Based on the Generalized Quantum Electrodynamics expression for the Podolsky propagator, which preserves gauge invariance for massive photons, we propose a model for the massive gluon propagator that reproduces well-known features of established stro
ng-interaction models in the framework of the Dyson-Schwinger equation. By adjusting the Podolsky mass and the coupling strength we thus construct a model with simple analytical properties known from perturbative theory, yet well suited to describe a confining interaction. We obtain solutions of the Dyson-Schwinger equation for the quark at space-like momenta on the real axis as well as on the complex plane and solving the bound-state problem with the Bethe-Salpeter equation yields masses and weak decay constants of the $pi, K$ and $eta_c$ in excellent agreement with experimental values, while the $D$ and $D_s$ are reasonably well described. The analytical simplicity of this effective interaction has the potential to be useful for phenomenological applications and may facilitate calculations in Minkowski space.
We calculate the masses and weak decay constants of flavorless ground and radially excited $J^P=1^-$ mesons and the corresponding quantities for the K^*, within a Poincare covariant continuum framework based on the Bethe-Salpeter equation. We use in
both, the quarks gap equation and the meson bound-state equation, an infrared massive and finite interaction in the leading symmetry-preserving truncation. While our numerical results are in rather good agreement with experimental values where they are available, no single parametrization of the QCD inspired interaction reproduces simultaneously the ground and excited mass spectrum, which confirms earlier work on pseudoscalar mesons. This feature being a consequence of the lowest truncation, we pin down the range and strength of the interaction in both cases to identify common qualitative features that may help to tune future interaction models beyond the rainbow-ladder approximation.
We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginar
y components in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.
Amongst the bound states produced by the strong interaction, radially excited meson and nucleon states offer an important phenomenological window into the long-range behavior of the coupling constant in Quantum Chromodynamics. We here report on some
technical details related to the computation of the bound states eigenvalue spectrum in the framework of Bethe-Salpeter and Faddeev equations.
We classify the quantum numbers of the extra $U(1)$ symmetries contained in $E_6$. In particular, we categorize the cases with rational charges and present the full list of models which arise from the chains of the maximal subgroups of $E_6$. As an a
pplication, the classification allows us to determine all embeddings of the Standard Model fermions in all possible decompositions of the fundamental representation of $E_6$ under its maximal subgroups. From this we find alternative chains of subgroups for Grand Unified Theories. We show how many of the known models including some new ones appear in alternative breaking patterns. We also use low energy constraints coming from parity-violating asymmetry measurements and atomic parity non-conservation to set limits on the $E_6$ motivated parameter space for a $Z$ boson mass of~1.2~TeV. We include projected limits for the present and upcoming QWEAK, MOLLER and SOLID experiments.
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetic fields of arbitrary strength, by solving the Schwinger-Dyson equation (SDE) for the fermion self-energy in the rainb
ow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass m for arbitrarily small values of electromagnetic coupling alpha. For intense fields it is also well known that m propto sqrt eB. Our approach allows us to span all regimes of parameters alpha and eB. We find that m propto sqrt eB provided alpha is small. However, when alpha increases beyond the critical value alpha_c which marks the onslaught of dynamical fermion masses in vacuum, we find m propto Lambda, the cut-off required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of eB and alpha. We also point out the relevance of our work for possible physical applications.
