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Isosinglet scalar mesons & glueballs

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

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Isosinglet scalar mesons & glueballs

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

  2. 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

  3. Scalar Mesons (JPC=0++)

  4. 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 a0 f0 f0    a0  2-quark model expt

  5. 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)

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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.”

  12. 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.

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

  14. 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

  15. 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)] 

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

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