Chiral Constituent Quark Model study of Interaction

Teresa Fernández Caramés

Department of Theoretical Physics

Universitat de Valencia

Prague, October 2006

Motivation.✰ To achieve a good description of hypernuclei, it is necessary to have a consistent description of and Ninteractions.

✰ An (1S) state has the same quantum numbers as the H dibaryon.

This dibaryon has been predicted almost 30 years ago with a mass slightlybelow the threshold, although it has not yet been found experimentally.

Experimental Status• There are no data of scattering.

• Very few data available on p scattering.

• 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 and Npotentials:

Baryonic Quark

Quark based potentials predict in general a repulsive core for interaction

Objectives✰ To obtain andN interaction 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.

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.

The Chiral Constituent Quark Model (CQM)

Semiphenomenological model: based on QCD and phenomenology

SU(2)xSU(2)

• NN, N,and NN* interactions.• Non-strange baryon spectrum.• Two and three body bound states.• Deuteron, triton binding energies.

• Meson spectra SU(3)xSU(3)

Advantages:

1. Universality: Vertex are at Quark level.

2. Antisymmetry effects.

Successfully described:

Non relativistic potential model

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.

One and two baryon wave functions.

Two baryon wave function:

antisymmetrizer operator:

One baryon wave functions:

Results: ( ) nteraction1S

exchange gives strong attraction.

potential is attractive at all distances.

The short range behaviour depends on the interplay between gluon and sigma exchanges.

Results: ( ) nteraction

1S

V OGEV V, y keep the same character as in

Repulsive contributions are now bigger.

Slightly repulsive at short distances.

Coincidence for R > 1.5 fm (no quark antisym.).

Different antisymmetrizer operators.

V is always the same.

Bound states: Fredholm determinant.

Lippman-Schwinger equation:

Bound states Poles of T matrix

E0 = - 1.1MeV

Conclusions.

and interaction potentials have been computed in the framework of a chiral constituent quark model, where all the parameters were previously fixed.

The interaction thus obtained is attractive at all distances.

The short range character of any of these interactions highly depends on the interplay between V on the one hand, and V + VOGE on the other hand. Therefore it becomes attractive in , slightly repulsive in and repulsive in NN.

A bound state has been found on the channel 1S , with a very small binding energy. This fact could explain the experimental absence of the H dibaryon.