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Pentaquarks: predictions, evidences &
implications
Maxim V. Polyakov
Liege Universitiy & Petersburg NPI
Outline:
- Predictions
- Post-dictions
- Implications
PARIS, March 2
Baryon Families
ms=150 MeV
W−
Gell-Mann, Neeman SU(3) symmetry
?
Quarks are confined inside
colourless hadrons
q
q
q
Mystery remains:
Of the many possibilities for
combining quarks with colour into
colourless hadrons, only two
configurations were found, till now…
Particle Data Group 1986 reviewing evidence for exotic baryons
states
“…The general prejudice against baryons not made of three quarks
and the lack of any experimental activity in this area make it likely
that it will be another 15 years before the issue is decided.
PDG dropped the discussion on pentaquark searches after 1988.
Baryon states
All baryonic states listed in PDG can be made of 3 quarks only
* classified as octets, decuplets and singlets of flavour SU(3)
* Strangeness range from S=0 to S=-3
A baryonic state with S=+1 is explicitely EXOTIC
• Cannot be made of 3 quarks
•Minimal quark content should be qqqqs , hence pentaquark
•Must belong to higher SU(3) multiplets, e.g anti-decuplet
observation of a S=+1 baryon implies a new large multiplet of
baryons (pentaquark is always ocompanied by its large family!)
important
Searches for such states started in 1966, with negative
results till autumn 2002 [16 years after 1986 report of PDG !]
…it will be another 15 years before the issue is decided.
Theoretical predictions for pentaquarks
1. Bag models [R.L. Jaffe ‘76, J. De Swart ‘80]
Jp =1/2- lightest pentaquark
Masses higher than 1700 MeV, width ~ hundreds MeV
Mass of the pentaquark is roughly 5 M +(strangeness) ~ 1800 MeV
An additional q –anti-q pair is added as constituent
2. Soliton models [Diakonov, Petrov ‘84,
Chemtob‘85, Praszalowicz ‘87, Walliser ‘92]
Exotic anti-decuplet of baryons with lightest S=+1
Jp =1/2+ pentaquark with mass in the range
1500-1800 MeV.
Mass of the pentaquark is rougly 3 M +(1/baryon size)+(strangeness) ~ 1500MeV
An additional q –anti-q pair is added in the form of excitation of nearly massless
chiral field
The question what is the width of the exotic pentaquark
In soliton picture has not been address untill 1997
It came out that it should be „anomalously“ narrow!
Light and narrow pentaquark is expected ->
drive for experiments
[D. Diakonov, V. Petrov, M. P. ’97]
2003 – Dawn of the Pentaquark
Q+ first particle which is made of more than 3 quarks !
Particle physics laboratories took the lead
Spring-8: LEPS (Carbon)
JLab: CLAS (deuterium & proton)
ITEP: DIANA (Xenon bubble chamber)
ELSA: SAPHIR (Proton)
CERN/ITEP: Neutrino scattering
CERN SPS: NA49 (pp scattering)
DESY: HERMES (deuterium)
ZEUS (proton)
COSY: TOF (pp-> Q+ S+)
SVD (IHEP) (p A collisions)
HERA-B (pA) Negative Result
What do we know about Theta ?
 Mass 1530 – 1540 MeV
Width < 10-20 Mev, can be even about 1 Mev as
it follows from reanalysis of K n scattering data
[Nussinov; Arndt et al. ; Cahn, Thrilling]
 Isospin probably is zero [CLAS, Saphir, HERMES ]
Compatible with anti-decuplet interpretation
 Spin and parity are not measured yet
Chiral Symmetry of QCD
QCD in the chiral limit, i.e. Quark masses ~ 0
LQCD
1 a a


 - 2 F F +  (i   +  A )
4g
Global QCD-Symmetry  Lagrangean invariant
under:

