BLED WORKSHOPS
IN PHYSICS
VOL. 1, NO. 1
Proceedins of the Mini-Workshop
Few-Quark Problems (p. 34)
Bled, Slovenia, July 8-15, 2000
Baryon Structure in the Low Energy Regime of QCD
Leonid Ya. Glozman?
Institute for Theoretical Physics, University of Graz, Universitätsplatz 5, A-8010 Graz,
Austria
I review the key problem of light and strange baryon spectroscopy, which sug-
gests a clue for our understanding of underlying dynamics. Then I discuss the
spontaneous breaking of chiral symmetry in QCD. In the region of spontaneously
broken chiral symmetry, where the Goldstone boson degree of freedom is impor-
tant, the structure of the elementary excitation of the QCD vacuum can be approx-
imately reproduced by absorption of the scalar interaction between bare (current)
quarks into the mass of the quasi particles - i.e. constituent quarks. This implies
that in the low-energy regime the proper chiral dynamics is due to the coupling of
Goldstone bosons and constituent quarks and that the nucleon should be viewed
as a system of confined constituent quarks that interact via the Goldstone bo-
son exchange (GBE) [1]. The GBE interaction contains both the ultraviolet (short
range) part, which is independent of pion mass, and the infrared (Yukawa) part.
The latter one is important for the long-range nuclear force, but it does not pro-
duce any significant effect in baryons because of their small matter radius. The
short-range part of the GBE interaction causes a flavor-spin dependent force be-
tween quarks and has a range -1 . While the infrared (Yukawa) part of the in-
teraction vanishes in the chiral limt, the ultraviolet one - does not [2]. This means
that the short-range part of the GBE interaction is “more fundamental” than its
Yukawa part. This short-range part of the GBE interaction stems from the 
5
structure of the vertex and hence is demanded by the Lorentz invariance. At the
microscopical level this short range interaction comes from the t-channel itera-
tions of that bare gluonic interaction between quarks that is responsible for chiral
symmetry breaking [3]. This is a typical antiscreening behavior; the interaction is
represented by a bare gluonic vertex at large momenta, but it blows up at small
momenta in the GBE channel due to the (Landau) pole that occures at q2 = 0.
I show how this explicitly flavor-dependent short-range part of GBE interaction,
when combined with the SU(6) symmetry (that is demanded by largeN
 limit in
QCD), solves the key problem of baryon spectroscopy and present baryon spectra
obtained in a simple analytical calculation [1] as well as in covariant three-body
calculations [4]. Finally I show recent lattice results [5–8] and comment on their
connection with the present physical picture.
? E-mail: lyg@physik.kfunigraz.ac.at
Baryon Structure in the Low Energy Regime of QCD 35
References
1. L. Ya. Glozman and D. O. Riska, Phys. Rep. 268, 263 (1996).
2. L. Ya. Glozman, Phys. Lett. B459 589 (1999)
3. L. Ya. Glozman and K. Varga, Phys. Rev.D61, 074008 (2000)
4. L. Ya. Glozman, W. Plessas, K. Varga, and R. Wagenbrunn, Phys. Rev. D58 094030
(1998)
5. K. F. Liu et al, Phys. Rev.D59 112001 (1999)
6. S. Sasaki, hep-ph/0004252
7. S. Aoki et al, Phys. Rev. Lett. 82, 4592 (1999)
8. J. I. Skullerud and A. G. Williams, hep-lat/0007028