Isosinglet scalar mesons & glueballs Hai-Yang Cheng Academia Sinica, Taipei August 28, 2011 Scalars 2011, Warsaw, Poland

Preamble Why are scalar mesons so special among even-parity mesons ?  model: pions are Goldstone bosons while  has nonzero v.e.v. <> ⇒ spontaneous chiral symmetry breaking (SB) In QCD, <qq>, <qGq> ⇒ dynamical SB, m2  mq<qq>  Scalar mesons are the Higgs sector of strong interactions can be very broad ⇒ difficult to identify (e.g. , ) possible tetraquark content possible glueball content

Scalar Mesons (JPC=0++)

 and  are much broader than f0 and a0 in widths It is commonly believed that the light scalars , , f0(980), a0(980) are composed mainly of four quarks forming an S-wave qqqq nonet, while scalars above 1 GeV: f0(1370), a0(1450), K*0(1430) and f0(1500)/f0(1710) form a P-wave qq nonet - - - Close, Torqvist inverted spectrum widths  and  are much broader than f0 and a0 in widths (, )  600-1000 MeV, (f0, a0)  50-100 MeV   much faster than f0  f0 a0 f0    a0  2-quark model expt

In 4-quark picture (Jaffe ’77) Mass degeneracy of f0 and a0 is natural  & K are OZI super-allowed (fall apart)  large width f0, a0 KK are OZI super-allowed, but suppressed by p.s. f0 & a0q are OZI allowed  small width Supported by LQCD calculations: 1. Prelovsek et al. [ PR, D82, 094507 (2010) ]  and  have sizable 4-quark components 2. Mathur et al. [ PR, D76, 114505 (2007)] qq state for a0(1450) and K0*(1430)

mixing of  and f0(980)  has a large glueball content ? [ Minkowski, Ochs (’99); Narison,…] In 2-quark picture: Ds+ f0(980)+,  f0(980)  large ss content of f0(980) (i) J/ f0 comparable to J/ f0, (ii) f0 width dominated by   qq component of f0(980) No universal mixing angle fit to all the data of J/, radiative  decay and f0 coupling to +- & K+K- ; it lies in the ranges 25o <  < 40o, 140o <  <165o In 4-quark scenario   175o based on mass spectrum Maiani et al. (’04)

Scalar glueball Three isosinglet scalars f0(1370), f0(1500), f0(1710) are observed, only two of them can be accommodated in qq QM  glueball content f0(1370) & f0(1500) decay mostly to 2 & 4, while f0(1710) mainly into KK  f0(1370), f0(1500) are nn states, ss state for f0(1710) Amsler & Close (’95) claimed f0(1500) discovered at LEAR as an evidence for a scalar glueball because its decay to ,KK,,’ is not compatible with a simple qq picture. Amsler’s argument (’02) against a qq interpretation of f0(1500): Let |f0(1500)> = |N>cos - |S>sin Non-observation of f0(1500) in  reaction demands   75o and hence ss dominance. This contradicts nn picture  f0(1500) is not a qq state

f0(1710):  is suppressed relative to KK  primarily ss dominated f0(1500): dominant scalar glueball  1550 MeV [Bali et al. ’93, Amsler et al. ’95] f0(1710):  is suppressed relative to KK  primarily ss dominated f0(1370): KK is suppressed relative to   dominated by nn states G ss nn Amsler, Close, Kirk, Zhao, He, Li… MS>MG>MN MG  1500 MeV, MS-MN  200-300 MeV

Difficulties with this model: Near degeneracy of a0(1450) and K0*(1430) cannot be explained due to the mass difference between MS and Mn If f0(1710) is ss dominated, [J/f0(1710)] = 6 [J/f0(1710)] [Close, Zhao] BES  [J/f0(1710)] = (3.31.3) [J/ f0(1710)] J/→gg and the two gluons couple strongly to glueball ⇒ If f0(1500) is primarily a glueball, it should be seen in “glue-rich” radiative J/ decay, namely, J/  f0(1500) >> J/ f0(1710) BES  [J/  f0(1710)] > 4 [J/ f0(1500)] If f0(1500) is composed mainly of glueball, then the ratio R=(f0(1500) )/(f0(1500) KK) = 3/4 flavor blind < 3/4 for chiral suppression Rexpt(f0(1500))=4.10.4, Rexpt(f0(1710))=0.41+0.11-0.17 Tension with LQCD

