Strange Multiquarks as Kaonic Molecules Bound by Hardcore Attraction

1
Strange Multiquarks as Kaonic Molecules Bound by
Hard-core Attraction
Pedro Bicudo and Gonçalo Marques
Dep Física IST CFIF , Lisboa

• Hadron 2003 Aschaffengurg

2
Strange Multiquarks as Kaonic Molecules Bound by
Hard-core Attraction
Pedro Bicudo and Gonçalo Marques
Dep Física IST CFIF , Lisboa
1. Computing multiquark binding with RGM 2. A
criterion for hard core attraction and repulsion
3. Results for the binding energy 4. Conclusion

• Hadron 2003 Aschaffengurg

3
We study the discovered Ds(2317) at BABAR, CLEO
and BELLE, and find that it belongs to a class of
strange multiquarks, which is equivalent to the
class of kaonic molecules bound by hard core
attraction. In this class of hadrons a kaon is
trapped by a s-wave meson or baryon. To describe
this class of multiquarks we apply the Resonating
Group Method, and extract the hard core
kaon-meson(baryon)interactions. We derive a
criterion to classify the attractive channels.
We find that the mesons f0(980), Ds(2457), Bs
scalar and axial, and also the baryons with the
quantum numbers of L, Sc, Sb and also scc, scb
and sbb belong to the new hadronic class of the
Ds(2317).
4
1. Computing multiquark binding with the
Resonating Group Method
The RGM is a convenient method to compute the
energy of multiquarks and to study hadronic
coupled channels. The RGM was first used by
Ribeiro (1978) to explain the N_N hard-core
repulsion. Deus and Ribeiro (1980) also found
that the RGM may lead to hard-core attraction .
5
1. Computing multiquark binding with the
Resonating Group Method
meson a
The RGM is a convenient method to compute the
energy of multiquarks and to study hadronic
coupled channels. The RGM was first used by
Ribeiro (1978) to explain the N_N hard-core
repulsion. Deus and Ribeiro (1980) also found
that the RGM may lead to hard-core attraction .
q1
r12
q2
rab
q4
q3
r34
meson b
6
We compute the matrix element of the
Hamiltonian... in an antizymmetrized. basis
of hadrons....
lt fa fb cab ( E - Si Ti - Siltj Vij - Si j Ai j
) (1- P13 )(1 Pab)
fa fb cab gt
7
We compute the matrix element of the
Hamiltonian... in an antizymmetrized. basis
of hadrons....
Annihilation interaction
lt fa fb cab ( E - Si Ti - Siltj Vij - Si j Ai j
) (1- P13 )(1 Pab)
fa fb cab gt
This is the quark model potential Vij li.lj
V0 li.lj Si.Sj Vss ...
8
We compute the matrix element of the
Hamiltonian... in an antizymmetrized. basis
of hadrons....
Annihilation interaction
lt fa fb cab ( E - Si Ti - Siltj Vij - Si j Ai j
) (1- P13 )(1 PAB)
fa fb cab gt
The antisymmetrizer produces the states
color-octet x color-octet, expected in
multiquarks
Relative coordinate
This is the quark model potential Vij li.lj
V0 li.lj Si.Sj Vss ...
color singlet meson
9
T1
V12
T2
x
T3
E -
-
T4
V34
1

