In the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called ...“normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.
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We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of ...physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
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The main aspects of chiral symmetry in QCD are presented. The necessity of its spontaneous breakdown is explained. Some low-energy theorems are reviewed. The role of chiral effective Lagrangians in ...the formulation and realization of chiral perturbation theory is emphasized. The consequences of the presence of anomalies are sketched.
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The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel ...transport operation in constructing gauge-invariant Green＇s functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphmsized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the qua.rk Green＇s function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large-Nc, 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.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Two particles interacting by photon exchange, form the bound states predicted by the non-relativistic Schrödinger equation with the Coulomb potential (Balmer series). More than 60 years ago, in the ...solutions of relativistic Bethe-Salpeter equation, in addition to the Balmer series, were found another series of energy levels. These new series, appearing when the fine structure constant
α
is large enough (
α
>
π
/4), are not predicted by the Schrödinger equation. However, this new (non-Balmer) states can hardly exist in nature, since in order to create a strong e.m. field with
α
>
π
/4 a point-like charge
Z
> 107 is needed. The nuclei having this charge, though exist starting with bohrium, are far from to be point-like.
In the present paper, we analyze the more realistic case of a strong interaction created by exchange of a massive particle. It turns out that in the framework of the Bethe-Salpeter equation this interaction still generates a series of new relativistic states, which are similar to those of the massless exchange case, and which are absent in the Schrödinger equation. The properties of these solutions are studied. Their existence in nature seems possible.
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We study, in two-dimensional QCD and in the large-
N
c
limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered phase factor along a straight line. The ...analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power −3/2, starting at positive mass squared values. Its expression is analytically determined.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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-Nc limit.
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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
ππ
S-wave scattering lengths with isospin
I=0, 2.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the ...presence of an external gluon field, functional relations between Green's functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Green's function having a phase factor along a single straight line. The related kernels involve Wilson loops with skew-polygonal contours and with functional derivatives along the sides of the contours.
The large-distance dynamics in quarkonium systems is investigated, in the large-
N
c
limit, through the saturation of Wilson loop averages by minimal surfaces. Using a representation for the quark ...propagator in the presence of the external gluon field based on the use of path-ordered phase factors, a covariant three-dimensional bound state equation of the Breit–Salpeter type is derived, in which the interaction potentials are provided by the energy–momentum vector of the straight segment joining the quark to the antiquark and carrying a constant linear energy density, equal to the string tension. The interaction potentials are confining and reduce to the linear vector potential in the static case and receive, for moving quarks, contributions from the moments of inertia of the straight segment. The self-energy parts of the quark propagators induce spontaneous breakdown of chiral symmetry with a mechanism identical to that of the exchange of one Coulomb-gluon. In the nonrelativistic limit, long range spin–spin potentials are absent; the moments of inertia of the straight segment provide negative contributions to the spin–orbit potentials going in the opposite direction to those of the pure timelike vector potential. In the ultrarelativistic limit, the mass spectrum displays linear Regge trajectories with slopes in agreement with their classical relationship with the string tension.
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