Claude Amsler

1
Experimental Evidence
for a large glue content in
the f0(1500) meson
(Phenomenological review on scalar mesons)
Claude Amsler Universität Zürich
2
u, d, s
L, S (0 or 1) SU3 JPC nonets
SU3
decays

• ss -gt kaons, no pions
• uudd -gt pions dominant

3
Non qq mesons glueballs
a lattice spacing r0 string tension
(from QQ) 0.5 fm
Lattice prediction
Michael 97
m(0)1611 30 160 m(2)2232 220 220
MeV
Lattice with mq -gt 8 (no qq loop)
However

• qq states in the 0 and 2 mass range
• where are the
  qq nonets?
• CP exotics (non qq) 0--,0-,1-,2- unfortunately
  above 3 GeV

• Quark loops mq lt 8
• ygt a Ggt ? qqgt Mixing with 2 nearby
• I0 qq, hence
  3 isoscalar states

4
Scalar glueball and scalar mesons
???????
G MeV
0
?
13P0
mgt1 GeV
( Godfrey Isgur 85)
former Q?????
gluonium (see later)?
... and f0(1500)
110 0
narrow
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f0(980) a0(980)

• KK widths are large at threshold 20 G?????
• a0 (I1) KK molecule or ss (dd - uu)
• f0 (I0) KK molecule or ss or ss (dd uu)

(Jaffe 77, Weinstein 82)
1) gg?width ?
if a0 KK state 0.6 keV
(Oller 98, Delbourgo 99)
(PDG)
(Barnes 82)
The gg?width cannot discriminate between qq,
KK and qqqq
2) ???????g and f0g?

• qqqq 10-4
• KK 10-5
• qq 10-5 (a0 )
• qq 5 x 10-5 (f0 )

(Achasov Gubin 97)
0 for ideal mixing ????????f ss
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f0(980) a0(980) contd
(Aloisio 02)
SND CMD-2 (Novosibirsk) 10-4
a0
2g
f0
(M.N.Achasov 00, Akhmetshin 99)
New data by KLOE (DAFNE)
3p
Compatible with qqqq states
m(p0p0)
m(p0?)
Why is f0 production much stronger than a0?
Expected to be equal for qqqq states
Possibly due to isospin mixing
a0 and f0 -gt KK- and K0K0
Driven by KK loop
(Close Kirk 01)
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Are f0 and a0 nonetheless qq states?
Ds -gt ppp-
(Aitala01)
A)
In Ds -gt ppp- 60 f0(980) ... but also 30
f0(1370) which is known not to be ss!
f0(980)
f0
E791
m (2p)
How about Ds -gt W ?
B)
(Ackerstaff 98)
f0(980) 0.1 f2(1270) ?????f(1020)
Inclusive Z0 decay
similar for f0(980), f2(1270), f(1020)
OPAL
Prediction for qqqq?
A) B) are not compelling arguments
xpp/Eb
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1380 CsI (Tl)
Crystal Barrel
Bochum - Bonn- Budapest - Carnegie Mellon - CERN
- Hamburg - Karlsruhe - LBL - Mainz - Munich -
Queen Mary - RAL - Strasbourg - UCLA - Zurich
LH2 PWC
CERN / LEAR 1989 -1996
gt 100 MeV/c
pp -gt p0 (M-gt p?p?, KK, hh??)
1.5 T
Jet driftchamber
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I0 pp S-Wave
I1 ?p S-Wave
pp -gt p?p??
pp -gt p?p??
pp -gt p???
Apart from phase space
2 isovectors a0(980), a0(1450)
M1470, G 265 MeV Consistent with pp-gt pKK
pp -gt p?p?p?
4 isoscalars below 1.6 GeV
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If qq, then f0(1370) and f0(1500) are both uudd
p (rest) p -gt three pseudoscalars
CRYSTAL BARREL
f0(1370)
p0hh
p0p0p0
p0KLKL
f2(1565)
f0(1500)
f2(1270)
f0(1500)
m2(KLp0)
m2(p0h)
f0(980)
f0(1500) small f0(1370) small
a0(980)
K(892)
f2(1525)
f0(1370) and f0(1500) KK/pp??????
none is ss
1360 23, 351 41MeV 1505 9, 111 12 MeV
G
M
(e.g. C. Amsler, RMP 70 (1998) 1293)
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f0(1710) is dominantly ss
pp -gt ps KK, pp pf _at_ 450 GeV
pp -gt phh?_at_ ?????eV/c
(Amsler 02)
(Barberis 99)
a0(980)
a2(1320)
Crystal Barrel
Swave
f0(1370)
f0(1500)
f0(1710)
m2(ph) GeV
m(KK-) GeV
f0(1370) f0(1500) f0(1710)
lt1 (0.5 0.2) ltlt1 (0.3 0.1) gtgt1 (5.5
0.8)
m2(ph) GeV
f0(1500)
no f0(1710)
10
lt 2
strong in central collisions
OZI rule ss meson suppressed in pp
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f0(1500) is mainly glue f0(1370)
(uudd), f0(1710) ss
nn
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Isospin I0 mixing
SU(3)
For the two isoscalars (PDG)
(the f partner has ??????? )
??q35.3o
Ideal mixing
Write a 54.7o q??then
a????
q????
a90o ?q35.3o ? for pure ss a0o
for pure nn
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0 (or 2) decay into two pseudoscalar mesons
Application of SU3
Decay of a 0 or 2 meson in nonet (a) into
two pseudo- scalar mesons (pp, KK, hh, hh)
g2 (a)
is a coupling
Formfactor with
???b 0.5 GeV/c
q split off momentum l angular momentum
SU(3)
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0 (or 2) decay into two pseudoscalar mesons
(Amsler Close 96)
SU(3)
? 0- mixing angle 36o
Examples
???pp??????for a90o , ss ???pp??????for a0o ,
nn ???????????for a0o , nn
Excellent fits to the decays of tensor
mesons (Peters Klempt 95, Amsler Close 96)
K
s
nn
K
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f0(1500,1710)-gt0- mesons
f0(1710)
a
1/3
as a function of a
scalars
(C. Amsler PL B541 (2002) 22)
-10o lt a lt 5o
f0(1500) is
Assuming qq
f0(1700) is dominantly
a? 117o
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Mass formula
Linear mass formula applied to the scalar nonet
q, ????a 120o
agrees with BR for f0(1710) -gt KK, pp
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f0(1500) does not couple to gg? (LEP)
gg?-gt KSKS
gg -gt pp-
(Acciarri 01,Braccini 01)
(Barate 00)
f2(1525)
f2(1270)
m(pp-) GeV
m(KSKS ) GeV
J2, some J 0 a2, f0(1710)
no f0(1500) no f0(1710)
with ??pp-?23
Ggglt 1.4 keV 95 CL
my guess, rate compatible with ss
no f0(1500) --gt KK (?)
Ggg (pp-) ?small, B?
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?gg-coupling
M -gt gg or ee- -gt gg (ee- ) -gt M (ee- )
g
M
g
G?? c g2gg m3
ggg cqeq2
M Scq qqgt
eq
constant for nonet of M
I0
I1
for ?a0, 90o (and equal masses) G?? 25 C 2
C 9 C
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gg?widths, first for tensor mesons
nonet constant
1) f2 (1270) and f2(1525)
a or q, ???q 27.3 0.8 o
Predicted
Agrees with mass formula
Measured
0.0328 0.0062
(PDG and Acciarri 01, L3)
2) from f2(1525) gg?width C 4.9 x 10
-14 MeV-2
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gg?width of f0(1500)
?c0/c?2 3.3 (exp 3.6 1.1)