1-
Relative energy overlap (E-Ta-Tb) (1-n faabgtlt
faab )
10



x
V23
V14
V24
V13

1

1-
Repulsive, a qq hyperfine potential cst.
(2/3)(mD-mN) faabgtlt faab
11

x
1
Attractive a qq spin independent potential -cst.
(2/3)(2mN-mD) fbabgtlt fbab
12
fa
fa
Recent breakthrough Quark Model c Symmetry
Breaking RGM show that the
annihilation interaction is identical to the V-
of p Salpeter equation ltAgt mp -
(2/3)(2mN-mD)
fb
fb
fp
f-p
13
2. A Criterion for hard-core repulsion and
attraction
We arrive at the criterion - whenever the two
interacting 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
u d s u
Annihilation attraction Veff. a -(2/3)(2mN-mD)
u d u s
Exchange repulsion Veff. a (2/3)(mD-mN)
14
To avoid repulsion, the s-wave partner of K-su
and k0sd kaon, must have no u, d or s
quarks. To secure attraction, the s-wave partner
of the kaon must have u, d or s quarks.
Moreover we exclude the wide s-wave resonances.
Finally the heavier flavors act as spectators,
they play no direct role in the kaon trapping.
We arrive at the list of binding candidates
Kls, Dlc,Dlc,Blb,Blb, Nlll,Sc
llc,Sbllb, lcc,lcb,lbb
15
3. Results for the binding energy
We arrive at the separable potentials for the
different kaon-hadron systems, VK-K 2
(1/9)(2mN-mD) fagtlt fa VK-D 2
(1/9)(2mN-mD) fagtlt fa VK-D 2
(1/9)(2mN-mD) fagtlt fa VK-B 2
(1/9)(2mN-mD) fagtlt fa VK-B 2
(1/9)(2mN-mD) fagtlt fa VK-N 4
(1/9)(2mN-mD) fagtlt fa VK-Sc (7/3)
(1/9)(2mN-mD) fagtlt fa VK-Sb (7/3)
(1/9)(2mN-mD) fagtlt fa VK-lcc 4
(1/9)(2mN-mD) fagtlt fa VK-lcb 4
(1/9)(2mN-mD) fagtlt fa VK-lbb 4
(1/9)(2mN-mD) fagtlt fa
16
Here we neglected the coupling to the channels
with low energy pions, because the pion coupling
at low energies is suppressed by the Adler zero.
We stress that recently we showed that the quark
models with chiral symmetry comply with the Adler
zero. We also assumed, to have a single
parameter, that the inverse radius parameters a
and b are identical for all channels, although
small channel dependences are expected.
Moreover we neglected the meson exchange
interactions because we expect them to be smaller
than the hard core interaction. In the same way
we did not consider here the coupling to a single
meson or baryon s-channel.
17
Because the potential is separable, it is
straightforward to compute the scattering T
matrix. T fagt (1-v g0 )-1 lt fa , g0(E,m,a)
lt fa E-p 2 /(2m ) -1 fagt
-0.5
0
E
E
The binding energy is determined from the pole
position of the T matrix We have binding
if -4 m v gt a2
-1
0
1/v
-2
g0(E,1,1)
-4
18
Binding energies all numbers are in MeV
19
4. Conclusion
- With the RGM we study multiquarks where the K
is trapped by an hard-core attraction to a s-wave
meson or baryon. This is essentially model
independent. - We find that the new hadronic
class of the scalar tetraquark Ds(2317) also
includes the tetraquarks f0(980) , axial Ds(2457)
, vector Bs(5720) , axial Bs(5766),and the
pentaquarks with quantum numbers L, Xc(2880) ,
Xc(2880) , and also scc , a scb and a sbb.
Immprovement needed in the very binding LK-N
pentaquark we plan to include the coupling to the
relevant p-S channel. Other aplications we
applied the RGM to the Q recently discovered at
SPring-8, at ITEP and at CLAS-Thomas Jefferson
Lab (talk tomorrow in Baryons IV). The baryonium
discovered at BES is another possible application.
20
A limited set of references Experimental
BABAR, PRL 90, 242001, (2003) hep-ex/0304021
CLEO hep-ex/0305100,
BELLE hep-ex/0307052
hep-ex/0307041 Theorerical Beveren Rupp PRL
91, 012003, (2003) RGM papers Ribeiro,
Z.Phys. C5,27 (1980), Deus Ribeiro, PRD21,1521,
1980. PCAC and QM Bicudo al, PRD 65, 076008
(2002)Bicudo, PRC 67, 035201 (2003).