Exotica Bad Honnef, January 2005

1
The pentaquark in the linear molecular heptaquark
model
Pedro Bicudo
Dep. Fis. CFIF, Inst. Sup. Técnico, Lissabon,
Portugal

• Exotica _at_ Bad Honnef, January 2005

2
The pentaquark in the linear molecular heptaquark
model
Pedro Bicudo
Dep. Fis. CFIF, Inst. Sup. Técnico, Lissabon,
Portugal
1. The excitation of Q 2. Linear heptaquark
molecules Q , X--, D- and others 3.
Technical chiral symmetry breaking in the quark
model 4. Outlook molecules, annihilation
Exotica _at_ Bad Honnef, January 2005
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1. The excitation of Q
4
1. The excitation of Q
T. Nakano al, hep-ex/0301020,
Phys.Rev.Lett.91012002 (2003)
5
In the Quark Model it is well known that the
cannot be a simple s-wave P - groundstate. The
mass is 1.535 GeV but it is too wide.
Q
! The pentaquark must be an excited state !
And we get the repulsive K-N exotic s-wave phase
shifts, which have been understood long ago, by
Bender al, B. Ribeiro and Barnes Swanson.
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Ex1 Chiral soliton
The exotic anti-decuplet, including the Q (with
the correct mass and with), and the X-- , was
predicted in 1997 by Diakonov, Petrov and
Polyakov in the Chiral Soliton Model.
This is based on the skyrmion (1962), where the
pion is an effective field and the baryons are
topological solitons. Skyrme showed that a
divergent pion field is equivalent to a spin 1/2
nucleon. The chiral soliton was upgraded to
flavour SU(3) by Guadagnini by Mazur, Nowak and
Praszalowicz and by Diakonov and Petrov
(1984).
p
p
N
p
p
p
p
p
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The rotational excitations in space x flavour
space of the SU(3) topological soliton, composed
of the p, K and h fields produces flavour
multiplets. The vertices of the anti- decuplet
are exotic pentaquarks!
Diakonov, Petrov, Polyakov, Z. Phys. A 359, 305
(1997) arXivhep-ph/9703373
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Ex2 Diquark string
Jaffe and Wilczeck Phys. Rev. Lett. 91, 232003
(2003) arXiv hep-ph/0307341 suggest an
anti-baryon structure for the Q where two (ud)
diquarks play the role of anti-quarks, in the
sense that the diquarks are tightly bound and
have color 3.
Indeed the quark model supports an attractive
interaction for a diquark with color 3. The
antisymmetry of the wave-function implies that
one of the space coordinates is excited to a
p-wave, resulting in the same parity of the
chiral soliton model. The masses of the other
pentaquarks are also predicted, Q M 1540 X--
M 1750 , G X-- is 50 wider than G Q D-
p M2710
ud
s
ud
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The model of Karliner and Lipkin, Phys. Lett. B
575, 249 (2003) arXivhep-ph/0307343 0402260
ressembles a double-bag structure for the Q . In
this case a color triplet (ud) plays the role of
the anti-quark, and a color anti-triplet (uds)
plays the role of the quark.
The p-wave prevents the overlap of the two
coloured sub-bags. This again produces a total
parity .
p-wave
ud s
ud
string
L(l1)/2 mr2
The confining linear potential, together with a
repulsive centrifugal barrier indeed suggests
that a resonance above threshold may exist.
V(r)
r
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Nevertheless, consider the 5th Quark Model
excitation
1st. excitation, radial M r 1-- - M r 1--
700 MeV 2nd excitation, angular M f1 1 -
M r 1-- 500 MeV 3rd excitation, spin M
K 1-- - M K 0- 400 MeV 4th excitation,
flavour M K 1-- - M r 1-- 150 MeV 5th
excitation, quark- antiquark creation M p 140
MeV
Close to the Q -K N mass?
The quark-antiquark pair creation is effectively
used in chiral lagrangians and chiral solitons,
and it is equivalent to the chiral doubling of
Nowak, Rho and Zahed, Phys. Rev. D 48, 4370
(1993) arXivhep-ph/9209272. Possibly
rotational excitations of the chiral soliton
partly correspond, in the Quark Model, to pion
creation.
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Moreover - whenever the two interacting
ground-sate hadrons have a common flavour, the
repulsion is increased, - when the two
interacting hadrons have a matching quark and
antiquark the attraction is enhanced. Exs
d u u s
d u u s
u d u s
Annihilation attraction Veff. a -(2/3)(2mN-mD)
u d u s
Exchange repulsion Veff. a (4/3)(mD-mN)
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2. Linear heptaquark molecules Q , X-- , D- p
and others
Ex3 Linear Heptaquark Molecules
The Theta (1540) as a heptaquark with the
overlap of a pion, a kaon and a nucleon, P. B. ,
G. M. Marques  Phys. Rev. D69, 011503(R) (2004),
hep-ph/0308073 The anti-decuplet candidate
Xi--(1862) as a heptaquark with the overlap of
two anti-kaons and a nucleon , P.B., Phys. Rev.
D 70, 111504(R) (2004), hep-ph/0403146 Are the
anti-charmed and bottomed pentaquarks molecular
heptaquarks? P. B., Phys. Rev. D 71, 011501(R)
(2005), hep-ph/0403295 Prediction of the masses
and decay processes of strange, charmed and
bottomed pentaquarks from the linear molecular
crypto-heptaquark model, P. B., hep-ph/0405086
Other K pi N papersOn the possible nature of
the Theta as a K pi N bound state, F.
Llanes-Estrada, E. Oset and V. Mateu,
Phys.Rev.C69, 055203 (2004) nucl-th/0311020.
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Q
Suppose that a q-q pair is added to the uudds .
udd ud ds or uud du us Then the new system
may bind. Moreover the heptaquark has an opposite
parity and therefore it is an independent
system (a chiral partner). The only possible
decay channel is to a p-wave KN, with a low
energy p annihilation which is naturally
suppressed. We proposed hep-ph/0308073 that
the Q is in fact a linear crypto-heptaquark
with the strong overlap of a KpN, where the p
is bound by the I1/2 pK and pN attractive
interactions-
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Q
The only favourable flavour combination
is, Total I1 I0
p I1/2 I1/2
K I1 N
I1/2 I1/2