Lattice calculations for scalar glueballs Quenched LQCD: JPC=0++ glueball in pure YM theory Morningstar, Peardon (’99): 1750 50 80 MeV Lee, Weingarten (’00): 1648 58 MeV Y. Chen (’06) : 1710 50  80 MeV Full QCD (unquenched): glueballs mix with quarks; no pure glueball UKQCD (’10): ~ 1.83 GeV Glueball spectrum is not significantly affected by quark degrees of freedom

Other scenarios: Lee, Weingarten (lattice): f0(1710) glueball ; f0(1500) ss ; f0(1370) nn Burakovsky, Page: f0(1710) glueball, but Ms-MN=250 MeV Giacosa et al. ( 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.” PDG (2008), PDG (2010): “The f0(1500), or alternatively, the f0(1710) have been proposed as candidates for the scalar glueball.”

approximate SU(3) symmetry in scalar meson sector (> 1GeV) Based on two simple inputs for mass matrix, Keh-Fei Liu, Chun-Khiang Chua and I have studied the mixing with glueball : approximate SU(3) symmetry in scalar meson sector (> 1GeV) a0(1450), K0*(1430), Ds0*(2317), D0*(2308)  MS should be close to MN a feature confirmed by LQCD LQCD  K0*(1430)=1.41±0.12 GeV, a0*(1450)=1.42±0.13 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 glueball spectrum from quenched LQCD MG before mixing should be close to 1700 MeV Mathur et al.

a0(1450) mass is independent of quark mass when mq ms Mathur et al. hep-ph/0607110 1.420.13 GeV a0(1450) mass is independent of quark mass when mq ms 13 13

x: quark-antiquark annihilation y: glueball-quarkonia mixing uu dd ss G 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 G 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

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, chiral suppression: A(G→qq)  mq/mG in chiral limit Carlson et al (’81); Cornwall, Soni (’85); Chanowitz (’07) Chiral suppression at hadron level should be not so strong perhaps 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 (’95)] 

In absence of chiral suppression (i. e In absence of chiral suppression (i.e. g=gKK=g), the predicted f0(1710) width is too small (< 1 MeV) compared to expt’l total width of 13718 MeV  importance of chiral suppression in GPP decay Consider two different cases of chiral suppression in G→PP: (i) (ii) Scenario (ii) with larger chiral suppression is preferred

: tends to be an SU(3) octet Amseler-Close-Kirk : primarily a glueball : tends to be an SU(3) octet : near SU(3) singlet + glueball content ( 13%) blue: nn red: ss green: G 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), (J/f0(1710)) = 4.1 ( J/ f0(1710)) versus 3.31.3 (expt) (J/ f0(1710)) >> (J/f0(1500)) in good agreement with expt. [J/→f0(1710)] > 4 [J/→f0(1500)] 17

Scalar glueball in radiative J/ decays LQCD: Meyer (0808.3151): Br(J/ G0)  910-3 Y. Chen et al. (lattice 2011): Br(J/ G0) = (3.60.7)10-3 BES measurements: Using Br(f0(1710) KK)=0.36  Br(J/f0(1710))= 2.410-3 Br(f0(1710) )= 0.15  Br(J/f0(1710))= 2.710-3

It is important to revisit & check chiral suppression effects Chiral suppression in LQCD [Sexton, Vaccarino, Weingarten (’95)]: (0++)=108  28 MeV If chiral suppression in scalar glueball decays is confirmed, it will rule out f0(1500) and (600) as candidates of 0++ glueballs (f0(1500) )/(f0(1500) KK)= 4.10.4 >> ¾ ()  600-1000 MeV: very broad

Conclusions We use two simple & robust results to constrain mixing matrix of f0(1370), f0(1500) and f0(1710): (i) empiric SU(3) symmetry in scalar meson sector > 1 GeV, (ii) scalar glueball mass  1700 MeV 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