5,602 research outputs found
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
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Shadowing for differential equations with grow-up
We consider the problem of shadowing for differential equations with grow-up.
We introduce so-called nonuniform shadowing properties (in which size of the
error depends on the point of the phase space) and prove for them analogs of
shadowing lemma. Besides, we prove a theorem about weighted shadowing for
flows. We compactify the system (using Poincare compactification, for example),
apply the results about nonuniform or weighted shadowing to the compactified
system, and then transfer the results back to the initial system using the
decompactification procedure.Comment: preprint, 19 pages, 3 figure
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
Eight-quark interactions as a chiral thermometer
A NJL Lagrangian extended to six and eight quark interactions is applied to
study temperature effects (SU(3) flavor limit, massless case), and (realistic
massive case). The transition temperature can be considerably reduced as
compared to the standard approach, in accordance with recent lattice
calculations. The mesonic spectra built on the spontaneously broken vacuum
induced by the 't Hooft interaction strength, as opposed to the commonly
considered case driven by the four-quark coupling, undergoes a rapid crossover
to the unbroken phase, with a slope and at a temperature which is regulated by
the strength of the OZI violating eight-quark interactions. This strength can
be adjusted in consonance with the four-quark coupling and leaves the spectra
unchanged, except for the sigma meson mass, which decreases. A first order
transition behavior is also a possible solution within the present approach.Comment: 4 pages, 4 figures, prepared for the proceedings of Quark Matter 2008
- 20th International Conference on Ultra-Relativistic Nucleus Nucleus
Collisions, February 4-10, Jaipur (India
- …