15
Q
The crypto-heptaquark or linear tri-hadronic
molecule model

K us
uud N
16
Q
The crypto-heptaquark or linear tri-hadronic
molecule model
p du
K us
uud N
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Q
The decay of the crypto-heptaquark molecule is
suppressed by the Adler Zero, and Ribeiro-Beveren
rearrangement rules
N uud p du
K us
N udd K
us
S-wave
3P0
P-wave
P-wave
At most a suppression factor gt 1/100 can be
understood
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Extending the pentaquark and the molecular
heptaquark picture to the full SU(3)
anti-decuplet we arrive at the following picture,
mass
parity
K-p-N
Q

K-K-N
N?

S?
K-N
-
K-N-K
X

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D- p
In what concerns anti-charmed pentaquarks like
the Dp observed at Hera, or anti-bottomed ones,
this extends the anti-decuplet to broken flavour
SU(4) or SU(5). Anti-charmed pentaquarks were
predicted by many authors, replacing the s by a
c. Again the pentaquark uuddc is unbound. A
linear-crypto-heptaquark may exist with a mass
close to the observed resonance at H1. We
consider the molecule, D - p -N M3.10
GeV with a positive energy of 15 MeV above
threshold. We understand qualitatively that this
system is less bound than the Q .
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Prediction of strange, charmed and bottomed
exotic pentaquarks.
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3. Technical chiral symmetry breaking in the
quark model.
Technical
Technical
Technical
Technical
Technical
Technical
Technical
Technical
Technical
Technical
Technical
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This all starts with vacum condensation
Chiral rotation
Symmetry axis
Pseudo-scalar condensate
Vacumm energy density
False vacuum
Technical
Quark-antiquark Scalar condensate
Vacuum
Light pion
0gt Exp q M( 3p0) q
Constituent quarks
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P. B., J. Ribeiro, Phys. Rev. D42,
1611-1624(1990) P. B, J. Ribeiro, Phys. Rev.
D42, 1625-1634 (1990) P. B, J. Ribeiro, Phys.
Rev. D42, 1635-1650 (1990)
quark
Technical
fp
meson
f-p
F. Llanes-Estrada, S. Cotanch, P. Bicudo, J.
Ribeiro, A. Szczepaniak , Nucl.Phys. A 710,
45-54, (2002) F. Llanes-Estrada, P. Bicudo,
Phys. Rev. D 68, 094014 (2003), (2003) P. Bicudo
, Phys.Rev.C67035201(2003)
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Recent breakthrough in the program to include c
Symmetry Breaking in the Quark Model The Axial
Ward Identity shows that the quark-antiquark
annihilation interaction is identical to the V-
of p Salpeter equation
lt f A f gt mp - (2/3)(2mN-mD)
Technical
K
K
Relevant for crypto-multiquarks, Possible ex
the Ds(2317)
A
D
D
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fa
fa
fb
fb
Hadronic interactions
fa
fa
Technical
fb
fb
Adding all possible diagrams with the RGM
method Of Ribeiro (1978), Oka, Toki we can
compute the multiquark mass, and the
hadron-hadron interactions.
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We arrive at the criterion for the short-range
interaction of ground-state hadrons - whenever
the two interacting ground-sate hadrons have a
