Enrique Ruiz Arriola, Granada

ABSTRACT

Chiral perturbation theory provides a systematic scheme to handle low energy QCD dynamics, but it is unable to describe the physically observed resonances due to the lack of exact unitarization. Unitarization can be implemented in many ways, and inspired in the Bethe-Salpeter It is shown how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the $\Delta$ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six $S$ and $P$ wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis. The extension and results of these ideas to the S-wave coupled channel pi-N problem and the N^* resonance is also discussed.

Michael Birse, Manchester

Wojciech Broniowski, Krakow

We analyze the light-flavor particle mass spectra and show that the Hagedorn hypothesis of the exponential growth of the number of states is surprisingly well satisfied in the mass region up to about 1.8 GeV. However, the Hagedorn temperature for baryons is significantly lower than for mesons. The effect can be explained in a natural way within dual string models.

Thomas Cohen, Maryland

Manuel Fiolhais, Coimbra

The following topics are the most interesting for me:
.The structure of constituent quarks and of baryons
.The pionic degree-of-freedom in effective interactions, in decaying states, and in electromagnetic matrix elements
.Comparison between different sigma models and the NJL model
.Projection of linear and angular momentum
.The role of confinement for the low-lying baryon spectrum

Yoshikazu Fujiwara, Kyoto

Gzipped PS abstract with figures (51k)

We have recently achieved a very accurate description of the nucleon-nucleon (NN) and the hyperon-nucleon (YN) interactions, by using the (3q)-(3q) RGM augmented by the effective meson-exchange potentials (EMEP) acting between quarks. [1] The new model incorporates full meson exchanges including vector mesons, and the momentum-dependent term of the scalar-meson exchange central component plays an important role to make realistic the high-momentum behavior of the single-particle potentials in the nuclear medium. The coupled-channel RGM equation is formulated in the momentum representation. This formulation, which we call Lippmann-Schwinger RGM (LS-RGM) [2], can be straightforwardly extended to the Bethe-Goldstone equation (G-matrix equation), and is now used to extract effective baryon-baryon interactions and single-particle potentials directly from the quark exchange kernel. [3, 4] The same technique can also be used for solving strangeness few-body systems, such as the hypertriton, in the Faddeev and variational approaches. In view of this progress, I would like to discuss the following problems (and many other questions) at the workshop:
1. What is the exact meaning of the G-matrix solutions directly derived from the quark-exchange kernel ?
2. What is the realistic \Lambda N interaction compatible with the very scarce YN scattering data and the known spectroscopic information on the s-shell \Lambda hypernuclei ? Are the \Lambda p and \Lambda n interactions different ? If so, what is the microscopic mechanism of the charge symmetry breaking ?
3. Is the \Sigma single-particle potential repulsive ? What is the isospin dependence of the \Sigma single-particle potential in the nuclear medium ?
4. Is the single-particle spin-orbit interaction of the \Lambda particle really small ? qWhere can we see the effect of the antisymmetric LS force (LS^- force), which is characteristic to the YN interaction ?
References
[1] Y. Fujiwara, C. Nakamoto and Y. Suzuki, Phys. Rev. Lett. 76 (1996) 2242; Phys. Rev. C54 (1996) 2180.
[2] Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki, KUNS-1626, nucl-th/9912060, Prog. Theor. Phys. 103, No. 4 (2000).
[3] M. Kohno, Y. Fujiwara, T. Fujita, C. Nakamoto and Y. Suzuki, KUNS-1625, nucl-th/9912059, Nucl. Phys. A670 (2000), 319 - 322.
[4] Y. Fujiwara, M. Kohno, T. Fujita, C. Nakamoto and Y. Suzuki, KUNS-1624, nucl-th/9912047, to be published in Nucl. Phys. A (2000).

