24,272 research outputs found

### Two photon decay and photoproduction of radial excitation of pion $\pi_0'$

Within the framework of non-local quark model of Nambu--Jona-Lasinio type the
two-photon decay of radial excited state of $\pi_0$-meson -- $\pi_0'$ -- is
found to be 3.6\KeV. The radial excitation of pion is described with the use
of polynomial formfactor of second order over $\vec q^2$ where $\vec q$ is the
transverse momentum, which corresponds to relative motion of quark-antiquark
pair within the energy range from 0 up to 1\GeV.
The probabilities of production of $\pi_0'$ and $(\pi_0'+\gamma)$ states in
the electron-positron colliders are estimated. The production of $\pi_0'$-meson
in the interaction of photon with electron or muon is as well considered
(Primakoff effect). The relevant total cross sections are 0.14 or 0.06\nb.Comment: 10 page

### The decays $\rho^{-}\to\eta\pi^{-}$ and $\tau^{-}\to\eta(\eta')\pi^{-}\nu$ in the NJL model

The widths of the decays $\rho^{-}\to\eta\pi^{-}$ and
$\tau^{-}\to\eta(\eta')\pi^{-}\nu$ are calculated in the framework of the NJL
model. It is shown that these decays are defined by the $u$ and $d$ quark mass
difference. It leads to the suppression of these decays in comparison with the
main decay modes. In the process $\rho^{-}\to\eta\pi^{-}$ the intermediate
scalar $a_0^{-}$ state is taken into account. For the $\tau$ decays the
intermediate states with $a_0^{-}$, $\rho^{-}(770)$ and $\rho^{-}(1450)$ mesons
are used. Our estimates are compared with the results obtained in other works.Comment: 6 pages, 5 figures, 1 tabl

### The processes $e^{+}e^{-} \to \pi\pi(\pi')$ in the extended NJL model

The process $e^{+}e^{-} \to \pi^{+}\pi^{-}$ is described in the framework of
the extended NJL model. Intermediate vector mesons $\rho^0(770)$, $\omega(782)$
and \rho'(1450)$are taken into account. Our results are in satisfactory
agreement with experimental data. The prediction for the process$e^{+}e^{-}
\to \pi\pi'(1300)$is given. Here the main contribution is given by the diagram
with intermediate$\rho'(1450)$ meson.Comment: 7 pages, 5 figure

### Supersymmetry and the Odd Poisson Bracket

Some applications of the odd Poisson bracket developed by Kharkov's theorists
are represented, including the reformulation of classical Hamiltonian dynamics,
the description of hydrodynamics as a Hamilton system by means of the odd
bracket and the dynamics formulation with the Grassmann-odd Lagrangian. Quantum
representations of the odd bracket are also constructed and applied for the
quantization of classical systems based on the odd bracket and for the
realization of the idea of a composite spinor structure of space-time. At last,
the linear odd bracket, corresponding to a semi-simple Lie group, is introduced
on the Grassmann algebra.Comment: 17 pages, LATEX 2e. Invited talk given at the International Symposium
"30 Years of Supersymmetry" (Theoretical Physics Institute, University of
Minnesota, Minneapolis, MN, USA, 13-27 October, 2000) due to the support
kindly offered by the Organizing Committee of this meeting and, especially,
by Keith Olive and Mikhail Shifma

### Dmitrij Volkov, super-Poincare group and Grassmann variables

A fundamental role of the Hermann Grassmann anticommuting variables both in
physics and mathematics is discussed on the example of supersymmetry. The talk
describes how the D. Volkov question about possibility of the existence of
Nambu-Goldstone fermions, realized by the Grassmannian variables, resulted in
the discovery of the super-Poincare group, its spontaneous breaking and
gauging.Comment: 9 pages, corrected version published in Annalen der Physik, invited
talk at the Grassmannian Conference in Fundamental Cosmology, Szczecin, 14-19
September 200

### THE NUMBER OF SPHALERON INSTABILITIES OF THE BARTNIK-McKINNON SOLITONS AND NON-ABELIAN BLACK HOLES

It is proven that there are precisely $n$ odd-parity sphaleron-like unstable
modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black
hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.Comment: one reference is adde

### On the cancellation of 4-derivative terms in the Volkov-Akulov action

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms
in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic
Nambu-Goldstone field. Here is presented a simple algebraic proof of the
cancellation based on using the Majorana bispinors and Fiertz identities. The
cancellation shows a difference between the Volkov-Akulov action and the
effective superfield action recently studied by Komargodski and Seiberg and
containing one 4-derivative term. We find out that the cancellation effect
takes place in coupling of the Nambu-Goldstone fermion with the Dirac field.
Equivalence between the KS and the VA Lagrangians is proved up to the first
order in the interaction constant of the NG fermions.Comment: 18 pages; the version accepted for publication in Phys. Rev. D; new
section regarding the proof of the equivalence between the
Komargodski-Seiberg and the Volkov-Akulov actions is added: some comments and
new references are include

### Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model,
where the quark loops (in the mean field approximation) and the meson loops (in
the $1/N_c$ approximation) are taken into account. We show that quark loop
contribution dominates, because the meson loops strongly conceal each other.
The sigma-pole contribution $(m^2_\sigma-t)^{-1}$ plays the main role and
contains strong t-dependence of the effective pion polarizability at the region
$|t|\geq 4M_\pi^2$. Possibilities of experimental test of this sigma-pole
effect in the reaction of Coulomb Nuclear Scattering are estimated for the
COMPASS experiment.Comment: 11 pages, 8 figure

### Abelian Current Algebra and the Virasoro Algebra on the Lattice

We describe how a natural lattice analogue of the abelian current algebra
combined with free discrete time dynamics gives rise to the lattice Virasoro
algebra and corresponding hierarchy of conservation laws.Comment: 11 pages, LATEX, HU-TFT-93-2

### Supersymmetric Model with Grassmann-odd Lagrangian

A supersymmetric $D = 1, N =1$ model with a Grassmann-odd Lagrangian is
proposed which, in contrast to the model with an even Lagrangian, contains not
only a kinetic term but also an interaction term for the coordinates entering
into one real scalar Grassmann-even (bosonic) superfield.Comment: 6 pages, LATEX 2e. The talk given at the International Conference
"Supersymmetries and Quantum Field Theory" (SSQFT'2000, NSC KIPT, Kharkov,
Ukraine, 25-29 July, 2000). To be published in the Proceedings of this
Conference. Corrections of misprint

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