Instability of string models of baryons: Character and manifestations

The character of the instability of a rotational state (rotation of the system at a constant speed) against small perturbations is studied in detail for the Y string model of the baryon. It is shown that the existing instability is due to the presence of repeated real-valued frequencies in the spectrum of small perturbations and that there are no complex-valued frequencies in this spectrum. This leads to a linear growth of small-perturbation amplitudes. A comparison of the Y configuration with the q-q-q linear string model of the baryon reveals a difference in the character of the instability of rotational states of these systems and in the manifestations of this instability. In particular, there are exponentially growing modes in the excitation spectrum of the linear model, which lead to an additional contribution to the baryon-state width.     

Instability of the Y string baryon model within classical dynamics

For the three-string baryon model (Y configuration), the known exact solution to the classical equations of motion that describes the rotational motion of the system at a constant speed is investigated for stability. In the spectrum of small perturbations of this solution, modes growing exponentially with time are found, whereby the instability of rotational motion is proven for the Y configuration. This result is confirmed within an alternative approach that makes it possible to determine the classical motion of the system from a specific initial position and initial velocities of string points. A comparison of the Y configuration with the model of a relativistic string with massive ends, in which case rotational motion is stable in the linear approximation, aids in revealing the most adequate string model from the point of view of describing baryon excitations on Regge trajectories.     

Proton decay in four dimensional superstring models

In this paper, we discuss the contraints that emerge from baryon nonconserving processes in theSU(4)×O(4) andSU(5)×U(1) models derived in the fermionic formulation of the four dimensional superstring. We examine dimension five baryon violating operators arising a) from Higgs exchange diagrams, and b) from non-renormalisable terms which arise from the exchange of massive string states. Both kinds of the above operators put non-trivial constraints on the matter field assignments and on the vevs of various singlet fields of the string models under consideration.     

Flavour and spin structure of linear baryons

Based on the string picture, we construct a phenomenological model for baryons and study their flavour symmetry, exchange degeneracy pattern and spin structure. Baryons on leading trajectories are assumed to have the configuration of two quarks being attached to the ends of a linear string and the third sitting in the middle, called linear baryons. For such linear baryons, a unitarization scheme can be constructed in a manner similar to the dual unitarity scheme for mesons but without recourse to the $\text{1}\text{N}$ expansion. We find that the interchange interaction of the middle quark with one of the other two quarks at the ends of the string can give rise to a large exchange degeneracy breaking of the baryon spectrum. With this non-planar correction, the model of linear baryons can account for the observed pattern of leading baryon states.     

Polyyne bending frequencies: why they vary with the square of the harmonic in the infinite limit

The vibrational frequencies of several linear polyynes HC _N H, HC _N I and IC _N I, for even-valued N up to 60, have been obtained using computational quantum chemistry. The bending normal modes have the appearance of classical transverse normal modes of a vibrating string fixed at both ends, for which the frequencies vary with the first power of the harmonic. Our calculations, however, reveal that in the limit of infinite chain length and infinite mass on the ends of the ‘molecular string’, the bending frequencies vary with the square of the harmonic, at all levels of theory. A derivation is presented to explain the discrepancy.     

Massive String Cloud Cosmologies in Saez-Ballester Theory of Gravitation

String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VI₀ metric in Saez-Ballester Scalar-Tensor theory of gravitation. The field equations are solved for massive string cloud with particles attached to them. A more general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered instead of taking any particular relationships like pure geometric string or the case of the p-string. The pure geometric string and p-string solutions can be easily inferred from the models. For all viable models the possible limiting values of the linear connection between the proper energy density and string tension density have been calculated. The physical and kinematical properties of the models have been discussed in detail.     

