45 research outputs found
One-Loop Determinant of Dirac Operator in Non-Renormalizable Models
We use proper-time regularizations to define the one-loop fermion determinant
in the form suggested by Gasser and Leutwyler some years ago. We show how to
obtain the polynomial by which this definition of ln det D needs to be modified
in order to arrive at the fermion determinant whose modulus is invarinat under
chiral transformations. As an example it is shown how the fundamental
symmetries associated with the NJL model are preserved in a consistent way.Comment: 8 pages, LaTe
Dispersion and uncertainty in multislit matter wave diffraction
We show that single and multislit experiments involving matter waves may be
constructed to assess correlations between the position and momentum of a
single free particle. These correlations give rise to position dependent phases
which develop dynamically and may play an important role in the interference
patterns. For large enough transverse coherence lenght such interference
patterns are noticeably different from those of a classical dispersion free
wave.Comment: 7 pages, 5 figures, revised manuscrip
Strong and Radiative Meson Decays in a Generalized Nambu--Jona-Lasinio Model
We investigate strong and radiative meson decays in a generalized
Nambu--Jona-Lasinio model. The one loop order calculation provides a
satisfactory agreement with the data for the mesonic spectrum and for radiative
decays. Higher order effects for strong decays of and are
estimated to be large. We also discuss the role of the flavour mixing
determinantal interaction.Comment: 7 pages, LaTeX, 2 figs available upon request, CRN 92-4
Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking
Low energy hadron phenomenology involving the (u,d,s) quarks is often approached through effective multi-quark Lagrangians with the symmetries of QCD. A very successful approach consists in taking the four-quark Nambu-Jona-Lasinio Lagrangian with the chiral UL(3) × UR(3) symmetry in the massless limit, combined with the UA(1) breaking six-quark flavour determinant interaction of 't Hooft. We review the present status and some very recent developments related to the functional integration over the cubic term in auxiliary mesonic variables that one introduces to bosonize the system. Various approaches for handling this functional, which cannot be integrated exactly, are discussed: the stationary phase approximation, the perturbative expansion, the loop expansion, their interrelation and importance for the evaluation of the effective action. The intricate group structure rules out the method of Airy's integral. The problem of the instability of the vacuum is stated and a solution given by including eight-quark interactions
Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field
It is shown how the strong interaction dynamics of a multi-quark Lagrangian affects the catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions. Attention is drawn to the local minima structure of the theory
Analytic perturbation theory versus 1/N expansion in the Gross-Neveu model
The 1/N expansion can be successfully used to calculate the Green functions
of the two-dimensional O(2N) Gross - Neveu model. In parallel, the methods of
analytic perturbation theory are also applied. Comparing the results of these
two calculations at leading order, we report on the surprising agreement
between them.Comment: Latex, 3 figures, 4 page
Stationary phase corrections in the process of bosonization of multi-quark interactions
The functional integration over the auxiliary bosonic variables of cubic
order related with the effective action of the Nambu -- Jona-Lasinio model with
't Hooft term has recently been obtained in the form of a loop expansion. Even
numbers of loops contribute to the action, while odd numbers of loops are
assigned to the measure. We consider the two-loop corrections and analyse their
effect on the low-lying pseudoscalar and scalar mass spectra, quark condensates
and weak decay constants. The results are compared to the leading order
calculations and other approaches.Comment: 22 pages, LaTeX, to appear in European Physics Journal
Lowering the critical temperature with eight-quark interactions
It is shown that eight-quark interactions, which are needed to stabilize the
ground state of the combined three flavor Nambu -- Jona-Lasinio and 't Hooft
Lagrangians, play also an important role in determining the critical
temperature at which transitions occur from the dynamically broken chiral phase
to the symmetric phase.Comment: 4 pages, 2 figure
Low-energy dynamics of the reaction
We calculate the one-quark-loop amplitude for the low energy
collision in the context of the Nambu and Jona-Lasinio
model with scalar and pseudoscalar four quark couplings to all orders in the
external momenta. We show that the NJL predictions for the
reaction are not far from the Born amplitude, which
is close to the data, and is compatible with the chiral perturbation theory
estimations. We determine the corrections given by the NJL model in leading
order of to the chiral loop amplitude for .
Numerical results for the cross sections and
for pion polarizabilities are given.Comment: 20 pages in LaTex, 3 figures in 1 Postscript fil
OZI violating eight-quark interactions as a thermometer for chiral transitions
This work is a follow-up of our recent observation that in the SU(3) flavor
limit with vanishing current quark masses the temperature for the chiral
transition is substantially reduced by adding eight-quark interactions to the
Nambu - Jona-Lasinio Lagrangian with U_A(1) breaking. Here we generalize the
case to realistic light and strange quark masses and confirm our prior result.
Additionally, we demonstrate that depending on the strength of OZI violating
eight-quark interactions, the system undergoes either a rapid crossover or a
first order phase transition. The meson mass spectra of the low lying
pseudoscalars and scalars at T=0 are not sensitive to the difference in the
parameter settings that correspond to these two alternatives, except for the
singlet-octet mixing scalar channels, mainly the sigma meson.Comment: LaTeX, 5 pages, 3 figure