The Pion Model

We revisit the problem of a mechanism that generates the mass spectrum of elementary particles. This has vexed physicists for several decades now. In this connection we deduce a formula that gives the masses of all known elementary particles, even though other quantum numbers are suppressed. These considerations become important in view of the LHC which is expected to attain 14 TeV by 2013.Comment: 10 pages late

Model-independent determination of the parity of Ξ\Xi hyperons

Based on reflection symmetry in the reaction plane, it is shown that measuring the transverse spin-transfer coefficient $K_{yy}$ in the $\bar{K}N \to K\Xi$ reaction directly determines the parity of the produced cascade hyperon in a model-independent way as $\pi_\Xi =K_{yy}$, where $\pi_\Xi =\pm 1$ is the parity. This result based on Bohr's theorem provides a completely general, universal relationship that applies to the entire hyperon spectrum. A similar expression is obtained for the photoreaction $\gamma N \to K K \Xi$ by measuring both the double-polarization observable $K_{yy}$ and the photon-beam asymmetry $\Sigma$. Regarding the feasibility of such experiments, it is pointed out that the self-analyzing property of the $\Xi$'s can be invoked, thus requiring only a polarized nucleon target.Comment: 4 pages, REVTeX, to be published in Phys. Rev.

Two-neutron halo nuclei in one dimension: dineutron correlation and breakup reaction

We propose a simple schematic model for two-neutron halo nuclei. In this model, the two valence neutrons move in a one-dimensional mean field, interacting with each other via a density-dependent contact interaction. We first investigate the ground state properties, and demonstrate that the dineutron correlation can be realized with this simple model due to the admixture of even- and odd-parity single-particle states. We then solve the time-dependent two-particle Schr\"odinger equation under the influence of a time-dependent one-body external field, in order to discuss the effect of dineutron correlation on nuclear breakup processes. The time evolution of two-particle density shows that the dineutron correlation enhances the total breakup probability, especially for the two-neutron breakup process, in which both the valence neutrons are promoted to continuum scattering states. We find that the interaction between the two particles definitely favours a spatial correlation of the two outgoing particles, which are mainly emitted in the same direction.Comment: 17 pages, 11 figure

Soft-core meson-baryon interactions. I. One-hadron-exchange potentials

The Nijmegen soft-core model for the pseudoscalar-meson baryon interaction is derived, analogous to the Nijmegen NN and YN models. The interaction Hamiltonians are defined and the resulting amplitudes for one-meson-exchange and one-baryon-exchange in momentum space are given for the general mass case. The partial wave projection is carried through and explicit expressions for the momentum space partial wave meson-baryon potentials are presented.Comment: 25 pages, 2 PostScript figures, revtex4, submitted to Phys. Rev.

One loop corrections to quantum hadrodynamics with vector mesons

The renormalized elastic $\pi\pi$ scattering amplitude to one loop is calculated in the chiral limit in the $\sigma$ model and in a Quantum Hadrodynamic model (QHD-III) with vector mesons. It is argued that QHD-III reduces to the linear $\sigma$ model in the limit that the vector meson masses become large. The pion decay constant is also calculated to 1-loop in the $\sigma$ model, and at tree level in QHD-III; it is shown that the coefficient of the tree level term in the scattering amplitude equals $F_\pi^{-2}$. The 1-loop correction of $F_\pi$ in QHD-III violates strong isospin current conservation. Thus,it is concluded that QHD-III can, at best, only describe the strongly interacting nuclear sector.Comment: 6 page

Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.Comment: Revtex4, 10 pages including 10 figures; corrected a sign error in Eq. 32; this is the final published versio

Reformulating the Schrodinger equation as a Shabat-Zakharov system

We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ODE.Comment: 18 pages, plain LaTe

Loop Quantum Gravity Modification of the Compton Effect

Modified dispersion relations(MDRs) as a manifestation of Lorentz invariance violation, have been appeared in alternative approaches to quantum gravity problem. Loop quantum gravity is one of these approaches which evidently requires modification of dispersion relations. These MDRs will affect the usual formulation of the Compton effect. The purpose of this paper is to incorporate the effects of loop quantum gravity MDRs on the formulation of Compton scattering. Using limitations imposed on MDRs parameters from Ultra High Energy Cosmic Rays(UHECR), we estimate the quantum gravity-induced wavelength shift of scattered photons in a typical Compton process. Possible experimental detection of this wavelength shift will provide strong support for underlying quantum gravity proposal.Comment: 12 pages, 2 eps figures, revised versio

Precise method for the determination of the neutron electric form factor based on a relativistic analysis of the process $d(e,e'n)p

We generalize the recoil polarization method for the determination of the proton form factor to the case of the disintegration of vector polarized deuterons by longitudinally polarized electrons, $\vec d(\vec e, e'n)p$. We suggest to measure for this reaction, in the kinematics of quasi-elastic $en$-scattering, the ratio $R_{xz}=A_x/A_z$ of the asymmetries induced by the $x$- and $z$-components of the deuteron vector polarization. In the framework of the relativistic impulse approximation the ratio $R_{xz}$ is sensitive to $G_{En}$ in a wide interval of momentum transfer squared, whereas it depends weakly on the details of the $np$-interaction and on the choice of the deuteron wave function. Moreover, in the range $0.5\le Q^2\le$1.5 GeV$^2$, the ratio $R_{xz}$ shows a smooth dependence on $Q^2$, making the analysis simpler.Comment: 7 pages, 4 figs, 1 tabl