An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model

Using the PCAC relation, we derive a compact formula for the pion decay constant $F_{\pi}$ in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum $P_{\mu}\to0$ it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express $F_{\pi}^{2}$ in terms of a single integral over the quark momentum fraction $u$. We interpret the integrand as a pion distribution amplitude $\phi(u)$. We discuss its properties and compare with the $\pi$DA's obtained in other models.Comment: To appear in the special issue of Acta Physica Polonica to celebrate the 65th Birthday of Professor Jan Kwiecinski. 14 pages, 4 figure

The Skyrme model predictions for the 27J=3/2{\bf 27}_{J=3/2} mass spectrum and the 273/2{\bf 27}_{3/2}-10ˉ\bar{\bf 10} mass splittings

The ${\bf 27}_{J=3/2}$-plet mass spectrum and the ${\bf 27}_{3/2}$-$\bar{\bf 10}$ mass splittings are computed in the framework of the minimal SU(3)$_f$ extended Skyrme model. As functions of the Skyrme charge $e$ and the SU(3)$_f$ symmetry breaking parameters the predictions are presented in tabular form. The predicted mass splitting ${\bf 27}_{3/2}$-$\bar{\bf 10}$ is the smallest among all SU(3)$_f$ baryonic multiplets.Comment: 4 pages, 2 tables, version to appear in Phys. Rev.

Baryon Exotics in the Quark Model, the Skyrme Model and QCD

We identify the quantum numbers of baryon exotics in the Quark Model, the Skyrme Model and QCD, and show that they agree for arbitrary colors and flavors. We define exoticness, E, which can be used to classify the states. The exotic baryons include the recently discovered qqqq qbar pentaquarks (E=1), as well as exotic baryons with additional q qbar pairs (E >=1). The mass formula for non-exotic and exotic baryons is given as an expansion in 1/N, and allows one to relate the moment of inertia of the Skyrme soliton to the mass of a constituent quark

Color Non-Singlet Spectroscopy

Study of the spectrum and structure of color non-singlet combinations of quarks and antiquarks, neutralized by a non-dynamical compensating color source, may provide an interesting way to address questions about QCD that cannot be addressed by experiment at the present time. These states can be simulated in lattice QCD and the results can be used to improve phenomenological models of hadrons. Here these ideas are applied to color triplet states of qqqq and qq bar q.Comment: References added and typos correcte