53 research outputs found
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.
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.
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
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