Moriond 2004P. Bicudo1 Are the (1540), (1860) and D*p(3100) Pentaquarks or Heptaquarks? Rencontres...

Moriond 2004 P. Bicudo 1

Are the (1540), (1860) and D*p(3100) Pentaquarks or

Heptaquarks?

Rencontres de Moriond 2004

Pedro Bicudo

Dep Física IST & CFIF , Lisboa


1. A QM criterion for hard core attraction and repulsion 2. Why the + cannot be a simple uudds or K-N state3. The -K, -N and K- -N systems4. SU(4) flavour: the K-N-K and anti-charmed systems5. Conclusion

Pedro Bicudo

Dep Física IST & CFIF , Lisboa

Hadron 2003 Aschaffengurg

Are the (1540), (1860) and D*p(3100) Pentaquarks or

Heptaquarks?


We study the +(1540) discovered at SPring-8.

We apply Quark Model techniques, that explain with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the short range attraction present in pion-nucleon and pion-pion non-exotic scattering. We find that a K-N repulsion which excludes the + as a K-N s-wave pentaquark.

We explore the + as a heptaquark, equivalent to a borromean boundstate, with positive parity and total isospin I=0. The attraction is provided by the pion-nucleon and pion-kaon interaction.

The other candidates to pentaquarks , observed at NA49, and D*p, observed at H1, are also studied as linear heptaquarks.


The Pentaquark uudds was discovered atLEPS: T. Nakano & al, hep-ex/0301020, Phys.Rev.Lett.91:012002 (2003)

DIANA: V.V. Barmin & al, hep-ex/0304040, Phys.Atom.Nucl.66:1715-1718,( 2003) Yad.Fiz.66:1763-1766, (2003)

After the Jefferson Lab confirmation, it was observed in several different experiences, with a mass of 1540 +-10 MeV and a decay width of 15+-15 MeV.

Recently the ddssu pentaquark --(1860) was observed at,NA49 : C. Alt & al., hep-ex/0310014, Phys.Rev.Lett.92:042003,2004

and the uuddc pentaquark was D*p(3100) observed at,H1 : hep-ex/0403017


1. A Quark Model criterion for repulsion/attraction


1. A Quark Model criterion for repulsion/attraction We use a standard Quark Model Hamiltonian.

The Resonating Group Method 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

q3

q2

q4

r12

r34

rab

meson a

meson b

1. A Quark Model criterion for repulsion/attraction We use a standard Quark Model Hamiltonian.

The Resonating Group Method 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 .


< a b ab|( E - i Ti - i<j Vij - i j Ai j ) (1- P13 )(1+ Pab) | a b ab >

We compute thematrix element of the Hamiltonian...

in an antizymmetrized………….

basis of hadrons……...………………….


< a b ab|( E - i Ti - i<j Vij - i j Ai j ) (1- P13 )(1+ Pab) | a b ab >




This is the standardquark model potential

Vij =i.j V0+i.j Si.Sj Vss +...

Annihilationinteraction


< a b ab|( E - i Ti - i<j Vij - i j Ai j ) (1- P13 )(1+ PAB) | a b ab >




color singlet meson

Relative coordinate

The antisymmetrizer produces the states

color-octet x color-octet, expected in multiquarks

Annihilationinteraction

This is the standardquark model potential

Vij =i.j V0+i.j Si.Sj Vss +...


T1

T3

T2

T4

V12

V34E -

1- 1+

-x

+

Relative energy overlap (E-Ta-Tb) (1-n |

ab>< ab |)


a’

a

b’

b

The exchange overlap

results in aseparable potential:

p

-p

K-p/2

-K+p/2

-K+p/2

K+p/2q

-q

= a’b’ (q)

ab |(p)


V13

1- 1+

x

+

+V14 V23 V24+++

Repulsive, qq hyperfine potential cst. (2/3)(m-mN) |

ab>< ab |


With no exchange the

i.j potential cancels

With exchange only the hyperfine part of thepotential contributes

V13 3

1

= 0

+3

1

4

1

= 0


1+x

+

Attractive qq spin independent potential -cst. (2/3)(2mN-m) |

ab>< ab |


Recent breakthroughin Quark Model + Symmetry Breaking + RGM:

Using the Axial Ward Identity we can show that the annihilationinteraction is identical to the V+- of p Salpeter equation:

< |A| > = m(2/3)(2mN-m)

a’

a

b’

b


We arrive at the criterion for the interaction of ground-state hadrons: - whenever the two interacting hadrons havea common flavour, the repulsion is increased,

- when the two interacting hadrons have a matching quark and antiquark the attraction is enhanced

Exs: ud

us

ud

su

Exchange:repulsion

Veff.(4/3)(m-mN)

Annihilation:attraction

Veff.-(2/3)(2mN-m)


2. Why the + cannot be a simple uudds or K-N state


Applying the criterion to the S=1 I=0 pentaquark, uud ds or ddu us

we find repulsion! All other systems are even more repulsive or unstable. The + is not a uudd+s pentaquark!

In other words, the s=1 s-wave K-N are repelled!Indeed we arrive at the separable K-N potential

VK-N= 2 -(4/3)K.N (mmN) N| >< |(5/4) + (1/3) K.NN


And we get the repulsive K-N exotic s-wave phase shifts, which have been undestood long ago, by Bender & al, Bicudo & Ribeiro and Barnes & Swanson.


