Electromagnetic Properties of Few-Body Systems Within a Point-Form Approach

We use a Poincare-invariant coupled-channel approach based on point-form relativistic quantum mechanics to investigate the electromagnetic properties of two-body bound systems with spin 0 and spin 1. Elastic scattering of an electron by the bound state is treated as a two-channel problem for a Bakamjian-Thomas-type mass operator. In this way retardation effects in the photon-exchange interaction are fully taken into account. The electromagnetic bound-state current is extracted from the one-photon-exchange optical potential. Wrong cluster properties, inherent in the Bakamjian-Thomas framework for more than 2 particles, are seen to cause spurious (unphysical) contributions in the current, which are associated with a dependence on the sum of the electron momenta. The Lorentz structure of our current resembles the one obtained from an explicitly covariant light-front approach, where spurious contributions also show up and are associated with a four-vector describing the orientation of the light front. For spin-0 systems, like a charged pion, the spurious contributions can be eliminated by choosing the total invariant mass of the electron-bound-state system large enough. In this case equivalence with the usual front-form expression for the form factor, resulting from a spectator current in the q^+=0 reference frame, is established. For spin-1 systems, like a charged rho meson or the deuteron, some spurious contributions cannot be completely eliminated by solely choosing an infinitely large invariant mass. Nevertheless, there is an unambiguous way how to separate them from the physical contributions such that one is left with a physical bound-state current with the required properties.Comment: 184 pages, dissertation, Graz (2011

Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space

We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We show that these equations are charge-conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking. In this introductory paper, we test the formalism by using a simplified kernel consisting of a momentum-space delta-function with a vector Lorentz structure, to which one adds a mixed scalar and vector confining interaction. The scalar part of the confining interaction is not chirally invariant by itself, but decouples from the equations in the chiral limit and therefore allows the NJL mechanism to work. With this model we calculate the quark mass function, and we compare our Minkowski-space results to lattice QCD data obtained in Euclidean space. In a companion paper, we apply this formalism to a calculation of the pion form factor.Comment: 17 pages, 12 figures, version published in Phys. Rev.

Pion electromagnetic form factor in the Covariant Spectator Theory

The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling relations.Comment: 11 pages, 8 figures, version published in Phys. Rev.

Singularity-free two-body equation with confining interactions in momentum space

We are developing a covariant model for all mesons that can be described as quark-antiquark bound states in the framework of the Covariant Spectator Theory (CST) in Minkowski space. The kernel of the bound-state equation contains a relativistic generalization of a linear confining potential which is singular in momentum space and makes its numerical solution more difficult. The same type of singularity is present in the momentum-space Schr\"odinger equation, which is obtained in the nonrelativistic limit. We present an alternative, singularity-free form of the momentum-space Schr\"odinger equation which is much easier to solve numerically and which yields accurate and stable results. The same method will be applied to the numerical solution of the CST bound-state equations.Comment: 4 pages, 2 figures, talk presented at the 22nd European Conference on Few-Body Problems in Physics (EFB22), Krakow, Poland, 9 - 13 September 201

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

We use the covariant spectator theory with an effective quark-antiquark interaction, containing Lorentz scalar, pseudoscalar, and vector contributions, to calculate the masses and vertex functions of, simultaneously, heavy and heavy-light mesons. We perform least-square fits of the model parameters, including the quark masses, to the meson spectrum and systematically study the sensitivity of the parameters with respect to different sets of fitted data. We investigate the influence of the vector confining interaction by using a continuous parameter controlling its weight. We find that vector contributions to the confining interaction between 0% and about 30% lead to essentially the same agreement with the data. Similarly, the light quark masses are not very tightly constrained. In all cases, the meson mass spectra calculated with our fitted models agree very well with the experimental data. We also calculate the mesons wave functions in a partial wave representation and show how they are related to the meson vertex functions in covariant form.Comment: 23 pages, 10 figures. Minor corrections of previous version. To be published in Phys. Rev.