Leonid Glozman, Graz

The typical momentum of valence current quarks in light baryons is well below the chiral symmetry breaking scale, implying that the low-energy properties of light baryons should be formed by the nonperturbative QCD dynamics, that is responsible for chiral symmetry breaking and confinement. The t-channel iterations of the QCD gluodynamics, which triggers the breaking of chiral symmetry, necessarily lead to the t-channel poles (antiscreening) in the quark-quark system which represent effective Goldstone boson exchange (meson exchange) interaction between valence quarks in baryons. Thus to understand the structure of the nucleon in the low-energy regime it is convenient to use an effective theory, that relies on constituent quarks with dynamical mass (quasiparticles, which are unambiguously implied by dynamical chiral symmetry breaking in the QCD vacuum), chiral (meson) fields and effective confining interaction between the quasiparticles. Such an approach provides a successful explanation of many low-energy observables of baryons and their interactions. Relations with the recent lattice data and large N_c expansion is also discussed.

Dubravko Klabucar, Zagreb

I am interested in comparative discussions of various quark models, and how one can physically meaningfully discriminate between them. The example I would provide, is the presently experimentally interesting form factor for the anomalous process gamma --> pi^+ pi^0 pi^-. It is calculated in two different constituent quark approaches as the quark ``box"-amplitude. Similarities between these two approaches are striking, which is to be expected because both are, after all, constituent approaches. Nevertheless, there are also differences, and hopefully they will, in conjunction with the expected data, provide clues which refinements would lead to still more realistic constituent quark description of hadronic physics.
The first approach is the simple quark loop model, where the intermediate fermion loop is the one of simple constituent quarks with the pseudoscalar coupling to pions. This also corresponds to the form factor, in the lowest order in pion interactions, of the sigma-model and of the chiral quark model. We give the analytic expression for the form factor in terms of an expansion in the pion momenta up to the order O(p^8) relative to the soft point result, and also perform its exact numerical evaluation. [See B. Bistrovic and D. Klabucar, Phys. Rev. D 61 (2000) 033006.]
The emphasis, however, is on the calculation in the coupled Schwinger-Dyson and Bethe-Salpeter approach, which amounts to a modern constituent quark model which is consistent both with the chiral symmetry constraints in the low-energy domain and with the perturbative QCD in the high-energy domain. [See, e.g., D. Kekez, B. Bistrovic and D. Klabucar, Int. J. Mod. Phys. A14 (1999) 161-194.] In this approach, dressed quarks in the fermion loop do not have the simple-minded constant constituent mass, but the momentum-dependent mass function following from the Schwinger-Dyson solution for the dressed quark propagator. It is in turn consistent with the solution for the bound-state pion Bethe-Salpeter amplitude, and then, in this approach, the light pseudoscalar mesons are simultaneously the quark-antiquark bound states and the (quasi) Goldstone bosons of dynamical chiral symmetry breaking. Thanks to this, and also to carefully preserving the vector Ward-Takahashi identity in the quark-photon vertex, the both fundamental anomalous amplitudes T(0,0)=e^2 /(4 pi^2 f_pi) and F(0,0,0)=e /(4 pi^2 f_pi^3) for respective decays pi^0 --> gamma gamma and gamma --> pi^+ pi^0 pi^- , are evaluated analytically and exactly in the chiral limit and the soft limit. Note that reproducing these results even only roughly, let alone analytically, is otherwise very problematic for bound-state approaches. [See, e.g., D. Kekez, B. Bistrovic and D. Klabucar, Int. J. Mod. Phys. A 14 (1999) 161-194.]
The form factors for finite transferred momenta obtained in both of these approaches, are compared with the ones predicted by the vector meson dominance and chiral perturbation theory, as well as with the scarce already available data. [See B. Bistrovic and D. Klabucar, Phys. Lett B 478 (2000) 127.]
While new measurements of the anomalous process gamma pi^+ --> pi^+ pi^0 are presently underway at CEBAF, the above predictions of the anomalous $\gamma \to 3\pi$ form factor are of special relevance also for the COMPASS experiment at CERN, judging by the e-print hep-ex/9903017 (by Moinester, Steiner and Prakhov).

