Scalar & Pseudoscalar Glueballs Hai-Yang Cheng (鄭海揚) Academia Sinica, Taipei May 25, 2012 University of Science & Technology of China

What is the effect of quark degrees of freedom on glueballs ? Glueball: color-singlet bound state of gluons as gluons have a self coupling Y. Chen et al. PR, D73, 014516 (2006) Lightest glueballs in pure YM theory: JPG=0++ 17105080 MeV JPG=2++ 239030120 MeV JPG=0-+ 2560±35±120 MeV What is the effect of quark degrees of freedom on glueballs ? Glueball will mix with qq states so that a pure glueball does not exist in nature Mass of 0-+ glueball could be drastically affected

Scalar glueball Chun-Khiang Chua, Keh-Fei Liu, HYC, PR, D74, 094005 (2006)

Scalar Mesons (JPC=0++)

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 et al. (’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 and lattice QCD 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 11 11

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)] 15

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: G.S. Huang (FPCP2012) G.S. Huang (FPCP2012) 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

Pseudoscalar glueball Hsiang-nan Li, Keh-Fei Liu, HYC Phys. Rev. D 79, 014024 (2009)

Br[J/(1405)]  O(10-3) larger than J/(1295), (2225) 1980: J/  + resonance (1.44 GeV) was seen by MarK II and identified as E(1420) [now known as f1(1420)] first discovered at CERN in 1963. Renamed the ¶(1440) by Crystal Ball & Mark II in 1982 1981: (1440) was proposed to be a pseudoscalar glueball by Donoghue, Johnson; Chanowitz; Lacaze, Navelet,… 2005: BES found a resonance X(1835) in J/ +-’ 2006: X(1835) as an 0-+ glueball by Kochelev, Min; Li; He, Li, Liu, Ma It is commonly believed that (1440) now known as (1405) is a leading candidate of G Br[J/(1405)]  O(10-3) larger than J/(1295), (2225)  KK, : (1475) in KK was seen, but (1405) in  was not Expt’l review: Masoni, Cicalo, Usai, J. Phys. G32, 293 (2006) 19

All yield m(0++) < m(0-+) Pseudoscalar glueball interpretation of (1405) is also supported by the flux-tube model (Faddeev et al.), but not favored by most of other calculations: LQCD ⇒  2.6 GeV [Chen et al; Morningstar, Peardon;UKQCD] QCDSR ⇒ mG > 1.8 GeV QM ⇒ 2.62 GeV > mG > 2.22 GeV All yield m(0++) < m(0-+) 20

-’-G mixing Consider flavor basis q=(uu+dd)/√2, s=ss. In absence of U(1) anomaly, q & s mix only through OZI-violating effects Extend Feldmann-Kroll-Stech (FKS) mechanism of -’ mixing to include G, where  =  + 54.7o, G is the mixing angle between G and 1 (8 is assumed not to mix with glueball). Mixing matrix depends only on  and G 21

Applying EOM: Six equations for many unknowns. We need to reply on large Nc rules (’t Hooft) 22

To leading order in 1/Nc, keep fq,s, neglect fq,sg, fsq, fqs keep mqq2  m2, mss2  2mK2-m2, neglect other mass terms KLOE analysis of  ’,  ⇒  = (40.4±0.6)o, G=(20 ±3)0 for fs/fq=1.3520.007 mG=(1.4±0.1) GeV This result for mG is stable against OZI corrections

Is this compatible with LQCD which implies mG > 2GeV ? Lattice results are still quenched so far. It has been noticed that mG in full QCD with dynamic fermions is substantially lower than that in quenched approximation [Cabadadze (1998)] Contrary to the mainstream, we conjecture that pseudoscalar glueball is lighter than the scalar one due to dynamic fermion or axial anomaly. It is important to have a full lattice QCD calculation quenched unquenched

-’-G mixing yields Data can be accommodated with G  30o supported by an analysis based on chiral Lagrangian with instanton effects, a solution for UA(1) problem [Song He, Mei Huang, Qi-Shu Yan, arXiv:0903.5032] Xin Liu, H.n. Li, Z.J. Xiao argued that B J/Ã(‘) decays imply large G content in ’ arXiv:1205.1214 -’-G mixing yields Data can be accommodated with G  30o

Conclusions 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 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 Analysis of -’-G mixing yields mG  1.4±0.1 GeV, suggesting that (1405) is a leading candidate of pseudoscalar glueball. A full lattice QCD calculation is needed. 26