Improvement of the Theta+ width estimation method on the Light Cone

Recently, Diakonov and Petrov have suggested a formalism in the Relativistic Mean Field Approximation allowing one to derive the 3-, 5-, 7-,... quark wavefunctions for the octet, decuplet and antidecuplet. They have used this formalism and many strong approximations in order to estimate the exotic Theta+ width. The latter has been estimated to ~4 MeV. Besides they obtained that the 5-quark component of the nucleon is about 50% of its 3-quark component meaning that relativistic effects are not small. We have improved the technique by taking into account some relativistic corrections and considering the previously neglected 5-quark exchange diagrams. We also have computed all nucleon axial charges. It turns out that exchange diagrams affect very little Diakonov's and Petrov's results while relativistic corrections reduce the Theta+ width to ~2 MeV and the 5- to 3-quark component of the nucleon ratio to 30%.Comment: 28 pages, 15 figures; typo corrected and few comments adde

Mixed quark-gluon condensate from instantons

We calculate the vacuum expectation value of the dimension-5 "mixed" quark-gluon operator, $O_\sigma = \bar\psi (\lambda^a /2) \sigma_{\mu\nu} \psi F_{\mu\nu}^a$, in the instanton vacuum. Within the $1/N_c$--expansion the QCD operator is replaced by an effective many-fermion operator, which is averaged over the effective theory of massive quarks derived from instantons. We find $m_0^2 \equiv \langle O_\sigma \rangle / \langle \bar\psi\psi \rangle \approx 4 \bar\rho^{-2} = 1.4 GeV^2$, somewhat larger than the estimate from QCD sum rules for the nucleon.Comment: 10 p, LaTeX, 1 figure included using eps

Justifying the exotic Theta+ pentaquark

The existence of a light S=+1 baryon resonance follows from Quantum Field Theory applied to baryons. This is illustrated in the Skyrme model (where Theta+ exists but is too strong) and in a new mean field approach where Theta+ arises as a consequence of three known resonances: Lambda(1405), N(1440) and N(1535).Comment: 3 p., contribution to the PANIC-08 proceeding

Chiral symmetry and pentaquarks

Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.Comment: Combined talks at Electron-Nucleus Scattering (Elba, June 20-25, 2004) and Pentaquarks-04 (Osaka, July 20-23, 2004) workshops. 18 p., 11 fig

Foundations of the Constituent Quark Model

'Constituent quarks' means massive quarks, in contrast to the nearly massless u,d,s quarks of the QCD lagrangian. The dynamical or constituent masses appear owing to the spontaneous chiral symmetry breaking in QCD. A realistic mechanism of the chiral symmetry breaking is provided by instantons. Therefore, I review the present status of the QCD instanton vacuum, emphasizing the mechanism of chiral symmetry breaking and of the generation of the constitutent quark mass. I end up with the Nambu--Jona-Lasinio-type effective theory to which QCD is reduced at low momenta.Comment: Lecture at the International School of Nuclear Physics, September 19 -- 27, 1995, Erice, Italy. 17 p. LaTeX, to be published in the Proceeding