Formfactor of the relativistic scalar bound state calculated in Minkowski space

We have calculated the electromagnetic elastic form factor of a two body scalar bound state. The Bethe-Salpeter equation is solved directly in the Minkowski space using the Perturbation Theory Integral Representation. At soft coupling regime the obtained results are compared with those following from a quasipotential spectator (Gross) approximation.Comment: 2 figure

Analytical solution for the correlator with Gribov propagators

Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences, and instead of Lehmann it rather satisfies Gribov integral representation.Comment: 13pp, 2figs. Integral representation for Gribov correlator derived and added, new results in new figure added. Sections reordere

The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space

The hadronic vacuum polarization function $\Pi_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $\Pi_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.Comment: New Appendix was added wherein the new method of extraction of the quark spectral function is explained in detail

Solution of Dynamical Spontaneous Chiral Symmetry Breaking in Minkowski Space, Linearized approximation

Chiral symmetry breaking and mass generation is studied in a vectorial, confining asymptotic free gauge theory. Using the Schwinger-Dyson equation in improved ladder approximation, we calculate the fermion propagator in the whole Minkowski space. The estimate for $f_{\pi}$ and the dependence of physical mass on a coupling strength is provided. We focus on the extraction of spectral function of fermion propagator in the strongly coupled regime. Our calculations indicate that up to the crossover between walking and QCD-like running dynamics, the real pole of the propagator is not excluded and very likely it is actually developed at zero temperature theory.Comment: 14 pages, 6 figure

Muon pair production with hadronic vacuum polarization re-evaluated using new precise data

The interference effect between leptonic radiative corrections and hadronic polarization functions is calculated via optical theorem for $\mu-$pair productions. Fine selected new data for the production cross section $\sigma_h(e^+e^-\rightarrow hadrons$) are used for calculation of hadronic vacuum polarization, which enter the dressed photon propagator in muon pair production. The result is compared with KLOE experiment for $\mu^{-}\mu^{+}$ production at $\phi$ meson energy, as well as the running fine structure coupling is compared with recent KLOE2 experiment for radiative return $\mu^{-}\mu^{+}$ production at $\omega/\rho$ meson energy.Comment: 11 figures, 15 page

On the decoupling solution for pinch technique gluon propagator

Within a simple Ansatz for renormalized gluon propagator and using gauge invariant pinch-technique for Schwinger-Dyson equation, the limits on the effective gluon mass is derived. We calculated scheme invariant running coupling, which in order to be well defined, gives the lower limit on the gluon mass. We conclude mass should be larger as $m>0.4\Lambda$ in order to avoid Landau ghost. The upper limit is estimated from assumed quark mass generation which requires gauge coupling must be large enough to trigger chiral symmetry breaking. It allows only small range of $m$, which lead to a reasonably large infrared coupling. Already for $m\simeq \Lambda$ we get no chiral symmetry breaking at all. Further, we observe that sometimes assumed or postulated Khallen-Lehmann representation for running coupling is not achieved for any value of $m$.Comment: 6p, error corrected, new upper boundary on the effective gluon mass estimated from CHS

Solving the Bethe-Salpeter equation for fermion-antifermion pseudoscalar bound state in Minkowski space

The new method of solution of the Bethe-Salpeter equation for quark-antiquark pseudoscalar bound state is proposed. With the help of integral representation the results are directly obtained in Minkowski space. Dressing of Greens functions is naturally considered providing thus the correct inclusion of the running coupling constant and the quark propagators as well as. The first numerical results are presented for a simplified ladder approximation.Comment: 19 pages, 1 figur

Gauge Technique approximation to the πγ\pi \gamma production and the pion transition form factor

The pion transition form factor $G(q^2)$ is computed on the entire domain of spacelike and timelike momenta using a quantum field theory continuum approach. In analytical continuation of the function $G(Q^2)$ we utilized the Gauge Technique with the quark propagator determined from Minkowski space solution of QCD Dyson-Schwinger equations. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.Comment: Typos and grammar corrected. New refs. adde

Lattice data inspired but Minkowski space calculated QCD fundamental propagator

We study the Dyson-Schwinger equation for the quark propagator in Minkowski space. In order to have analytical behaviour at the timelike axis of momenta under control, we use the Stieltjes and the Hilbert transformation for the interaction kernels and discuss the solution from the perspective of these transformations. In addition, a lattice fit for the gluon propagator and approximation for quark-gluon vertex are employed, and within the model the quark propagator is obtained through the solution of Dyson-Schwinger equation in Minkowski space. The resulting propagators in all studied cases do not show up particle like pole and production thresholds. Instead of, the quark propagator satisfies Hilbert transformation and the associated dynamical mass function becomes complex without a presence of particle like branch point.Comment: Explanatory section redone, split an enlarged into two new Sections, new simplify results added for LA, typos corrected the 26 pp, 6 fig

Electromagnetic production of pions and quark dynamical mass in Minkowski space

Mechanism for generation of vector meson resonances is studied in the framework of QCD Dyson-Schwinger equations, which are defined and actually solved in Minkowski space. It is suggested that the timelike pion form factor is generated by the interference of the background quark loops together with the resonant structure predominantly created in the photon-quark-antiquark vertex. It is suggested that QCD Green's functions involving quark fields are oscillating for timelike arguments, which makes the interference effect among various QCD Green's functions quite strong and important for the correct description of production processes. A further peculiarities of dynamical chiral symmetry breaking and confinement phenomena as viewed in Minkowski space are discussed.Comment: too simple for correct description of the pion formfacto