Michio Kohno, Kitakyushu

Vladimir Kukulin, Moscow

List of open problems which I would like to discuss at the workshop:
--Experimental evidencies for dibaryons (both narrow and broad ). Here we can present our new arguments in favor of existence just for the broad dibaryons (with width around 100 MeV) only,which have been established experimentally in NN phase shift analyses.
--Chiral symmetry restoration in high-density nuclear and quark matter.The possible signals for on-going process of phase transition.
--Two-pion production in p-p collisions at 1-2 GeV and ABC-puzzle. Here we can present our arguments to strong relationship between our new driving mechanism (of nuclear force) and the enhancement of two-pi production at p-p collisions at E(p) around 1.2-1.5 GeV.
--I would like to work just on this problem during the workshop.
--Reliability of the recent NN-phase shift analysis at E>1 GeV.(Maybe somebody can give some review about this?).

Judith McGovern, Manchester

Steven Moszkowski, Los Angeles

A few suggestions:
1. THE EFFECTIVE INTERACTION BETWEEN CONSTITUENT QUARKS
It would be nice to have discussions about the relative merits of flavor dependent vs color dependent interactions between quarks. I happen to have some bias in favor of the former, i.e. Goldstone Boson exchange, and according to your first circular some of the participants have worked on GBE themselves. On the other hand, at a recent meeting (APS Long Beach) one of the believers in gluon exchange explained to me his quite passionate views on the subject. This problem has not been settled and I think it would be good to see where we stand at this time.
2. BARYON-BARYON AND MESON-MESON EFFECTIVE INTERACTIONS
There are several areas of interest here:
(i) The application of the large Nc approximation, according to which, for example, the meson-meson interaction is of order 1/Nc.
(ii) The origin of the repulsive core in the NN interaction: vector meson exchange or quark substructure.
(iii) Possible short range non-locality, such as is required by the Moscow potential.
3. DIMESONS, DIBARYONS, PENTAQUARKS
These are of interest for several reasons: First of all, the Goldstone boson and gluon exchange models give different predictions for some of the above. Also, since it requires only 300 MeV to excite a nucleon, one would expect some dibaryon states to exist. I think it would be nice to have some discussion on the current state of these.
4. COMPARISON OF DIFFERENT SIGMA MODELS AND THE NJL MODEL
In addition, perhaps there could be some discussion of the implications of the instanton model. Also, in this connection, I would like to make a short presentation of recent work done with Joao Providencia. The equation of state for quark matter calculated with NJL has a serious defect, namely the effective mass at saturation density vanishes. However, Providencia suggested adding to the well-known scalar coupling in NJL a density dependent term. With this generalized NJL model, it is possible to obtain a reasonable equation of state, at least at low density.

Zoltan Papp, Debrecen

Willibald Plessas, Graz

The chiral constituent quark model based on Goldstone-boson-exchange as the effective hyperfine interaction between constituent quarks has performed well for the description of the spectroscopy of all light and strange baryons [1]. Originally the model was constructed with the spin-spin component of the pseudoscalar exchange only [2]. Recently it has been extended to include all force components (central, tensor, spin-orbit) and furthermore vector and scalar exchanges [3,4]. Also, rigorous semirelativistic solutions of the three-quark problem have been provided [5]. We shall discuss the present status of the development of the Goldstone-boson-exchange chiral quark model.
The model, in different variants, has already been applied (by several groups) to various problems beyond baryon spectroscopy. One has thus obtained valuable insight into its performance more generally in low- and intermediate-energy hadron processes. We shall summarize the corresponding results and discuss them in comparison to other constituent quark models and/or (effective) approaches to low-energy QCD.
[1] L.Ya. Glozman, Z. Papp, W. Plessas, K. Varga, and R.F. Wagenbrunn: Effective Q-Q interactions in constituent quark models. Phys. Rev. C 57, 3406 (1998).
[2] L.Ya. Glozman, W. Plessas, K. Varga, and R.F. Wagenbrunn: Unified description of light- and strange-baryon spectra. Phys. Rev D 58, 094030 (1998).
[3] R.F. Wagenbrunn, L.Ya. Glozman, W. Plessas, and K. Varga: Goldstone-boson-exchange dynamics in the constituent-quark model for baryons. Few-Body Systems Suppl. 10, 387 (1999).
[4] R.F. Wagenbrunn, L.Ya. Glozman, W. Plessas, and K. Varga: Semirelativistic constituent-quark model with Goldstone-boson-exchange hyperfine interactions. Few-Body Systems Suppl. 11, 25 (1999).
[5] Z. Papp, A. Krassnigg, and W. Plessas: Faddeev approach to confined three-quark problems. Preprint nucl-th/0002006.