Because we checked all our only approximations, say the use a variational method, and neglecting the meson exchange interactions, we estimate that something even more exotic is probably occuring!

Suppose that a q-q pair is added to the system.Then the new system may bind. Moreover the hepatquark had a different parity and therefore it is an independent system (a chiral partner).

Here we propose that the + is in fact a heptaquark with the strong overlap of a K++N, where the is bound by the I=1/2 +K and +N attractive interactions.


2. The K-N, -K, -N and -K-N systems


2. The K-N, -K, -N and -K-N systems

We arrive at the separable potentials for the different 2-body systems,

VK-N= 2 -(4/3)K.N (mmN) N| >< | (5/4) + (1/3) K.NN

V-N= 2 (2mN-m) N.N| >< | 9 N

V-K= 8 (2mN-m) N.K| >< | 27 N

where the and parameters differ from exchange to annihilation channels


Because the potential is separable, it is simple to compute the scattering T matrix. Here we show the 2-body non-relativistic case :

T=| > (1-v g0 )-1 < | ,

g0(E,,)= < | [E-p 2 /(2m ) + i ]-1 | >

The binding energy is determined from the pole position of the T matrix:

We have binding if-4 v > -4

00-1

g0(E,1,1)

E -0.5

-21/v

E


We move on. Because the pion is quite light we start by computing the pion energy in an adiabatic K-N system. Again we use the T matrix, in this case with a relativistic pion.

This is our parameter set, tested in 2-body channels,

Where all numbers are in units of Fm-1

-ex v-th a-th a-exK-N (I=0) 1.65 0.50 3.2 3.2 -0.14 -0.13+-0.04K-N (I=1) 1.65 1.75 3.2 3.2 -0.30 -0.31+-0.01

-N (I=1/2) 0.61 -0.73 3.2 11.4 0.25 0.246+-0.007-N (I=3/2) 0.61 0.36 3.2 3.2 -0.05 -0.127+-0.006-K (I=1/2) 0.55 -0.97 3.2 10.3 0.35 0.27+-0.08-K (I=3/2) 0.55 0.49 3.2 3.2 -0.06 -0.13+-0.06


The only favorable flavor combination is,

Total I=1I=0

I=1/2 I=1/2

K I=1 N

I=1/2 I=1/2


Again we use the T matrix, in this case with a relativistic pion under the action of two separable

potentials centered in two different points.

a|

N

-a|

K

z

x

y

0

rNrK

rK


We get for the pion energy as a function of the K-N distance,

Indeed we get quite a bound pion, but it only binds at very short K-N distances.


However when we remove the adiabaticity, by allowing the K and N to move in the pion field, we find that the pion attraction overcomes the K-N repulsion but not yet thethe K-N kinetic energy.

We are planning to include other relevant effects to the +K+N system, starting by the 3-body +K+N interaction

and the coupling to the K+N p-wave channel.


4. SU(4) flavour: the K-N-K and anti-charmed systems


Extending the pentaquark and the molecular heptaquark picture to the full SU(3) anti-decuplet we arrive at the following picture,

-The --(1860) cannot be a ddssu pentaquark because this suffers from repulsion.

- Adding a q-q pair we arrive at a I=1/2 K-N-K where the the K-N system has isospin I=1,an attractive system. We find that the K-N-K molecule is bound, although we are not yet able to arrive at a binding energy of -60 MeV.

- Then the I=1/2 elements of the exotic anti-decuplet are K-K-N molecules.

- Only the I=1 elements are pentaquarks, or equivalently overlapping K-N systems


This figure summarizes the anti-decuplet spectrum


In what concerns anti-charmed pentaquarks like the very recently observed D*p, or anti-bottomed ones, this extends the anti-decuplet to 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, and we are researching the possible molecular heptaquarks that may exist in these systems.


5. Conclusion

- We conclude that the (1540), (1860) and D*p(3100) hadrons very recently discovered cannot really be s-wave pentaquarks.

- We also find that they may be a heptaquark states, with two repelled clusters K and N clusters bound third cluster.

- More effects need to be included, say exact Fadeev eq., the K-N p-wave coupled channel, and medium range interactions.

- This is a difficult subject with the interplay of many effects. The theoretical models should not just explain the pentaquarks, they should be more comprehensive. They should at least explain all the ground-state hadrons and their interactions.


This work:The Theta+ (1540) as a heptaquark with the overlap of a pion, a kaon and a nucleonP.Bicudo, G. M. Marques Phys. Rev. D69 rapid communication (2004) 011503 , hep-ph/0308073

The family of strange multiquarks related to the Ds(2317) and Ds(2457)P. Bicudo, hep-ph/0401106

The anti-decuplet candidate Xi--(1862) as a heptaquark with the overlap of two anti-kaons and a nucleon P. Bicudo, hep-ph/0403146

+ Other tests of this idea:On the possible nature of the Theta+ as a K pi N bound state F. J. Llanes-Estrada, E. Oset and V. Mateu, nucl-th/0311020.

+ Chiral doubling: M.A. Nowak, M. Rho and I. Zahed, Phys. Rev.D 48, 4370 (1993) hep-ph/9209272.

Some references:

Moriond 2004P. Bicudo1 Are the (1540), (1860) and D*p(3100) Pentaquarks or Heptaquarks? Rencontres...

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