8,467 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
Pricing tranched credit products with generalized multifactor models
The market for tranched credit products (CDOs, Itraxx tranches) is one of the fastest growing
segments in the credit derivatives industry. However, some assumptions underlying the standard
Gaussian onefactor
pricing model (homogeneity, single factor, Normality), which is the pricing
standard widely used in the industry, are probably too restrictive. In this paper we generalize the
standard model by means of a two by two model (two factors and two asset classes). We assume
two driving factors (business cycle and industry) with independent tStudent
distributions,
respectively, and we allow the model to distinguish among portfolio assets classes. In order to
illustrate the estimation of the parameters of the model, an empirical application with Moody's
data is also included
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
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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