common flavour, the repulsion is increased, -
when the two interacting hadrons have a matching
quark and antiquark the attraction is
enhanced. Exs
d u u s
d u u s
u d u s
Annihilation attraction Veff. a -(2/3)(2mN-mD)
u d u s
Exchange repulsion Veff. a (4/3)(mD-mN)
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Q
Proceeding with a quantitative study we arrive at
the separable potentials for the different
2-body systems, VK-N 2 -(4/3)tK.tN
(mD-mN) Nb2 fbgtlt fb (5/4)
(1/3) tK.tN 3 Na2 Vp-N
2 (2mN-mD) Nb2 tp.tN fbgtlt fb
9 Na2 Vp-K
8 (2mN-mD) Nb2 tp.tK fbgtlt fb
27 Na2 (where the a and
b parameters may differ from exchange to
annihilation channels)
Repulsive attractive when I1/2 attractive
when I1/2
Technical
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Q
This is our parameter set, tested in 2-body
channels,
Technical
Where all numbers are in units of Fm-1
We move on. Because the pion is quite light we
start by computing the pion energy in an
adiabatic K-N system.
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Q
Indeed we get quite a bound pion, but it only
binds at very short K-N distances. I also
overcomes the K-N repulsion.
Technical
However when we remove the adiabaticity, by
allowing the K and N to move in the pion field,
we are not yet able to overcome the the K-N
kinetic energy. -50 MeV are missing.
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4. Outlook molecules, annihilation
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4. Outlook molecules, annihilation
Molecular multiquarks -needed medium range
interaction We still fail, a -50 MeV is missing!
This suggests that the attractive medium range
interaction (two pion exchange) should be
included. Ex. N-N interaction
Ex. N-N interaction
Equivalent to add many p to the Fock space
V N-N
core repulsion (Ribeiro)
R Fm
1
0
Long Range One Pion Exchange Potential (Yukawa)
Sigma or pp exchange potential
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Data copied from J. Haidenbauer, G. Krein,
Phys. Rev. C68 (2003) 052201 hep-ph/0309243 who
used the SAID program
The Medium Range Interaction is Indeed Found by
the Hamburg, Inversion OnLine http//smithers.phy
snet2.uni-ham burg.de/OnLine/online.htm
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Molecular multiquarks -where are the pure
pentaquarks? the diquark picture should not be
wrong, moreover it is confirmed by the lattice,
however higher energies or wider decays are
expected P M1.7 to 2 GeV, decays with
string-breaking P- M1.53 GeV, decays with
flip-flop
ud
s
ud
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Molecular multiquarks -nuclear effects See M.
Vicente-Vacas, D. Cabrera, O. Li, V. Magas, E.
Oset
N
p du
K us
uud N
N
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• Annihilation
• The tetraquarks are easy to get,
• Ex. of Ds,

s u u c
s u u c
''THE FAMILY OF STRANGE MULTIQUARKS AS KAONIC
MOLECULES BOUND BY HARD CORE ATTRACTION''P.
B., Nucl. Phys. A, in press (2004)
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• Annihilation
• Crypto-exotics are harder to implement in the
  lattice

large Distance