• 2 relativistic
• 15/4 non rel.

50o lt a lt 100o
f0(1500)
Ggg(a, 0)
if qq ss, contradicts
small KK
Ggglt 1.4 keV 95CL

• then f0(1500) is not qq
• not produced in gg
• glue!

some mixing with qq likely
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(e.g. Amsler Close 96)
Mixing with qq states
Sss
1710 1500 1370
G
Nnn
pp KK hh hh 3 4 1 0
Cancellation
However, KK is much smaller than pp?
n
s
A f0(1500) -gt KK
x
?
n
s
hh, hh
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Mixing with qq states
(Close Kirk 01)
Mass matrix
, (assumes here flavor independence)
Fit to CB and WA102 data, favored solution
errors 10
MG1443 MeV MN1377, MS1674 MeV
f0(1710) is mostly ss 50 glue in f0(1370) and
f0(1500)
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Tensor mesons and tensor glueball
Experimental evidence for I0, 2 states
(PDG00)
6 mesons expected 9 reported
2 glueball expected at 2232 300 MeV
23P2 perhaps f2(1640), f2(1950), a2(1620),
K2(1980)
requires systematic study 1600 - 2500 MeV
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Prominent glueball candidate fJ(2220) (or x?
pp -gt pp, hh
(Amsler 02)

• MarkIII, BES J/?-gtg x
• narrow (23 8) MeV
• presumably spin 2

CBarrel
BES
B (J/y-gt g x) gt gt 0.29
x??
J/??-gt g?pp
expect
Crystal Ball g incl.
(Bai 96)
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Summary1

• f0(980) and a0 (980) are qqqq states
• large radiative f decays

• ground state qq scalar nonet is around 1400 MeV
• a0(1450), K0(1430), f0(1370), f0(1710)

1) f0(1710) is clearly mostly ss

• 2 PS decay modes (WA102)
• no signal in pp annihilation

2) qq nonet can be built, a 117 o
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Summary2

• f0(1500) must have a large glue content
• 1) qq conflict KK gg?
• 2) lack of coupling to gg

Mixing of glue with qq is possible, but not
needed (?)

• gg?? coupling to glueballs?
• high statistics gg data needed (to see the
  scalars)
• systematic study of f0(1710) branching ratios,
• e.g 4p, KK2p

• no clear candidate for the 2 glueball yet

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Thank you