1. Gluonic Excitations of
Hadrons
Curtis A. Meyer
Carnegie Mellon University
February 7, 2003
February 7, 2003
Curtis A. Meyer

2. Outline of Talk Introduction Meson Spectroscopy Glueballs Expectations
Experimental Data
Interpretation
Hybrid Mesons
The Future
February 7, 2003
Curtis A. Meyer

3. is the theory of quarks and gluons
QCD
is the theory of quarks and gluons
white
3 Colors
3 Anti-colors
8 Gluons, each of which
has a color an an anti-color
Charge. u d s c b t
Six Flavors of quarks
February 7, 2003
Curtis A. Meyer

4. Jets at High Energy Direct evidence for gluons come from high energy
jets. But this doesn’t tell us anything about the
“static” properties of glue. We learn something about s
2-Jet
3-Jet
gluon bremsstrahlung
February 7, 2003
Curtis A. Meyer

5. Deep Inelastic Scattering
As the nucleon is probed to smaller and smaller x,
the gluons become more and more important. Much
of the nucleon momentum and most of its spin is
carried by gluons!
Glue is important to
hadronic structure.
February 7, 2003
Curtis A. Meyer

6. Strong QCD See and systems. Color singlet objects observed in nature:
white
Nominally, glue is
not needed to
describe hadrons.
Focus on “light-quark mesons”
Allowed systems: , ,
February 7, 2003
Curtis A. Meyer

7. Normal Mesons Non-quark-antiquark 0-- 0+- 1-+ 2+- 3-+ …
quark-antiquark pairs
orbital
r3,w3,f3,K3
r2,w2,f2,K2
r1,w1,f1,K1
p2,h2,h’2,K2
L=2
3--
2--
1--
2-+ u d s u d s
radial
a2,f2,f’2,K2
a1,f1,f’1,K1
a0,f0,f’0,K0
b1,h1,h’1,K1
L=1
2++
1++
0++
1+-
J=L+S
P=(-1) L+1
C=(-1) L+S
G=C (-1) I
(2S+1) L J
1S0 = 0 -+
3S1 = 1--
r,w,f,K*
p,h,h’,K
L=0
1--
0-+
February 7, 2003
Curtis A. Meyer

8. Nonet Mixing The I=0 members of a nonet can mix: SU(3) physical states
Ideal Mixing:
February 7, 2003
Curtis A. Meyer

9. Spectrum exotic nonets Lattice 1-+ 1.9 GeV 0++ 1.6 GeV 2 + – 2 + +
1.0
1.5
2.0
2.5
qq Mesons
L = 0 1 2 3 4
Each box corresponds
to 4 nonets (2 for L=0)
exotic
nonets
0 – +
0 + –
1 + +
1 + –
1– +
1 – –
2 – +
2 + –
2 + +
0 + +
Glueballs
Hybrids
Radial
excitations
Lattice
GeV
GeV
(L = qq angular momentum)
February 7, 2003
Curtis A. Meyer

10. Glueball Mass Spectrum
QCD is a theory of quarks and gluons
What role do gluons play in the meson
spectrum?
Lattice calculations predict a spectrum
of glueballs. The lightest 3 have JPC
Quantum numbers of 0++ , 2++ and
0-+.
The lightest is about 1.6 GeV/c2
f0(1710)
f0(1500)
a0(1450)
K*0(1430)
f0(1370)
a0(980)
Morningstar et al.
f0(980)
February 7, 2003
Curtis A. Meyer

11. Glue-rich channels
Where should you look experimentally for Glueballs? G M
Radiative J/ Decays
0-+ (1440)
0++ f0(1710)
Large signals
Proton-Antiproton Annihilation
Central Production
(double-pomeron exchange)
February 7, 2003
Curtis A. Meyer

12. Decays of Glueballs? Glueballs should decay in a flavor-blind fashion.
’=0 is true for any SU(3) singlet and for any
pseudoscalar mixing angle. Only an SU(3)
“8” can couple to ’.
Flavor-blind decays have always been cited
as glueball signals.
February 7, 2003
Curtis A. Meyer

13. Crystal Barrel Results
Crystal Barrel Results: antiproton-proton annihilation at rest
f0(1500) a pp, hh, hh’, KK, 4p
Discovery of the f0(1500)
Solidified the f0(1370)
f0(1370) a 4p
Establishes the scalar nonet
Crystal Barrel Results
Discovery of the a0(1450)
250,000 hhp0 Events
700,000 p0p0p0 Events
f2(1565)+s
f0(1500)
f2(1270)
f0(980)
f0(1500)
February 7, 2003
Curtis A. Meyer

14. The f0(1500) Is it possible to describe the f0(1500) as a member
of a meson nonet?
Use SU(3) and OZI
suppression to compute
relative decays to pairs
of pseudoscalar mesons
Get an angle of about 143o
90% light-quark
10% strange-quark
Both the f0(1370) and f0(1500) are
February 7, 2003
Curtis A. Meyer

15. WA102 Results CERN experiment colliding p on a hydrogen target.
Central Production Experiment
Recent comprehensive data set
and a coupled channel analysis.
February 7, 2003
Curtis A. Meyer

