596 research outputs found
String Models, Stability and Regge Trajectories for Hadron States
Various string models of mesons and baryons include a string carrying 2 or 3
massive points (quarks or antiquarks). Rotational states (planar uniform
rotations) of these systems generate quasilinear Regge trajectories and may be
used for describing excited hadron states on these trajectories. For different
string models of baryon we are to solve the problem of choice between them and
the stability problem for their rotational states. An unexpected result is that
for the Y string baryon model these rotations are unstable with respect to
small disturbances on the classical level. This instability has specific
feature, disturbances grow linearly, whereas for the linear string baryon model
they grow exponentially and may increase predictions for baryon's width
. The classical instability of rotational states and nonstandard Regge
slope are the arguments in favor of the stable simplest model of string with
massive ends both for baryons and mesons. Rotational states of this model with
two types of spin-orbit correction are used to describe Regge trajectories for
light, strange, charmed, bottom mesons and for , , ,
and baryons.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1004.151
Quasirotational Disturbances of the Relativistic String with Massive Ends and Higher Radial Excitations of Hadrons
For the relativistic string with massive ends the small disturbances of its
rotational motion (quasirotational states) are investigated. They are presented
in the form of Fourier series with the two types of oscillatory modes. They
have the form of stationary waves correspondently in the rotational plane and
in the orthogonal direction. The calculated values of the energy and angular
momentum of these states give us possibility to describe higher radial
excitations for hadrons with the help of the planar quasirotational oscillatory
modes of the string with massive ends.Comment: 10 pages, no figures, LaTe
Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state
Observational manifestations of accelerated expansion of the universe, in
particular, recent data for Type Ia supernovae, baryon acoustic oscillations,
for the Hubble parameter and cosmic microwave background constraints are
described with different cosmological models. We compare the CDM, the
models with generalized and modified Chaplygin gas and the model with quadratic
equation of state. For these models we estimate optimal model parameters and
their permissible errors with different approaches to calculation of sound
horizon scale . Among the considered models the best value of
is achieved for the model with quadratic equation of state, but it has
2 additional parameters in comparison with the CDM and therefore is
not favored by the Akaike information criterion.Comment: 20 pages, 4 figures, revised version for JCA
Quasirotational Disturbances of Linear String Baryon Configuration
For the linear string baryon model -- the small disturbances of its
rotational motion (quasirotational states) are investigated. The spectrum of
these states is obtained in the form of Fourier series and the complex
eigenfrequencies are found in this spectrum. So the classic rotational motions
of the linear string baryon model are unstable (unlike the similar motions for
the string with massive ends). This instability differs from its analog for the
three-string baryon model.Comment: 9 pages, no figures, LaTe
Instability of Classic Rotational Motion for Three-String Baryon Model
The dynamics of baryon string model Y (three-string) is considered with using
the approach that implies defining a classical motion of the system on the base
of given initial position and initial velocities of string points. The analysis
resulted, in particular, in the necessity of regarding more wide (than it was
supposed earlier) class of parametrizations of the world surface for the
adequate description of the three-string model. This approach let us to
ascertain that the classic rotational motions (flat uniform rotations) for this
string configuration are unstable. Any small asymmetric disturbances grow and
inevitably result in falling a quark into the junction.Comment: 8 pages, 3 figures, LaTe
Excited States of Rotating Relativistic String with Massive Ends
For the relativistic string with massive ends arbitrary small disturbances of
the uniform rotation of the rectilinear string are investigated. There are two
classes of these oscillations with different spectra of frequencies. They are
stationary waves oscillating in the rotational plane and in the orthogonal
direction. These states are presented in the form of Fourier series that helps
to quantize string excitations in the linear vicinity of the classical
rotation. These string oscillations may be applied to describing daughter Regge
trajectories in the framework of the considered modelComment: 12 pages, no figures, LaTeX, submitted to Theor. Math. Phy
Quasirotational Motions and Stability Problem in Dynamics of String Hadron Models
For the relativistic string with massive ends (the meson model) and four
various string baryon models (q-qq, q-q-q, Y and ) we consider the
classical quasirotational motions, which are small disturbances of the planar
uniform rotations of these systems. For the string meson model the two types of
these solutions are obtained. They describe oscillatory motions in the form of
stationary waves in the rotational plane and in the orthogonal direction. This
approach and the suggested method of determining an arbitrary motion of the
system on the base of initial data let us solve the stability problem for the
rotational motions for all mentioned string configurations. It is shown that
the classic rotational motions are {\it stable} for the string meson model (or
its analog q-qq) and for the baryon configuration, but they are {\it
unstable} for the string baryon models Y and q-q-q. For the latter two systems
any small asymmetric disturbances grow with growing time. The motion of the
q-q-q configuration become more complicated and quasiperiodic but quarks do not
merge. In the case of Y model the evolution of disturbances results in falling
a quark into the junction. These features of the classic behavior are important
for describing the hadron states on the Regge trajectories and for choosing and
developing the most adequate QCD-based string hadron models.Comment: 11 pages, 5 figures, RevTe
Unstable States for Closed String with Massive Point
The stability problem for the hypocycloidal rotational states of the closed
relativistic string with a point-like mass is solved with the help of analysis
of small disturbances of these states. Both analytical and numerical
investigations showed an unexpected result: the mentioned states turned out to
be unstable. This conclusion is based upon the presence of roots with positive
imaginary parts (increments) in the spectrum of frequencies of small
disturbances. But these increments were small enough, so this instability had
not been detected in previous numerical experiments. For the linear rotational
states (the particular case of hypocycloidal states) the stability was
confirmed. These results are important for applications of this model in hadron
spectroscopy.Comment: 9 pages, 4 figure
String Baryon Model "Triangle": Hypocycloidal Solutions
The considered model of baryon consists of three pointlike masses (quarks)
bounded pairwise by relativistic strings forming a curvilinear triangle.
Classic analytic solutions for this model corresponding to a planar uniform
rotation about the system center of mass are found and investigated. These
solutions describe a rotating curve composed of segments of a hypocycloid. The
curve is a curvilinear triangle or --- a more complicated configuration with a
set of internal massless points moving at the speed of light. Different
topological types of these motions are classified in connection with different
forms of hypocycloids in zero quark mass limit. An application of these
solutions to description of baryon states on the Regge trajectories is
considered.Comment: 9 pages, 2 figures, LaTeX, to appear in Rhys. Rev.
Contribution to Hadrons' Width from Classical Instability of Y Configuration and Other String Hadron Models
We consider various hadron models with a string carrying massive points
(quarks): Y configuration, linear baryon model -- and the closed
string. For these models classical rotational states (planar uniform rotations)
are tested for stability with respect to small disturbances. It is shown that
rotations of all mentioned models are unstable, but nature of this instability
is different. For the model Y the instability results from existence of
multiple real frequencies in the spectrum of small disturbances, but for the
linear model and the closed string the similar spectra contain complex
frequencies, corresponding to exponentially growing modes of disturbances. This
classical rotational instability is important for describing excited hadrons,
in particular, for the linear model and the closed string it results in
additional contribution in width of hadron states.Comment: 12 pages, 7 figures, REVTe
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