1,440 research outputs found
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.
Application of the Covariant Spectator Theory to the study of heavy and heavy-light mesons
As an application of the Covariant Spectator Theory (CST) we calculate the
spectrum of heavy-light and heavy-heavy mesons using covariant versions of a
linear confining potential, a one- gluon exchange, and a constant interaction.
The CST equations possess the correct one-body limit and are therefore
well-suited to describe mesons in which one quark is much heavier than the
other. We find a good fit to the mass spectrum of heavy-light and heavy-heavy
mesons with just three parameters (apart from the quark masses). Remarkably,
the fit parameters are nearly unchanged when we fit to experimental
pseudoscalar states only or to the whole spectrum. Because pseudoscalar states
are insensitive to spin-orbit interactions and do not determine spin-spin
interactions separately from central interactions, this result suggests that it
is the covariance of the kernel that correctly predicts the spin-dependent
quark-antiquark interaction
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.
A covariant constituent-quark formalism for mesons
Using the framework of the Covariant Spectator Theory (CST) [1] we are
developing a covariant model formulated in Minkowski space to study mesonic
structure and spectra. Treating mesons as effective states, we
focused in [2] on the nonrelativistic bound-state problem in momentum space
with a linear confining potential. Although integrable, this kernel has
singularities which are difficult to handle numerically. In [2] we reformulate
it into a form in which all singularities are explicitely removed. The
resulting equations are then easier to solve and yield accurate and stable
solutions. In the present work, the same method is applied to the relativistic
case, improving upon the results of the one-channel spectator equation (1CSE)
given in [3].Comment: 6 pages, 5 figures, Presented at EEF70, Workshop on Unquenched Hadron
Spectroscopy: Non-Perturbative Models and Methods of QCD vs. Experimen
Quarkonia and heavy-light mesons in a covariant quark model
Preliminary calculations using the Covariant Spectator Theory (CST) employed
a scalar linear confining interaction and an additional constant vector
potential to compute the mesonic mass spectra. In this work we generalize the
confining interaction to include more general structures, in particular a
vector and also a pseudoscalar part, as suggested by a recent study. A
one-gluon-exchange kernel is also implemented to describe the short-range part
of the interaction. We solve the simplest CST approximation to the complete
Bethe-Salpeter equation, the one-channel spectator equation, using a numerical
technique that eliminates all singularities from the kernel. The parameters of
the model are determined through a fit to the experimental pseudoscalar meson
spectra, with a good agreement for both quarkonia and heavy-light states.Comment: 4 pages, 2 figures; 21st International Conference on Few-Body
Problems in Physics, May 18 - 22, 2015, Chicago, US
Relativistic phenomenology of meson spectra with a covariant quark model in Minkowski space
In this work, we perform a covariant treatment of quark-antiquark systems. We
calculate the spectra and wave functions using a formalism based on the
Covariant Spectator Theory (CST). Our results not only reproduce very well the
experimental data with a very small set of global parameters, but they also
allow a direct test of the predictive power of covariant kernels
Testing saturation with diffractive jet production in deep inelastic scattering
We analyse the dissociation of a photon in diffractive deep inelastic
scattering in the kinematic regime where the diffractive mass is much bigger
than the photon virtuality. We consider the dominant q\bar{q}g component
keeping track of the transverse momentum of the gluon which can be measured as
a final-state jet. We show that the diffractive gluon-jet production
cross-section is strongly sensitive to unitarity constraints. In particular, in
a model with parton saturation, this cross-section is sensitive to the scale at
which unitarity effects become important, the saturation scale. We argue that
the measurement of diffractive jets at HERA in the limit of high diffractive
mass can provide useful information on the saturation regime of QCD.Comment: 12 pages, 5 figures, misprints corrected, published versio
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