16. Model for Mixing meson 1 meson Glueball r2 meson Glueball r3
flavor blind? r
Solve for mixing scheme
F.Close: hep-ph/
February 7, 2003
Curtis A. Meyer

17. Meson Glueball Mixing Physical Masses f0(1370),f0(1500),f0(1710)
Bare Masses:
m1,m2,mG
(G) (S) (N)
f0(1370)   0.07
f0(1500)  0.04 –0.700.07
f0(1710)   0.02
octet piece
m1=137720 m2=167410 mG=144324
Lattice of about 1600
February 7, 2003
Curtis A. Meyer

18. Glueball Expectations
Antiproton-proton: Couples to
Observe: f0(1370),f0(1500)
Central Production: Couples to G and in phase.
Observe: f0(1370),f0(1500), weaker f0(1710).
Radiative J/: Couples to G, |1>, suppressed |8>
Observe strong f0(1710) from constructive |1>+G
Observe f0(1500) from G
Observe weak f0(1370) from destructive |1>+G
Two photon: Couples to the quark content of states,
not to the glueball. Not clear to me that
has been seen.
February 7, 2003
Curtis A. Meyer

19. Higher mass glueballs?
Part of the CLEO-c program will be to search for
glueballs in radiative J/ decays.
Lattice predicts that the 2++ and the 0-+ are the
next two, with masses just above 2GeV/c2.
Radial Excitations of the 2++ ground state
L= States + Radial excitations
f2(1950), f2(2010), f2(2300), f2(2340)…
2’nd Radial Excitations of the  and ’,
perhaps a bit cleaner environment! (I would
Not count on it though….)
I expect this to be very challenging.
February 7, 2003
Curtis A. Meyer

20. Lattice QCD Flux Tubes Realized
From G. Bali
Color Field: Because of self interaction, confining flux tubes form between static color charges
Confinement arises from flux tubes and their excitation leads to a new spectrum of mesons
February 7, 2003
Curtis A. Meyer

21. Hybrid Mesons built on quark-model mesons excited flux-tube m=1
ground-state
flux-tube
m=0
1-+ or 1+-
normal mesons
S=0,L=0,m=1
J=1 CP=+
JPC=1++,1--
(not exotic)
S=1,L=0,m=1
J=1 CP=-
CP={(-1)L+S}{(-1)L+1}
={(-1)S+1}
JPC=0-+,0+-
1-+,1+-
2-+,2+-
exotic
m=0 CP=(-1) S+1
m=1 CP=(-1) S
Flux-tube Model
February 7, 2003
Curtis A. Meyer

22. QCD Potential ground-state excited flux-tube flux-tube m=1 m=0
linear potential
ground-state
flux-tube
m=0
excited flux-tube
m=1
Gluonic Excitations provide an
experimental measurement of
the excited QCD potential.
Observations of exotic quantum number nonets are the
best experimental signal of gluonic excitations.
February 7, 2003
Curtis A. Meyer

23. Hybrid Predictions Flux-tube model: 8 degenerate nonets
1++, ,0+-,1-+,1+-,2-+,2+- ~1.9 GeV/c2
S=0
S=1
Lattice calculations nonet is the lightest
UKQCD (97) 0.20
MILC (97) 0.30
MILC (99) 0.10
Lacock(99) 0.20
Mei(02) 0.10
~2.0 GeV/c2
1-+
0+-
2+-
Splitting  0.20
In the charmonium sector:
0.08
0.11
Splitting = 0.20
February 7, 2003
Curtis A. Meyer

24. Decays of Hybrids Decay calculations are model dependent, but the 3P0
model does a good job of describing normal meson
decays.
0++ quantum numbers (3P0)
The angular momentum in the flux tube stays in one of
the daughter mesons (L=1) and (L=0) meson.
L=0: ,,,,…
L=1: a,b,h,f,…
,, … not preferred.
1b1,f1,,a ,21,11,9 MeV (partial widths)
February 7, 2003
Curtis A. Meyer

25. E852 Results p-p -> hp- p a2 p1 (18 GeV) p1(1400)
Mass = MeV/c2
Width= MeV/c2
p1(1400)
The a2(1320) is the dominant
signal. There is a small (few %)
exotic wave. a2 p1
Interference effects show
a resonant structure in 1-+ .
(Assumption of flat background
phase as shown as 3.)
February 7, 2003
Curtis A. Meyer

26. Crystal Barrel Results: antiproton-neutron annihilation
CBAR Exotic
Crystal Barrel Results: antiproton-neutron annihilation
Same strength as the a2.
Mass = MeV/c2
Width= MeV/c2
Produced from states with one unit
of angular momentum.
p1(1400)
Without p1 c2/ndf = 3, with = 1.29
hp0p-
February 7, 2003
Curtis A. Meyer

27. Significance of signal.
February 7, 2003
Curtis A. Meyer

28. E852 Results At 18 GeV/c to partial wave analysis suggests
February 7, 2003
Curtis A. Meyer

29. understood acceptance
An Exotic Signal
Correlation of
Phase
&
Intensity
Exotic
Signal
p1(1600)
Leakage
From
Non-exotic Wave
due to imperfectly
understood acceptance
3p m= G=
ph’ m= G=
February 7, 2003
Curtis A. Meyer