hadron
 u 
A A  u
SU (2)V :       '  exp -i   
multiplets
 d 
 d 
 u 
 u 
A A
SU (2) A :       '  exp -i   5  
 d 
 d 
Symmetry of Lagrangean is not the same
as the symmetry of eigenstates
No Multiplets
Symmetry is
sponteneousl
broken
Three main features of the SCSB
3
 Order parameter: chiral condensate  qq > -250MeV  0
[vacuum is not „empty“ !]
 Quarks get dynamical masses: from the „current“
masses of about m=5MeV to about M=350 MeV
 The octet of pseudoscalar meson is anomalously
light (pseudo) Goldstone bosons.
  > 0
5MeV
current-quarks (~5 MeV) 
Constituent-quarks (~350
MeV)
Spontaneous
Chiral symmetry
breaking
  > 0
350MeV
Particles  Quasiparticles
QuarkModel
•Three massive quarks
•2-particle-interactions:
•confinement potential
•gluon-exchange
•meson-exchage
Nucleon
•(non) relativistisc
• chiral symmetry is not respected
•Succesfull spectroscopy (?)
Chiral
Soliton
Mean Goldstone-fields
(Pion, Kaon)
Nucleon
Large Nc-Expansion of
QCD
Chiral
Soliton
•Three massive quarks
• interacting with each other
• interacting with Dirac sea
• relativistic field theory
Nucleon
•spontaneously broken chiral symmetry
is full accounted
Quantum
numbers
Quantum #
Coupling of spins,
isospins etc. of 3 quarks
mean field  non-linear
system  soliton 
rotation of soliton
Quantum #
Natural way for light baryon
exotics. Also usual „3-quark“
Quark-anti-quark
pairs
„stored“
Quantum
in #
Coherent :1p-1h,2p-2h,....
baryons
should contain
a lot
of
chiral mean-field
antiquarks
Antiquark
distributions:
unpolarized
flavour
asymmetry
d-bar
minus ubar
d ( x) - u ( x)
Pobylitsa et
al
Soliton picture predicts large polarized flavour asymmetry
Fock-State: Valence and Polarized
Dirac Sea
Dirac-Equation:
 -i +  MU i  ii
Natural way for light baryon
exotics. Also usual „3-quark“
Soliton
baryons should contain a lot of
antiquarks
Quark-anti-quark pairs „stored“
in chiral mean-field
Quantum numbers originate from 3 valence quarks AND Dirac sea !
Quantization of the mean field
Idea is to use symmetries
if we find a mean field  a minimizing the energy
than the flavour rotated R ab b mean field
also minimizes the energy
 Slow flavour rotations change energy very little
 One can write effective dynamics for slow rotations
[the form of Lagrangean is fixed by symmeries and
axial anomaly ! See next slide]
 One can quantize corresponding dynamics and get
spectrum of excitations
[like: rotational bands for moleculae]
Presently there is very interesting discussion whether large Nc
limit justifies slow rotations [Cohen, Pobylitsa, Klebanov, DPP....].
Tremendous boost for our understanding of soliton dynamics!
-> new predictions
SU(3): Collective Quantization
Lcoll
L
J 
W a
NcB
8
J 2 3
a
I1 3 a a I 2 7 a a
3 8
 M0 + W W + W W +
W
2 a 1
2 a 4
2
3
7
1
1
a ˆa
a ˆa
ˆ
ˆ
Hˆ coll 
J
J
+
J
J + constraint


2 I1 a 1
2 I 2 a 4
2Jˆ 8
Y'  1
3
 Jˆ a , Jˆ b   if abc Jˆ c


Calculate eigenstates of Hcoll
and select those, which fulfill
the constraint
From
WessZumino
-term
SU(3): Collective Quantization
Lcoll
I1 3 a a I 2 7 a a
3 8
 M0 + W W + W W +
W
2 a 1
2 a 4
2
L
J 
W a
NcB
8
J 2 3
3
7
1
1
a ˆa
a ˆa
ˆ
ˆ
Hˆ coll 
J
J
+
J
J + constraint


2 I1 a 1
2 I 2 a 4
3, 3, 6 ,8,10,10, 27,...
2Jˆ 8
Y'  1
+
+
+
1
3
1
3
J=T 
....
Known from
2
2
2
delta-nucleon
3
3
splitting
 Jˆ a , Jˆ b   if abc Jˆ c
10-8 =
10-8 =


