109 research outputs found
Nucleons or diquarks? Competition between clustering and color superconductivity in quark matter
We study the instabilities of quark matter in the framework of a generalized
Nambu--Jona-Lasinio model, in order to explore possible competition between
three-quark clustering to form nucleons and diquark formation leading to color
superconductivity. Nucleon and solutions are obtained for the
relativistic Faddeev equation at finite density and their binding energies are
compared with those for the scalar and axial-vector diquarks found from the
Bethe-Salpeter equation. In a model with interactions in both scalar and axial
diquark channels, bound nucleons exist up to nuclear matter density. However,
except at densities below about a quarter of that of nuclear matter, we find
that scalar diquark formation is energetically favored. This raises the
question of whether a realistic phase diagram of baryonic matter can be
obtained from any model which does not incorporate color confinement.Comment: 23 pages (RevTeX), 5 figures (epsf
Baryons in O(4) and Vibron Model
The structure of the reported excitation spectra of the light unflavored
baryons is described in terms of multi-spin valued Lorentz group
representations of the so called Rarita-Schwinger (RS) type (K/2, K/2)* [(1/
2,0)+ (0,1/2)] with K=1,3, and 5. We first motivate legitimacy of such pattern
as fundamental fields as they emerge in the decomposition of triple fermion
constructs into Lorentz representations. We then study the baryon realization
of RS fields as composite systems by means of the quark version of the U(4)
symmetric diatomic rovibron model. In using the U(4)/ O(4)/ O(3)/ O(2)
reduction chain, we are able to reproduce quantum numbers and mass splittings
of the above resonance assemblies. We present the essentials of the four
dimensional angular momentum algebra and construct electromagnetic tensor
operators. The predictive power of the model is illustrated by ratios of
reduced probabilities concerning electric de-excitations of various resonances
to the nucleon.Comment: Phys. Rev. D (in press, 2001
Production Processes as a Tool to Study Parameterizations of Quark Confinement
We introduce diquarks as separable correlations in the two-quark Green's
function to facilitate the description of baryons as relativistic three-quark
bound states. These states then emerge as solutions of Bethe-Salpeter equations
for quarks and diquarks that interact via quark exchange. When solving these
equations we consider various dressing functions for the free quark and diquark
propagators that prohibit the existence of corresponding asymptotic states and
thus effectively parameterize confinement. We study the implications of
qualitatively different dressing functions on the model predictions for the
masses of the octet baryons as well as the electromagnetic and strong form
factors of the nucleon. For different dressing functions we in particular
compare the predictions for kaon photoproduction, , and
associated strangeness production, with experimental data.
This leads to conclusions on the permissibility of different dressing
functions.Comment: 43 pages, Latex, 28 eps files included via epsfig; version to be
published in Physical Review
Selected nucleon form factors and a composite scalar diquark
A covariant, composite scalar diquark, Fadde'ev amplitude model for the
nucleon is used to calculate pseudoscalar, isoscalar- and isovector-vector,
axial-vector and scalar nucleon form factors. The last yields the nucleon
sigma-term and on-shell sigma-nucleon coupling. The calculated form factors are
soft, and the couplings are generally in good agreement with experiment and
other determinations. Elements in the dressed-quark-axial-vector vertex that
are not constrained by the Ward-Takahashi identity contribute ~20% to the
magnitude of g_A. The calculation of the nucleon sigma-term elucidates the only
unambiguous means of extrapolating meson-nucleon couplings off the meson
mass-shell.Comment: 12 pages, REVTEX, 5 figures, epsfi
Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be
calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic
content is enumerable. We illustrate that fact using a vertex obtained via the
complete resummation of dressed-gluon ladders. While this vertex is planar, the
vertex-consistent kernel is nonplanar and that is true for any dressed vertex.
In an exemplifying model the rainbow-ladder truncation of the gap and
Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses,
that are changed little by including higher-order corrections. Repulsion
generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel
for quark-quark scattering is sufficient to guarantee that diquark bound states
do not exist.Comment: 16 pages, 12 figures, REVTEX
Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
The coupled system of renormalized Dyson-Schwinger equations for the quark,
gluon and ghost propagators of Landau gauge QCD is solved within truncation
schemes. These employ bare as well as non-perturbative ansaetze for the
vertices such that the running coupling as well as the quark mass function are
independent of the renormalization point. The one-loop anomalous dimensions of
all propagators are reproduced. Dynamical chiral symmetry breaking is found,
the dynamically generated quark mass agrees well with phenomenological values
and corresponding results from lattice calculations. The effects of unquenching
the system are small. In particular the infrared behavior of the ghost and
gluon dressing functions found in previous studies is almost unchanged as long
as the number of light flavors is smaller than four.Comment: 34 pages, 10 figures, version to be published by Phys. Rev.
K -> pi pi and a light scalar meson
We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi
transitions using a Dyson-Schwinger equation model. Exploiting the feature that
QCD penguin operators direct K^0_S transitions through 0^{++} intermediate
states, we find an explanation of the enhancement of I=0 K -> pi pi transitions
in the contribution of a light sigma-meson. This mechanism also affects
epsilon'/epsilon.Comment: 7 pages, REVTE
Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
We compute the axial and pseudoscalar form factors of the nucleon in the
Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev
equation for the nucleon wave function and determine the matrix elements of the
axialvector and pseudoscalar isotriplet currents. Our only input is a
well-established and phenomenologically successful ansatz for the
nonperturbative quark-gluon interaction. As a consequence of the axial
Ward-Takahashi identity that is respected at the quark level, the
Goldberger-Treiman relation is reproduced for all current-quark masses. We
discuss the timelike pole structure of the quark-antiquark vertices that enters
the nucleon matrix elements and determines the momentum dependence of the form
factors. Our result for the axial charge underestimates the experimental value
by 20-25% which might be a signal of missing pion-cloud contributions. The
axial and pseudoscalar form factors agree with phenomenological and lattice
data in the momentum range above Q^2 ~ 1...2 GeV^2.Comment: 17 pages, 7 figures, 1 tabl
Dynamical Chiral Symmetry Breaking in Effective Models of QCD in the Bethe-Salpeter Approach
Dynamical breaking of chiral symmetry in effective models of QCD is studied.
Introducing a cut-off function or a non-local interaction, the Noether current
must be modified and thus the Ward-Takahashi identity and the PCAC relation are
modified accordingly. We point out that the pion decay constant must be defined
consistently with the Noether current so that the low-energy relations are
satisfied. We define the proxy of the Noether current for general effective
models, which is consistent with loop expansion of the
Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion
decay constant in terms of the Bethe-Salpeter amplitude is derived.
The effective Pagels-Stokar formula is proposed which is useful to estimate
the decay constant without solving the Bethe-Salpeter equation.Comment: 25 pages, LaTe
Analytic properties of the Landau gauge gluon and quark propagators
We explore the analytic structure of the gluon and quark propagators of
Landau gauge QCD from numerical solutions of the coupled system of renormalized
Dyson--Schwinger equations and from fits to lattice data. We find sizable
negative norm contributions in the transverse gluon propagator indicating the
absence of the transverse gluon from the physical spectrum. A simple analytic
structure for the gluon propagator is proposed. For the quark propagator we
find evidence for a mass-like singularity on the real timelike momentum axis,
with a mass of 350 to 500 MeV. Within the employed Green's functions approach
we identify a crucial term in the quark-gluon vertex that leads to a positive
definite Schwinger function for the quark propagator.Comment: 42 pages, 16 figures, revtex; version to be published in Phys Rev
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