11

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, m2 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

33

Scalar Mesons (JScalar Mesons (JPCPC=0=0++++))

)1710(

)1370(

0

0

f

f

)600(

qq

22qq

)1500(0f)1470(0

0a

)1430(*0K)1430(*

0K

)1430(*0K)1430(*

0K

)1470(0a )1470(0

a

)800(

)980(0f)980(0

a )980(0a

)980(00a

)800(

)800( )800(

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

- -

-

a0

f0

a0

f0

2-quark model expt

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

Close, Torqvist

5

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)

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 & a0q are OZI allowed small width

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)

, cossin ,sincos)980(0 nnssnnssf

cossin ,sincos)980(0 dduussnndduussnnf

175o based on mass spectrum Maiani et al. (’04)

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

2

dduunn

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

2

dduunnN

2

0 sin9

1cos

29

5)(

f

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

0 2

0

2

N

S

G

My

My

yyMG ss nn

SNGf

SNGf

SNGf

07.091.040.0)1370(

35.041.084.0)1500(

93.009.036.0)1710(

0

0

0

MS>MG>MN MG 1500 MeV, MS-MN 200-300 MeV

Amsler, Close, Kirk, Zhao, He, Li…

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)] = (3.31.3) [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) ) = 3/4 flavor blind

< 3/4 for chiral suppression

Rexpt(f0(1500))=4.10.4, 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

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.”

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 (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.

131313

Mathur et al.

hep-ph/0607110

a0(1450) mass is independent of quark mass when mq ms

1.420.13 GeV

14

0000

000

000

000

s

sssss

s

s

G

S

D

U

yyy

yxxx

yxxx

yxxx

M

M

M

M

M

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

GMy

yxM

M

M

300

3300

000

000

mixedslightly are glueball and )1370(

octet :14746/)2()1500(

MeV 191474 ,14742/)(

0

0

0

f

ssdduuf

MMdduua DU

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

a0 octet singlet G

15

Chiral suppression in scalar glueball decay

If G→PP coupling is flavor blind, 91.04

3)(/)( KKGG

PDG),,(/ from S BE0.41

),(/ from BES 0.13

WA102 04.020.0

))1710((

))1710((

0.110.17-

0

0

KKJ

KKJKKf

f

If f0(1710) is primarily a glueball, how to understand its decay to PP ?

chiral suppression: A(G→qq) mq/mG in chiral limit

364.0423.0

372.0402.0

603.0579.0 099.3:654.2:834.0::

ggg KK

LQCD [ Sexton, Vaccarino, Weingarten (’95)]

[Chao, He, Ma] : mq is interpreted as chiral symmetry breaking scale

[Zhang, Jin]: instanton effects may lift chiral suppression

? /)(/)( 22su mmKKGG

Chiral suppression at hadron level should be not so strong perhaps due to nonperturbative chiral symmetry breaking and hadronization

Carlson et al (’81); Cornwall, Soni (’85); Chanowitz (’07)

16

Consider two different cases of chiral suppression in G→PP:

(i)

(ii)

59.1:55.1:1:: ggg KK

74.4:15.3:1:: ggg KK

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 137eV importance of chiral suppression in GPP decay

Scenario (ii) with larger chiral suppression is preferred

1717

SNGf

SNGf

SNGf

52.078.036.0)1370(

84.054.003.0)1500(

17.032.093.0)1710(

0

0

0

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 3.31.3 (expt)

(J/ f0(1710)) >> (J/f0(1500))

in good agreement with expt.

[J/→f0(1710)] [J/→f0(1500)]

: primarily a glueball

: tends to be an SU(3) octet

: near SU(3) singlet + glueball content ( 13%)

MN=1474 MeV, MS=1498 MeV, MG=1666 MeV, MG>MS>MN

Amseler-Close-Kirk

blue: nnred: ssgreen: G

18

Scalar glueball in radiative J/ decays

LQCD: Meyer (0808.3151): Br(J/ G0) 910-3

Y. Chen et al. (lattice 2011): Br(J/ G0) = (3.60.7)10-3

30

40

40

42.10.90

40

100.3)(1.5 )1710(/

101.03.1 )1710(/

101.04.0 )1710(/

108.5 )1710(/

100.321.01 )1500(/

fJ

fJ

fJ

KKfJ

fJ

40 109.2))1500(/( fJBr

Using Br(f0(1710) KK)=0.36 Br(J/f0(1710))= 2.410-3

Br(f0(1710) )= 0.15 Br(J/f0(1710))= 2.710-3

BES measurements:

19

364.0423.0

372.0402.0

603.0579.0 099.3:654.2:834.0::

ggg KK

Chiral suppression in LQCD [Sexton, Vaccarino, Weingarten (’95)]:

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) )= 4.10.4 >> ¾

() 600-1000 MeV: very broad

(0++)=108 28 MeV

It is important to revisit & check chiral suppression effects

2020

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