2I1
2I 2
a
Spin and parity are predicted !!!
3
3
10-10 =
2I 2 2I1
General idea: 8, 10, anti-10, etc are various excitations
of the same mean field  properties are interrelated
Example [Gudagnini ‘84]
8(m* + mN ) + 3mS  11m + 8mS*
Relates masses in 8 and 10, accuracy 1%
To fix masses of anti-10 one needs to know the
value of I2 which is not fixed by masses of 8 and 10
DPP‘97
~180 MeV
In linear order in ms
Input to fix I2
Jp =1/2+
Mass is in expected range (model calculations of I2)
P11(1440) too low, P11(2100) too high
Decay branchings fit soliton picture better
Decays of the anti-decuplet
,K,
h
All decay constants for 8,10 and anti-10 can be expressed
in terms of 3 universal couplings: G0, G1 and G2
 decuplet
1
[G0 + G1 ]2
2
 anti-decuplet
1
G0 - G1 - G2  0 In NR limit ! DPP‘97
2
[G0 - G1 -
1
G2 ]2
2
„Natural“ width ~100 MeV
Q < 15 MeV
Correcting a mistake in widths of usual decuplet one gets < 30 MeV
[Weigel 98, Jaffe 03]
Where to stop ?
The next rotational excitations of baryons are (27,1/2)
and (27,3/2). Taken literary, they predict plenty of
exotic states. However their widths are estimated
to be > 150 MeV. Angular velocities increase, centrifugal
forces deform the spherically-symmetric soliton.
In order to survive, the chiral soliton has to stretch into
sigar like object, such states lie on linear Regge trajectories
[Diakonov, Petrov `88]
,K,
h
,K,
h
Very interesting issue! New theoretical tools should be developed!
New view on spectroscopy?
- -
CERN NA49 reported evidence for – - with mass around
1862 MeV and width <18 MeV
For  symmetry breaking effects expected to be large [Walliser, Kopeliovich]
Update of  N S term gives 180 Mev -> 110 MeV [Diakonov, Petrov]
Small width of  is trivial consequence of SU(3) symmetry
Are we sure that  is observed ? -> COMPASS can check this! And go for charm
Non strange partners revisited
N(1710) is not seen anymore in most recent pi N
scattering PWA [Arndt et al. 03]
If Theta is extremely narrow N* should be also
narrow 10-20 MeV. Narrow resonance easy to miss
in PWA. There is a possiblity for a narrow N* at
1680 MeV [Arndt et al. 03]
In the soliton picture mixing with usual nucleon
is very important. Pi N mode is suppressed,
Eta N and pi Delta modes are enhanced.
Anti-decuplet nature of N* can be checked by
Photoexcitation. It is excited much stronger
From the neuteron, not from the proton [Rathke, MVP]
Theory Response to the Pentaquark
• Kaon+Skyrmion
• Q+ as isotensor pentaquark
• di-quarks + antiquark
More than 130 papers • colour molecula
• Kaon-nucleon bound state
since July 1, 2003.
• Super radiance resonance
• QCD sum rules
• Lattice QCD P=Rapidly developing
• Higher exotic baryons multiplets
theory: > 2.3 resubmissions • Pentaquarks in string dynamics
per paper in hep
• P11(1440) as pentaquark
• P11(1710) as pentaquark
• Topological soliton
• Q+(1540) as a heptaquark
• Exotic baryons in the large Nc limit
• Anti-charmed Q+c , and anti-beauty Q+b
• Q+ produced in the quark-gluon plasma
• …….
Constituent quark model
If one employs flavour independent forces between quarks
(OGE) natural parity is negative, although P=+1 possible to arrange
With chiral forces between quarks natural parity is P=+1
[Stancu, Riska; Glozman]
•No prediction for width
•Implies large number of excited pentaquarks
Missing Pentaquarks ?
(And their families)
Mass difference  -Q ~ 150 MeV
Diquark model [Jaffe, Wilczek]
No dynamic explanation of
Strong clustering of quarks
(ud)
L=1
Dynamical calculations suggest large mass
[Narodetsky et al.; Shuryak, Zahed]
(ud)
JP=3/2+ pentaquark should be close in
mass [Dudek, Close]
Anti-decuplet is accompanied by an octet of pentaquarks.
P11(1440) is a candidate
No prediction for width
Mass difference  -Q ~ 200 MeV -> Light  pentaquark
s
Diquark-triquark [Karliner, Lipkin]
No dynamic explanation of
Strong clustering of quarks
JP=1/2+ is assumed, not
computed
No prediction for width
u
s
d
u
d
Implications of the Pentaquark
 Views on what hadrons “made of” and how do they
“work” may have fundamentally changed
- renaissance of hadron spectroscopy
- need to take a fresh look at what we thought we
knew well.
 Quark model & flux tube model are incomplete and
should be revisited
 Does Q start a new Regge trajectory? -> implications
for high energy scattering of hadrons !
 Can Q become stable in nuclear matter? -> astrophysics?
 Issue of heavy-light systems should be revisited (“BaBar”
Resonance, uuddc-bar pentaquarks ). It seems that
the chiral physics is important !
Summary
 Assuming that chiral forces are essential in binding of quarks
one gets the lowest baryon multiplets
(8,1/2+), (10, 3/2+), (anti-10, 1/2+)
whose properties are related by symmetry
 Predicted Q pentaquark is light NOT because it is a sum of
5 constituent quark masses but rather a collective excitation
of the mean chiral field. It is narrow for the same reason
 Where are family members accompaning the pentaquark
Are these “well established 3-quark states”? Or we should
look for new “missing resonances”? Or we should reconsider
fundamentally our view on spectroscopy?