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 $\Gamma$. 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 $N$, $\Delta$, $\Sigma$, $\Lambda$ and $\Lambda_c$ 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 $H(z)$ and cosmic microwave background constraints are described with different cosmological models. We compare the $\Lambda$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 $r_s(z_d)$. Among the considered models the best value of $\chi^2$ is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the $\Lambda$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 $q$-$q$-$q$ 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 $\Delta$) 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 $\Delta$ 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 $n=3$ massive points (quarks): Y configuration, linear baryon model $q$-$q$-$q$ 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