isosinglet scalar mesons & glueballs
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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(
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
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