Some solutions of the equations of motion of the relativistic string with massive ends

The classical theory is discussed for the relativistic string with point masses at its ends. The dynamical equations are solved for the class of motions of this system when the time evolution parameter τ is the proper time of both massive string ends. In this case the solution of the boundary equations is given by the almost periodic functions. Constraints on the normal modes resulting from the orthonormal gauge conditions differ essentially from the Virasoro ones. Incidentally one obtains an exact solution for the half-infinite string with mass at one end. It is also proved that the exact solution for the string with massive ends cannot be a periodic function.     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Rosette motion and string scattering of 20 MeV electrons in MgO single crystals

Analytical estimates and computer simulations were undertaken to perceive the motion of negative particles through a lattice structure, the interaction being classical binary scattering. Three distinct modes of particle motion along atomic strings were found depending on the magnitude of the transverse energy and the angular momentum L of the particle with regard to the string axis. At small and large L increased scattering on the strings as compared with random penetration dominates. At medium L and negative transverse energy (bound state particles in the attractive potential) a rosette motion along the string occurs. In this case small impact parameters to the string atoms are avoided and thus an increased penetrability of the negative particles results. The influence of thermal lattice vibrations on these motions was studied.

Experimentally, the negative particle motion modes manifested themselves in the penetration profiles of 20 MeV electrons through an 8 μm MgO single crystal.     

Dual Superconductivity in Restricted Chromo-Dynamics (RCD)

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux), it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Originally present global SU(2) symmetry in RCD has been broken to U(1) reducing the four dimensional action to two dimensional one by using an Ansatz which incorporates a non-trivial coordinate dependent phase between the components of SU(2) doublet. Analyzing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. The conditions for this current to be maximum at a transverse distance from the string have also been obtained.     

Dirac quasinormal modes of Born-Infeld black hole spacetimes

Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.     

String junction effects for forward and central baryon production in hadron-nucleus collisions

The process of baryon number transfer due to string junction propagation in rapidity space is considered. It leads to a significant effect in the net baryon production in pA collisions at mid-rapidities and an even more significant effect in the forward hemisphere for the cases of πA interactions. The results of numerical calculations in the framework of the Quark-Gluon String Model are in reasonable agreement with the data. Special consideration is given to Λ produced in π^-A collisions extracted from the data of the WA89 Collaboration.     

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹ ₁\sigma^{1}_{~1} of the shear tensor s^j _i\sigma^{j}_{~i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.     

Chiral soliton model vs. pentaquark structure for Θ(1540)

The exotic baryon Θ⁺(1540 MeV) is visualized as an expected (iso) rotational excitation in the chiral soliton model. It is also argued as a pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast these two points of view; observe the similarities and differences between the two pictures. Collective excitation, the characteristic of chiral soliton model, points toward small mixing of representations in the wake ofSU (3) breaking. In contrast, constituent quark models prefer near ‘ideal’ mixing, similar to ω-φ mixing.     

Raman band shapes and the dynamics of liquid N2O4

The Raman spectra of the totally symmetric A _g modes, v ₁, v ₂ and v ₃, of the N₂O₄ molecule have been measured in the liquid state at 262, 279 and 297 K. The vibrational and the rotational correlation functions are calculated. The long-time exponential decay of the rotational correlation functions of all the A _g modes reflects an asymptotic diffusional behaviour of molecular reorientation. The rotational relaxation rate is found to increase with increasing temperature. A marked point of inflection from the short time inertial correlation to the long time exponential decay appears at about 0·35 ps for the v ₂ mode. This is an indication of orientational rebound arising from the librational motion in a temporary solvent cage. The isotropic bandwidth increases in the order v ₁ < v ₂ < v ₃, which is also the order of decreasing vibrational frequency. The temperature dependence of the peak frequency and of the bandwidth are also found to increase in the same order. These observations are analysed qualitatively in terms of two models of vibrational dephasing which take into account the effect of vibrational anharmonicity.     

Is there a tachyon in the Nambu-Goto string with massive ends?

The dependence of Casimir energy on quark mass is investigated in the model of relativistic strings with massive quarks attached to the ends. The quark dynamics are treated in the nonrelativistic approximation, and the equations of motion and boundary conditions are linearized. The Casimir energyE as a function of quark massm is found by two methods (numerically and analytically). Different subtraction procedures for both approaches result in different functional dependences ofE onm. But both cases have values ofm for which the Casimir energy is definitely positive. The sign of this energy is known to coincide with the sign of the squared mass of the ground state in the string spectrum. Hence, the obtained result indicates that it is possible at least in principle to solve the tachyon problem in the model of relativistic strings with massive ends.