293 research outputs found
Qualitative solution of QCD sum rules
We show how such important features of QCD as chiral symmetry breaking or the
formation of a mass-gap can be directly traced from QCD sum rules for two point
functions assuming, in the large number of colors limit, exact duality between
the operator product expansion and the spectrum described by linearly (or
nearly linear) rising Regge trajectories as predicted by string theory. We see
how the presence of chiral symmetry breaking is intimately related to
confinement in this scenario, as expected from general arguments, and how Regge
trajectories change when chiral symmetry is broken. As a result the whole meson
mass spectrum can be parametrized with a good accuracy by the constant
only, thus realizing the program proposed by Migdal some time ago.Comment: Version published in JHE
The Extended Chiral Quark Model confronts QCD
We discuss the truncation of low energy effective action of QCD below the
chiral symmetry breaking (CSB) scale, including all operators of dimensionality
less or equal to 6 which can be built with quark and chiral fields. We perform
its bosonization in the scalar, pseudoscalar, vector and axial-vector channels
in the large-N_c and leading-log approximation. Constraints on the coefficients
of the effective lagrangian are derived from the requirement of Chiral Symmetry
Restoration (CSR) at energies above the CSB scale in the scalar-pseudoscalar
and vector-axial-vector channels, from matching to QCD at intermediate scales,
and by fitting some hadronic observables. In this truncation two types of
pseudoscalar states (massless pions and massive Pi'-mesons), as well as a
scalar, vector and axial-vector one arise as a consequence of dynamical chiral
symmetry breaking. Their masses and coupling constants as well as a number of
chiral structural constants are derived. A reasonable fit of all parameters
supports a relatively heavy scalar meson (quarkonium) with the mass \sim 1 GeV
and a small value of axial pion-quark coupling constant g_A \simeq 0.55.Comment: Talk at QCD99, Montpellier, July 1999, 7 pages, Late
Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
We give the classification of second-order polynomial SUSY Quantum Mechanics
in one and two dimensions. The particular attention is paid to the irreducible
supercharges which cannot be built by repetition of ordinary Darboux
transformations. In two dimensions it is found that the binomial superalgebra
leads to the dynamic symmetry generated by a central charge operator.Comment: 10 pages, LaTeX, preprint SPbU-IP-94-0
Structural Vertices of Extended SU(3)-Chiral Lagrangians in the Large-N_c Approach
The main goal of this paper is to elaborate the model-framework
parametrization of effective coupling constants of the extended chiral
lagrangian which is suitable for the description of the low-energy matrix
elements of vector, axial-vector, scalar and pseudoscalar currents as well as
of the matrix elements of the pseudoscalar gluon density. We establish the
connection between the structural coupling constants of the phenomenological
chiral lagrangian and the coefficients of effective lagrangians obtained in the
QCD-bosonization models by means of the derivative expansion. The large-N_c
relations for corresponding structural constants are elaborated. On this way we
find the new set of OZI rules. In particular, one of them predicts the
branching ratio of the decays or .Comment: 7 pages, LaTeX, Preprint SPbU-IP-94-1, Talk at the Workshop on Chiral
Perturbation Theory and Other Effective Theories (Karreb{\ae}ksminde,
Denmark, Sept.1993
Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in
one-dimensional QM. Its structure is determined by the type of conjugation
operation (Hermitian conjugation or transposition) and described with the help
of the Super-Hamiltonian projection on the zero-mode subspace of a supercharge.
We show that the SUSY algebra with transposition symmetry is always polynomial
in the Hamiltonian if supercharges represent differential operators of finite
order. The appearance of the extended SUSY with several (complex or real)
supercharges is analyzed in details and it is established that no more than two
independent supercharges may generate a Nonlinear superalgebra which can be
appropriately specified as {\cal N} = 2 SUSY. In this case we find a
non-trivial hidden symmetry operator and rephrase it as a non-linear function
of the Super-Hamiltonian on the physical state space. The full {\cal N} = 2
Non-linear SUSY algebra includes "central charges" both polynomial and
non-polynomial (due to a symmetry operator) in the Super-Hamiltonian.Comment: 28 pages, Latex, minor improvements and removed misprint
On the possibility of P-violation at finite baryon-number densities
We show how the introduction of a finite baryon density may trigger
spontaneous parity violation in the hadronic phase of QCD. Since this involves
strong interaction physics in an intermediate energy range we approximate QCD
by a \sigma model that retains the two lowest scalar and pseudoscalar
multiplets. We propose a novel mechanism based on interplay between lightest
and heavy meson states which cannot be realized solely in the Goldstone boson
(pion) sector and thereby is unrelated to the one advocated by Migdal some time
ago. Our approach is relevant for dense matter in an intermediate regime of few
nuclear densities where quark percolation does not yet play a significant role.Comment: 9 pages, reduced to publish in Phys.Lett.B, a relevant ref. is added
and the title is changed as compared to previous version
Patterns of Lorentz symmetry breaking in QED by CPT-odd interaction
A tiny Lorentz symmetry breaking can be mediated in Electrodynamics by means
of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its
presence makes the vacuum optically active that has been recently estimated
from astrophysical data. We examine two possibilities for the CS vector to be
time-like or space-like, under the assumption that it originates from v.e.v. of
some pseudoscalar matter. It is shown that: a) a time-like CS vector makes the
vacuum unstable under pairs creation of tachyonic photon modes with the finite
vacuum decay rate, i.e. it is unlikely realized at macroscopic time scales; b)
on the contrary, the space-like CS vector does not yield any tachyonic modes
and, moreover, if its dynamical counterpart is substantially described by a
scale invariant interaction, then the QED radiation effects induce the
dynamical breaking of Lorentz symmetry, i.e. the occurrence of space-like CS
vector appears to be rather natural.Comment: 9 pages, LaTeX, version to appear in Phys.Lett.
Local realizations of -Oscillators in Quantum Mechanics
Representations of the quantum q-oscillator algebra are studied with
particular attention to local Hamiltonian representations of the Schroedinger
type. In contrast to the standard harmonic oscillators such systems exhibit a
continuous spectrum. The general scheme of realization of the q-oscillator
algebra on the space of wave functions for a one-dimensional Schroedinger
Hamiltonian shows the existence of non-Fock irreducible representations
associated to the continuous part of the spectrum and directly related to the
deformation. An algorithm for the mapping of energy levels is described.Comment: 12 pages, LaTeX, Phys. Lett. A, to be publishe
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples
Matching Regge Theory to the OPE
The spectra of masses and decay constants for non-strange meson resonances in
the energy range 0--2.5 GeV is analyzed. It is known from meson phenomenology
that for given quantum numbers these spectra approximately follow linear
trajectories with a universal slope. These facts can be understood in terms of
an effective string description for QCD. For light meson states the
trajectories deviate noticeably from the linear behavior. We investigate the
possible corrections to the linear trajectories by matching two-point
correlators of quark currents to the Operator Product Expansion (OPE). We find
that the allowed modifications to the linear Regge behavior must decrease
rapidly with the principal quantum number. After fitting the lightest states in
each channel and certain low-energy constants the whole spectrum for meson
masses and residues is obtained in a satisfactory agreement with phenomenology.
We briefly speculate on possible implications for the QCD effective string.Comment: 24 pages, Latex, significant changes in discussion of fits, more refs
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