Jean Marc Richard, Grenoble

Georges Ripka, Saclay

The quantum fluctuations of the quark condensate are studied in a Nambu Jona-Lasinio model. Two Lorenz invariant regularizations are considered: a sharp 4-momentum cut-off and a soft gaussian regulator. The quantum fluctuations of the quark condensate are found to be large although chiral symmetry is not restored. Instabilities of the ground state appear when the system is probed by a source term proportional to the squared quark condensate. The instabilities are traced to unphysical poles introduced by the regulator and their effect is greatly enhanced when a sharp cut-off is used.

Floarea Stancu, Liege

We study the nucleon-nucleon interaction in the chiral constituent quark model of Refs. [1,2] by using the resonating group method, convenient for treating the interaction between composite particles. The calculated phase shifts for the ^3S_1 and ^1S_0 channels show the presence of a strong repulsive core due to the combined effect of the quark interchange and the spin-flavour structure of the effective quark-quark interaction. Such a symmetry structure stems from the pseudoscalar meson exchange between the quarks and is a consequence of the spontaneus breaking of the chiral symmetry. We perform single and coupled channel calculations and show the role of coupling of the \Delta\Delta and hidden color CC channels on the behaviour of the phase shifts. The addition of a sigma-exchange quark-quark interaction brings the ^1S_0 phase shift closer to the experimental data. We intend to include a tensor quark-quark interaction to improve the description of the ^3S_1 phase shift [3].
It would be interesting to discuss to what extent the NN data can distinguish between various quark models. In this spirit results obtained for other hadron-hadron systems, including exotics [4], should also be considered.
1 L.Ya.~Glozman and D.O.~Riska, Phys. Rep. 268, 263 (1996)
2 L.Ya. Glozman, Z. Papp, W. Plessas, K. Varga and R. Wagenbrunn, Nucl.Phys. A623 (1997) 90c
3 D. Bartz and Fl. Stancu, in preparation
4 Fl.~Stancu, Phys. Rev. D58, 111501 (1998); Fl.~Stancu, Hadron Physics "Effective Theories of Low Energy OCD", eds. A. H. Blinn, B. Hiller, M. C. Ruivo, C. A. Sousa and E. van Beveren, American Institute of Physics, Melville, New York 2000, p.83

Bojan Golli, Ljubljana

Mitja Rosina, Ljubljana

1. It has been hypothesized that the binding energy of heavy dimesons might discriminate between constituent quark models using gluon-exchange (OGE) or meson-exchange (=Goldstone boson exchange, OGBE) spin-spin interaction, or both. It was expected that models with meson-exchange interaction might bind B + B* and D + D* much more strongly than models with gluon-exchange interaction alone. The additional meson-exchange interaction does not affect separate ligh-heavy mesons , it would give, however, an additional strong attractive potential energy when in the dimeson the two light quarks meet in I+S=0 state.
The argument is wrong. The two light quarks in the dimesons feel the heavy antidiquark similarly as they feel the heavy quark in Lambda_b and Lambda_c baryons and have therefore similar wavefunction and energy contribution in all these cases. Any interaction (OGE, OGBE or combination of both) which fits Lambda_b and Lambda_c will give similar results for dimeson binding energy and one cannot discriminate. Calculations which simply added OGBE to OGE (which was well fitted to the heavy baryons) gave strong binding of dimesons, but were irrelevant (since they would overbind heavy baryons too). Much still has to be understood and remains open to criticism.
The binding might depend on the choice of the b and c quark masses. For rather heavy masses used by the Grenoble group our phenomenological estimate gives similar result as theirs: BB* bound by about 100 Mev and DD* unbound. We are exploring what happens if we use lighter quark masses. What are actually the "correct" c and b constituent quark masses?
I shall try to review which features of dimesons and dibaryons could discriminate between meson-exchange and gluon-exchange models and betwen different choices of masses.