424 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.
Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
Using the covariant spectator theory (CST), we present two one boson exchange
kernels that have been successfully adjusted to fit the 2007 world np data
(containing 3788 data) below 350 MeV. One model (which we designate WJC-1) has
27 parameters and fits with a chi2/N = 1.06. The other model (designated WJC-2)
has only 15 parameters and fits with a chi2/N = 1.12. Both of these models also
reproduce the experimental triton binding energy without introducing additional
irreducible three-nucleon forces. One result of this work is a new phase shift
analysis, updated for all data until 2006, which is useful even if one does not
work within the CST. In carrying out these fits we have reviewed the entire
data base, adding new data not previously used in other high precision fits and
restoring some data omitted in previous fits. A full discussion and evaluation
of the 2007 data base is presented.Comment: 43 pages, 27 figures, and 13 table
Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon- exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.Fundação para a Ciência e a Tecnologia (FCT), U.S. Department of Energ
Chiral-symmetry breaking and pion structure in the Covariant Spectator Theory
We introduce a covariant approach in Minkowski space for the description of
quarks and mesons that exhibits both chiral-symmetry breaking and confinement.
In a simple model for the interquark interaction the quark mass function is
obtained and used in the calculation of the pion form factor. We study the
effects of the mass function and of the different quark pole contributions on
the pion form factor.Comment: 6 pages, 5 figures, presented at Excited QCD 201
Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the covariant spectator theory
The pion form factor is calculated in the framework of the charge-conjugation invariant covariant spectator theory. This formalism is established in Minkowski space, and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half-planes in order to preserve charge conjugation invariance (referred to as the C-symmetric complete impulse approximation). We find that for small pion mass these contributions are significant at all values of the four-momentum transfer Q(2) but, surprisingly, do not alter the shape obtained from the spectator poles alone
Quark Mass Function from an OGE-type Interaction in Minkowski Space
We present results for the quark mass function in Minkowski space calculated from an interaction kernel that consists of an effective one-gluon-exchange and a constant interaction. We analyze the gauge dependence of our results and compare them in the spacelike region to the available lattice QCD data.Fundação para a Ciência e a Tecnologia (FCT), United States Department of Energ
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