Download The Chiral Constituent Quark Model (cCQM)

Chiral Constituent Quark Model study of
LL 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 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.
• 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 LL and NL potentials:
Baryonic
Quark
Quark based potentials predict in general a repulsive
core for LL interaction.
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 LL and NL 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.
The Chiral Constituent Quark Model (cCQM)
Semiphenomenological model: based on QCD and phenomenology
Non relativistic potential model
Successfully described:
• NN, ND, DD and NN* interactions.
• Non-strange baryon spectrum.
• Two and three body bound states.
• Deuteron, triton binding energies.
• Meson spectra
Advantages:
1.
SU(2)xSU(2)
2.
SU(3)xSU(3)
Universality: Vertex
are at Quark level.
Antisymmetry effects.
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.
One baryon wave functions:
Two baryon wave function:
LL antisymmetrizer operator:
Results: (1S ) 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.
Results: ( S ) NL Interaction.
1
 Vs , VOGE y V keep the same character as in LL.
 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.
Bound states: Fredholm determinant.
Lippman-Schwinger equation:
Bound states
Poles of T matrix
E0 = - 1.1 MeV
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
V + 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 channel 1S , with a
very small binding energy. This fact could explain the
experimental absence of the H dibaryon.