30. Exotic Signals 1(1400) Width ~ 0.3 GeV, Decays: only 
weak signal in p production (scattering??)
strong signal in antiproton-deuterium.
1(1600) Width ~ 0.3 GeV, Decays ,’,(b1)
Only seen in p production, (E852 + VES)
In a nonet, there should only be one 1 state.
p1 IG(JPC)=1-(1-+)
h’1 IG(JPC)=0+(1-+)
h1 IG(JPC)=0+(1-+)
K1 IG(JPC)= ½ (1-)
Both of these are lighter than expectations, and
The decay modes are not what is expected.
February 7, 2003
Curtis A. Meyer

31. Photoproduction of Exotics q q _ _ q _ _ Quark spins anti-aligned
before q
after
A pion or kaon beam,
when scattering occurs,
can have its flux tube excited
 or 
beam
Much data in hand with some
evidence for gluonic excitations
(tiny part of cross section) _ _ q
after
before 
beam
Almost no data in hand
in the mass region
where we expect to find exotic hybrids
when flux tube is excited
Quark spins aligned _ _
February 7, 2003
Curtis A. Meyer

32. Exotics in Photoproduction g  ,, 1-+ nonet p1 IG(JPC)=1-(1-+)
h’1 IG(JPC)=0+(1-+)
h1 IG(JPC)=0+(1-+)
K1 IG(JPC)= ½ (1-) N g e X
p1  rp
h1  rb1 , wf
h’1  fw
Couple to V.M + e
g  ,,
February 7, 2003
Curtis A. Meyer

33. 0+- and 2+- Exotics N g e X In photoproduction, couple to r, w or f?
b0 IG(JPC)=1+(0+-)
h0 IG(JPC)=0-(0+-)
h’0 IG(JPC)=0-(0+-)
K0 I(JP)=½(0+)
a1,f0,f1
wf0,wf1,ra1
ff0,ff1,ra1
wp, a1,f0,f1
b2 IG(JPC)=1+(2+-)
h2 IG(JPC)=0-(2+-)
h’2 IG(JPC)=0-(2+-)
K2 I(JP)= ½(2+)
“Similar to p1 ”
wh,rp,wf0,wf1,ra1
fh,rp,ff0,ff1,ra1
Kaons do not have exotic QN’s
February 7, 2003
Curtis A. Meyer

34. Exotics and QCD
In order to establish the existence of gluonic excitations,
We need to establish the nonet nature of the 1-+ state.
We need to establish at other exotic QN nonets – the
0+- and 2+-.
In the scalar glueball sector,
the decay patterns have
provided the most sensitive
information. I expect the
same will be true in the
hybrid sector as well.
DECAY PATTERS ARE CRUCIAL
February 7, 2003
Curtis A. Meyer

35. The Scalar Mesons What about 2++ and 0-+ ? Three States f0(1370)
Overpopulation
Strange Decay Patterns
Seen in glue-rich reactions
Not in glue-poor
What about 2++ and 0-+ ?
J/Y Decays?
Awaiting CLEO-c
Glueball and Mesons
are mixed. Scheme is
model dependent.
Crystal Barrel proton-antiproton annihilation
The Scalar Mesons
Central Production WA102
Three States
f0(1370)
f0(1500)
f0(1710)
0++ rr
0++ ss
1.5
2.5
1.5
2.5
February 7, 2003
Curtis A. Meyer

36. What will we learn?
There is an clear signal for hybrid mesons – Exotic quantum
numbers – but confirmation requires the observation of
a nonet, not just a single state.
Mapping out more than one exotic nonet is necessary to
Establishing the hybrid nature of the states.
Decay patterns will be useful for the exotic QN states,
And necessary for the non-exotic QN states.
February 7, 2003
Curtis A. Meyer

37. Summary The first round of J/ experiments opened the door
to exotic spectroscopy, but the results were confused.
LEAR at CERN opened the door to precision, high-statistics
spectroscopy experiments and significantly improved both
our understanding of the scalar mesons and the scalar
glueball.
Pion production experiments at BNL (E852) and VES
Opened the door to states with non-quark-anti-quark
Quantum numbers.
CERN central production (WA102) provided solid new data
on the scalar sector, and a deeper insight into the scalar
glueball.
February 7, 2003
Curtis A. Meyer

38. The Future The CLAS experiment at Jefferson Lab is opening a
small window to meson spectroscopy in photoproduction.
CLEO-c will reopen the J/ studies with 100 times
Existing statistics. One goal is to find and study the
Pseudoscalar (0-+) and tensor glueball (2++)
The GlueX experiment will be able to do for hybrids
what Crystal Barrel and WA102 (together) did for
glueballs. What are the properties of static glue in
hadrons and how is this connected to confinement.
The antiproton facility at GSI (HESR) will look for hybrids
in the charmonium system.
February 7, 2003
Curtis A. Meyer

39. Gluonic Excitations Workshop at JLab May 14-16, 2003. February 7, 2003
Curtis A. Meyer