 1 : 1.55 : 1.59 (ii) g ππ : g KK : gηη = 1 : 3.15 : 4.74 Scenario (ii) with larger chiral suppression is preferred 21 Amseler-Close-Kirk f 0 (1710) = 0.93 G + 0.32 N + 0.17 S : primarily a glueball f 0 (1500) = 0.03 G − 0.54 N + 0.84 S : tend to be an SU(3) octet f 0 (1370) = −0.36 G + 0.78 N + 0.52 S : near SU(3) singlet + glueball content (∼ 13%) MN=1474 MeV, MS=1498 MeV, MG=1666 MeV, MG>MS>MN MS-MN ∼ 25 MeV is consistent with LQCD result ⇒ near degeneracy of a0(1450), K0*(1430), f0(1500) Because nn content is more copious than ss in f0(1710), Γ(J/ψ→ωf0(1710)) = 4.1 Γ( J/ψ →φf0(1710)) versus 6.6±2.7 (expt) If f0(1710)=ss, one needs large doubly OZI ∼ 5 OZI [Close, Zhao] Γ(J/ψ →γf0(1710)) >> Γ(J/ψ→γf0(1500)) in good agreement with expt. Γ(J/ψ→γf0(1710)) ∼ 5 Γ(J/ψ→γf0(1500)) 22 f0(1710) is not seen in pp→π0f0 at LEAR (2002), but now observed in pp→π0ηη at Fermilab (2006) 2γ-quarkonium coupling f0(1370): f0(1500): f0(1710) = 9.3 : 1.0 : 1.5 2γ coupling of f0(1500) is weak even if it has no glue content 23 Conclusions We use two recent lattice results to constrain mixing matrix of f0(1370), f0(1500) and f0(1710): (i) scalar glueball mass ∼ 1700 MeV, (ii) SU(3) symmetry in scalar meson sector > 1 GeV Exact SU(3) ⇒ f0(1500) is an SU(3) octet, f0(1370) is an SU(3) singlet with small mixing with glueball. This feature remains to be true even when SU(3) breaking is considered Chiral suppression in G→PP decays is essential. Hadronic and radiative J/ψ decays all indicate prominent glueball nature of f0(1710) 24