Spectrum of quarks in QCD2

The properties of the gauge invariant two-point quark Green's function are studied in the large-Nc limit of two-dimensional QCD. The analysis is done by means of an exact integrodifferential equation. The Green's function is found infrared finite, with singularities in the momentum squared variable represented by an infinite number of threshold type branch points with a power -3/2, starting at positive mass squared values, with cuts lying on the positive real axis. The expression of the Green's function is analytically determined.Comment: 3 pages. Talk given at the XXIst International Europhysics Conference on High Energy Physics, Grenoble, France, 21-27 July 201

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-$N_c$ limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.Comment: 6 pages, PDFLatex uses elsarticle class. Invited talk at the Conference Light Cone: Relativistic Hadronic and Particle Physics, 10-15 December 2012, Delhi, Indi

The pionium lifetime in generalized chiral perturbation theory

Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential-constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination $(a_0^0-a_0^2)$ of the $\pi\pi$ S-wave scattering lengths with isospin I=0,2.Comment: 14 pages, 1 figure (included in the text), Late

On the role of dynamical quark mass generation in chiral symmetry breaking in QCD

The phenomenon of dynamical quark mass generation is studied in QCD within the framework of a gauge invariant formalism. An exact relationship is established between the equation satisfied by the scalar part of the two-point gauge invariant quark Green's function and the quark-antiquark bound state equation in the chiral limit. A possible nontrivial solution of the former yields a massless pseudoscalar solution of the bound state equation with vanishing total momentum. The result is also corroborated by the corresponding Ward-Takahashi identity. The problem is explicitly solved in two-dimensional QCD in the large-$N_c$ limit.Comment: 5 pages, PDFLaTeX, uses elsarticle class. Talk given at the International Conference QCD 15, Montpellier, 29 June - 3 July 201

Pionium lifetime corrections

Pionium lifetime corrections are evaluated in the frameworks of constrained Bethe-Salpeter equation and chiral perturbation theory. Corrections of order $O(\alpha)$ are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. The total correction is found to be of the order of $(6.1\pm 2.0)$.Comment: 9 pages, Latex. Uses Dubna98.sty. Talk given at the Int. Workshop "Hadronic Atoms and Positronium in the Standard Model", Dubna, 26-31 May 1998. To appear in the Proceeding

Relevance of the strange quark sector in chiral perturbation theory

Results obtained in recent years in the strange quark sector of chiral perturbation theory are reviewed and the theoretical relevance of this sector for probing the phase structure of QCD at zero temperature with respect to the variation of the number of massless quarks is emphasized.Comment: 10 pages, 1 figure. Talk given at the Conference Quark Confinement and the Hadron Spectrum VI, Villasimius, Cagliari, Italy, 21-25 September 2004. To appear in the Proceedings (AIP

Incorporation of anomalous magnetic moments in the two-body relativistic wave equations of constraint theory

Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the resulting potential is entirely determined, up to magnetic type form factors, from that of the initial potential descibing the mutual interaction in the absence of anomalous magnetic moments. The wave equations are reduced to a single eigenvalue equation in the sectors of pseudoscalar and scalar states ($j=0$). The requirement of a smooth introduction of the anomalous magnetic moments imposes restrictions on the behavior of the form factors near the origin, in $x$-space. The nonrelativistic limit of the eigenvalue equation is also studied.Comment: 25 pages, Latex file, no figur

The gauge invariant quark Green's function in two-dimensional QCD

The gauge invariant quark Green's function, defined with a path-ordered phase factor along a straight line, is studied in two-dimensional QCD in the large-N_c limit by means of an exact integrodifferential equation. It is found to be infrared finite with singularities represented by an infinite number of threshold type branch points with a power of -3/2, starting at positive mass squared values. The Green's function is analytically determined.Comment: 7 pages, 2 figures. Talk given at the Beppe Nardulli Memorial Workshop, QCD@Work - Theory and Experiment, 20-23 June 2010, Martina Franca, Ital

Gauge-invariant approach to quark dynamics

The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.Comment: 21 pages, 5 figures. Based on the talk given at the Workshop Dyson-Schwinger equations in modern mathematics and physics, ECT*, Trento, 22-26 September 2014. Review article contribution to the special issue of Frontiers of Physics (Eds. M. Pitschmann and C. D. Roberts