24 research outputs found
On the analytic properties of chiral solitons in the presence of the --meson
A thorough study is performed of the analytical properties of the fermion
determinant for the case that the time components of (axial) vector fields do
not vanish. For this purpose the non--Hermitian Euclidean Dirac Hamiltonian is
generalized to the whole complex plane. The Laurent series are proven to reduce
to Taylor series for the corresponding eigenvalues and --functions as long as
field configurations are assumed for which level crossings do not occur. The
condition that no level crossings appears determines the radius convergence.
However, the need for regularization prohibits the derivation of an analytic
energy functional because real and imaginary parts of the eigenvalues are
treated differently. Consistency conditions for a Minkowski energy functional
are extracted from global gauge invariance and the current field identity for
the baryon current. Various treatments of the Nambu--Jona--Lasinio soliton are
examined with respect to these conditions. Motivated by the studies of the
Laurent series for the energy functional the Euclidean action is expanded in
terms of the --field. It is argued that for this expansion the
proper--time regularization scheme has to be imposed on the operator level
rather than on an expression in terms of the one--particle eigenenergies. The
latter treatment is plagued by the inexact assumption that the Euclidean Dirac
Hamiltonian and its Hermitian conjugate can be diagonalized simultaneously. It
is then evident that approaches relying on counting powers of the
--field in the one--particle eigenenergies areComment: UNITU-THEP-13/1994, 34 LaTeX pages, 5 figures appended as postscript
fil
Hadron widths in mixed-phase matter
We derive classically an expression for a hadron width in a two-phase region
of hadron gas and quark-gluon plasma (QGP). The presence of QGP gives hadrons
larger widths than they would have in a pure hadron gas. We find that the
width observed in a central Au+Au collision at
GeV/nucleon is a few MeV greater than the width in a pure hadron gas. The part
of observed hadron widths due to QGP is approximately proportional to
.Comment: 8 pages, latex, no figures, KSUCNR-002-9
RPA-Approach to the Excitations of the Nucleon, Part II: Phenomenology
The tensor-RPA approach developed previously in part I is applied to the
Nambu-Jona-Lasinio (NJL) model. As a first step we investigate the structure of
Dirac-Hartree-Fock solutions for a rotationally and isospin invariant
ground-state density. Whereas vacuum properties can be reproduced, no solitonic
configuration for a system with unit baryon number is found. We then solve the
tensor-RPA equation employing simple models of the nucleon ground state. In
general the ph interaction effects a decrease of the excited states to lower
energies. Due to an enhanced level density at low energies the obtained spectra
cannot be matched with the experimental data when a standard MIT-bag
configuration is used. However, when the size of the nucleon quark core is
reduced to approximately 0.3 fm a fair description of the baryon spectrum in
the positive-parity channel is achieved. For this purpose the residual
interaction turns out to be crucial and leads to a significant improvement
compared with the mean-field spectra.Comment: 33 pages, Latex, 9 Postscpript figures, section on the excited states
has been completely rewritten after error was detected, results are now much
more encouragin
Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
We compute the pion light-cone wave function and the pion quark distribution
amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars
regularization method and as a result the distribution amplitude satisfies
proper normalization and crossing properties. In the chiral limit we obtain the
simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and
= -M / f_pi^2 for the second moment of the pion light-cone
wave function, where M is the constituent quark mass and f_pi is the pion decay
constant. After the QCD Gegenbauer evolution of the pion distribution amplitude
good end-point behavior is recovered, and a satisfactory agreement with the
analysis of the experimental data from CLEO is achieved. This allows us to
determine the momentum scale corresponding to our model calculation, which is
close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis
of the pion parton distribution function. The value of is, after the
QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear
integral relation between the pion distribution amplitude and the parton
distribution function of the pion, which holds at the leading-order QCD
evolution.Comment: mistake in Eq.(38) correcte