Chiral Constituent Quark Model study of LL Interaction

1. Chiral Constituent Quark Model study of LL Interaction Teresa Fernández Caramés Department of Theoretical Physics Universitat de Valencia Prague, October 2006

2. Motivation. • To achieve a good description of hypernuclei, it is necessary to have a consistent description of LL and NL interactions. • An (1S) LL state has the same quantum numbers as the H dibaryon. This dibaryon has been predicted almost 30 years ago with a mass slightly below the LL threshold, although it has not yet been found experimentally. Experimental Status • There are no data of LL scattering. • Very few data available on Lp scattering.

3. Some information can be extracted from hypernuclei binding energy. These data provide conditions on the mass of H: • Many experimental searches of the H dibaryon have been performed, always with negative results. Theoretical Status Different approaches to LLand NL potentials: Baryonic Quark Quark based potentials predict in general a repulsive core for LL interaction.

4. Regarding the H dibaryon, there is a wide range of predictions. Obtained results cover almost any possibility. Conclusion: there is no general conclusion at all. Objectives • To obtain LLandNLinteraction potentials by using a constituent quark model whose parameters are already fixed from other sectors, so that it is fully predictive. • To study what can we infer from this model about the H dibaryon.

5. NN, ND, DD and NN* interactions. • Non-strange baryon spectrum. • Two and three body bound states. • Deuteron, triton binding energies. Advantages: • Universality: Vertex • are at Quark level. 2.Antisymmetry effects. The Chiral Constituent Quark Model (cCQM) Semiphenomenological model: based on QCD and phenomenology Non relativistic potential model Successfully described: SU(2)xSU(2) • Meson spectra SU(3)xSU(3)

6. The Born-Oppenheimer approximation What is it? It is a very simple approximation that assumes that the quark movement is much faster than the relative movement between the baryons. We can integrate out quark degrees of freedom. Potential only depends on R Can we employ it here? Yes, because in spite of being much simpler, results obtained by RGM are very similar. We need two things: • Interaction matrix element. • Two baryon wave function.

7. One baryon wave functions: Two baryon wave function: LL antisymmetrizer operator: One and two baryon wave functions.

8. Results: ( ) LL Interaction • s exchange gives strong attraction. • LL potential is attractive at all distances. • The short range behaviour depends on the interplay between gluon and sigma exchanges.

9. keep the same character as in LL. , y Results: ( ) NL Interaction. • Repulsive contributions are now bigger. • Slightly repulsive at short distances. • Different antisymmetrizer operators. • Coincidence for R > 1.5 fm (no quark antisym.). • Vs is always the same.

10. Bound states Poles of T matrix E0 = - 1.1MeV Bound states: Fredholm determinant. Lippman-Schwinger equation:

11. Conclusions. • LL and NL interaction potentials have been computed in the framework of a chiral constituent quark model, where all the parameters were previously fixed. • The LL interaction thus obtained is attractive at all distances. • The short range character of any of these interactions highly depends on the interplay between Vs on the one hand, and Vp + VOGE on the other hand. Therefore it becomes attractive in LL, slightly repulsive in NL and repulsive in NN. • A LL bound state has been found on the channel1S , with a very small binding energy. This fact could explain the experimental absence of the H dibaryon.