Moriond 2004P. Bicudo1 Are the  (1540),  (1860) and D*p(3100) Pentaquarks or Heptaquarks? Rencontres de Moriond 2004 Pedro Bicudo Dep Física IST & CFIF, Lisboa

Moriond 2004P. Bicudo2 1. A QM criterion for hard core attraction and repulsion 2. Why the  + cannot be a simple uudds or K-N state 3. The  -K,  -N and K-  -N systems 4. SU(4) flavour: the K-N-K and anti-charmed systems 5. Conclusion Pedro Bicudo Dep Física IST & CFIF, Lisboa Hadron 2003 Aschaffengurg Are the  (1540),  (1860) and D*p(3100) Pentaquarks or Heptaquarks?

Moriond 2004P. Bicudo3 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.

Moriond 2004P. Bicudo4 The Pentaquark uudds was discovered at LEPS: T. Nakano & al, hep-ex/ , Phys.Rev.Lett.91: (2003) DIANA: V.V. Barmin & al, hep-ex/ , Phys.Atom.Nucl.66: ,( 2003) Yad.Fiz.66: , (2003) After the Jefferson Lab confirmation, it was observed in several different experiences, with a mass of MeV and a decay width of MeV. Recently the ddssu pentaquark  -- (1860) was observed at, NA49 : C. Alt & al., hep-ex/ , Phys.Rev.Lett.92:042003,2004 and the uuddc pentaquark was D*p(3100) observed at, H1 : hep-ex/

Moriond 2004P. Bicudo5 1. A Quark Model criterion for repulsion/attraction

Moriond 2004P. Bicudo6 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.

Moriond 2004P. Bicudo7 q1q1 q3q3 q2q2 q4q4 r 12 r 34 r ab 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.

Moriond 2004P. Bicudo8 <  a  b  ab | ( E -  i T i -  i<j V ij -  i j A i j ) (1- P 13 )(1+ P ab ) |  a  b  ab > We compute the matrix element of the Hamiltonian... in an antizymmetrized…………. basis of hadrons……...………………….

Moriond 2004P. Bicudo9 <  a  b  ab | ( E -  i T i -  i<j V ij -  i j A i j ) (1- P 13 )(1+ P ab ) |  a  b  ab > We compute the matrix element of the Hamiltonian... in an antizymmetrized…………. basis of hadrons……...…………………. This is the standard quark model potential V ij = i. j V 0 + i. j S i.S j V ss +... Annihilation interaction

Moriond 2004P. Bicudo10 <  a  b  ab | ( E -  i T i -  i<j V ij -  i j A i j ) (1- P 13 )(1+ P AB ) |  a  b  ab > We compute the matrix element of the Hamiltonian... in an antizymmetrized…………. basis of hadrons……...…………………. color singlet meson Relative coordinate The antisymmetrizer produces the states color-octet x color-octet, expected in multiquarks Annihilation interaction This is the standard quark model potential V ij = i. j V 0 + i. j S i.S j V ss +...

Moriond 2004P. Bicudo11 T1T1 T3T3 T2T2 T4T4 V 12 V 34 E x + Relative energy overlap   (E-Ta-Tb) (1-n |   ab ><   ab |)

Moriond 2004P. Bicudo12    a’ aa    b’ bb The exchange overlap results in a separable potential: p -p K-p/2 -K+p/2 K+p/2 q -q  =  a’b’  (q)   ab |(p)

Moriond 2004P. Bicudo13 V x + + V 14 V 23 V Repulsive,  qq hyperfine potential   cst. (2/3)(m  -mN) |   ab ><   ab |

Moriond 2004P. Bicudo14 With no exchange the i. j potential cancels With exchange only the hyperfine part of the potential contributes V =

Moriond 2004P. Bicudo15 1+ x + Attractive  qq spin independent potential  -cst. (2/3)(2mN-m  ) |   ab ><   ab |

Moriond 2004P. Bicudo16 Recent breakthrough in Quark Model +  Symmetry Breaking + RGM: Using the Axial Ward Identity we can show that the annihilation interaction is identical to the V+- of p Salpeter equation: = m  (2/3)(2mN-m  )     a’ aa   b’ bb

Moriond 2004P. Bicudo17 We arrive at the criterion for the interaction of ground-state hadrons: - 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: udusudus udsuudsu Exchange: repulsion V eff.  (4/3)(m  -mN) Annihilation: attraction V eff.  -(2/3)(2mN-m  )

Moriond 2004P. Bicudo18 2. Why the  + cannot be a simple uudds or K-N state

Moriond 2004P. Bicudo19 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  V K-N = 2 -(4/3)  K.  N (m  mN) N   |   ><   | (5/4) + (1/3)  K.  N  N  

Moriond 2004P. Bicudo20 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.

Moriond 2004P. Bicudo21 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.

Moriond 2004P. Bicudo22 2. The K-N,  -K,  -N and  -K-N systems

Moriond 2004P. Bicudo23 2. The K-N,  -K,  -N and  -K-N systems We arrive at the separable potentials for the different 2-body systems,  V K-N = 2 -(4/3)  K.  N (m  mN) N   |   ><   | (5/4) + (1/3)  K.  N  N    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

Moriond 2004P. Bicudo24 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 g 0 ) -1 <   |,  g 0 (E, ,  )= The binding energy is determined from the pole position of the T matrix: We have binding if -4  v >   g 0 (E,1,1) E /v E

Moriond 2004P. Bicudo25 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

Moriond 2004P. Bicudo26 The only favorable flavor combination is, Total I=1 I=0  I=1/2 I=1/2 K I=1 N I=1/2

Moriond 2004P. Bicudo27 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|Na|N -a | K z x y 0  rNrN rKrK rKrK

Moriond 2004P. Bicudo28 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.

Moriond 2004P. Bicudo29 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 the the 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.

Moriond 2004P. Bicudo30 4. SU(4) flavour: the K-N-K and anti-charmed systems

Moriond 2004P. Bicudo31 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

Moriond 2004P. Bicudo32 This figure summarizes the anti-decuplet spectrum

Moriond 2004P. Bicudo33 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.

Moriond 2004P. Bicudo34 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.

Moriond 2004P. Bicudo35 This work: The Theta+ (1540) as a heptaquark with the overlap of a pion, a kaon and a nucleon P.Bicudo, G. M. Marques Phys. Rev. D69 rapid communication (2004) , hep-ph/ The family of strange multiquarks related to the Ds(2317) and Ds(2457) P. Bicudo, hep-ph/ The anti-decuplet candidate Xi--(1862) as a heptaquark with the overlap of two anti- kaons and a nucleon P. Bicudo, hep-ph/ 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/ Chiral doubling: M.A. Nowak, M. Rho and I. Zahed, Phys. Rev.D 48, 4370 (1993) hep-ph/ Some references: