Possible altitudinal, latitudinal, and directional dependence of the relativistic Sagnac effect in Chern-Simons modified gravity
Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada,  (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.

title: Uniqueness of collinear solutions for the relativistic three-body problem
abstract: Continuing work initiated in an earlier publication [Yamada, Asada,  104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow-motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points L{sub 1}, L{sub 2}, and L{sub 3}. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end lengthmore » is shorter than the Newtonian one.« less

title: Three-body-interaction effects on the relativistic perihelion precession for the Sun-Jupiter-Saturn system
abstract: The relativistic perihelion precession due to the three-body interaction is derived. We consider a hierarchical coplanar three-body system, such as the Sun, Jupiter and Saturn, in which both the secondary object as the largest planet corresponding to Jupiter (mass $m_2$) and the third one corresponding to Saturn (mass $m_3$) orbit around the primary object corresponding to Sun (mass $m_1 \gg m_2 \gg m_3$), where the mean orbital radius of the third body is larger than that of the secondary one (denoted as $\ell$). We investigate the post-Newtonian effects on the motion of the third body (semimajor axis a, eccentricity e for the Keplerian orbital elements). Under some assumptions with a certain averaging, the relativistic perihelion precession of the third mass by the post-Newtonian three-body interaction is expressed as $6 G m_2 \ell^2 c^{-2} a^{-3} n (1+9e^2/16) (1-e^2)^{-3} $, where G and c denote the gravitational constant and the speed of light, respectively, and the mean motion for the third body is denoted as $n = 2\pi a^{3/2} G^{-1/2} (m_1+m_2)^{-1/2}$. For the Sun-Jupiter-Saturn system, it is $7.8 \times 10^{-6}$ arcsec/cy. This is larger than the Lense-Thirring effect by Sun but it cannot yet explain the recently reported value for the anomalous perihelion precession of Saturn as $-0.006 \pm 0.002$ arcsec/cy by Iorio (2009) based on the analyses by Pitjeva with the EPM2008 ephemerides.

title: Post-Newtonian effects of planetary gravity on the perihelion shift
abstract: We consider a coplanar system comprising of a massive central body (a star), a less massive secondary (a planet) on a circular orbit, and a test particle on a bound orbit exterior to that of the secondary. The gravitational pull exerted on the test particle by the secondary acts as a small perturbation, wherefore the trajectory of the particle can be described as an ellipse of a precessing perihelion. While the apsidal motion is defined overwhelmingly by the Newtonian portion of the secondary’s gravity, the post-Newtonian portion, too, brings its tiny input. We explore whether this input may be of any astrophysical relevance in the next few decades. We demonstrate that the overall post-Newtonian input of the secondary’s gravity can be split into two parts. One can be expressed via the orbital angular momentum of the secondary and another via its orbital radius. Despite some moderately large numerical factors showing up in the expressions for these two parts, the resulting post-Newtonian contributions from the secondary’s gravity into the apsidal motion of the test particle turn out to be small enough to be neglected in the near-future measurements.

title: Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
abstract: Continuing work initiated in earlier publications [Yamada, Asada,  104019 (2010); ibid.83, 024040 (2011)], we investigate the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that the equilateral triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if all three masses are equal. When a test mass is included, the equilateral configuration is possible for two cases: (1) one mass is finite and the other two are zero, or (2) two of the masses are finite and equal, and the third one is zero, namely, a symmetric binary with a test mass. The angular velocity of the post-Newtonian equilateral triangular configuration is always smaller than the Newtonian one, provided that the masses and the side length are the same.

title: Moment Approach to Determining the Orbital Elements of an Astrometric Binary with a Low Signal-to-Noise Ratio
abstract: A moment approach to the orbit determination of an astrometric binary with a low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period, such as Cyg X-1, and also at a star wobbled by planets. As an exact solution to the nonlinearly coupled equation, the orbital elements are written in terms of the second and third moments of projected positions that are measured by astrometry. This may hold the possibility of the true orbit estimate.

title: Candidates for Chiral Particles
abstract: We find possible candidates for the new type of q bar q meson, mesonic chiralons, whose existence is predicted in the covariant level-classification scheme of hadrons with U(12)_SF * O(3,1)_L symmetry, by assigning all the known light-unflavored and strange mesons, with masses below about 1.8 GeV, to U(12)_SF * O(3,1)_L multiplets.

title: Light-quark meson spectrum in the covariant oscillator quark model with one-gluon-exchange effects
abstract: The covariant oscillator quark model, which was extended recently to include one-gluon-exchange effects, is applied to investigate the mass spectrum of light-quark mesons. In the meson rest frame our effective potential due to one-gluon exchange is given as the sum of a Coulomb-type, orbit-orbit-like, spin-orbit, and hyperfine interaction, and has similar general features as in the standard nonrelativistic quark model. However, there are essential differences between them. First, our scheme is manifestly covariant and the potential is concerned with the squared masses of hadrons. Second, our effective one-gluon-exchange potential is greatly modified due to the covariant nature and the retardation effect. Owing to these modifications our model reproduces quite well the experimental behavior of the spectra of radially excited states as well as orbitally excited states.

title: One-gluon exchange effects on linear meson trajectories in the covariant oscillator quark model
abstract: SummaryWe investigate one-gluon exchange effects on the linear Regge trajectories of all quark-antiquark meson systems, from light through heavy quarks, in the framework of the covariant oscillator quark model. This model gives linearly rising trajectories to both orbitally and radially excited states in the limit of neglecting perturbative QCD effects. We find that the spin-independent one-gluon exchange interaction barely affects the orbital excitations, preserving the well-known linearity of the leading Regge trajectories, but for the radial excitations it makes an appropriate contribution, in conformity with the observed behaviour largely deviating from the linear trajectories. We also calculate the hyperfine mass splittings of all ground-stateS-wave mesons. For as yet unknown mass splittings, we findM(B*c)−M(Bc)≈50 MeV andM(Y)−M(ηb)≈49 MeV.

title: HYBRID MESONS AND DOUBLING OF THE FOUR FLAVOR NONETS WITH J(PC) = (0,1,2)++ AND 1+-: THREE RELATED TALKS PRESENTED AT HADRON '89

title: On the existence of light-scalar mesons kappa(800) and kappa-prime(1150): The ~U(12) scheme and BES II data
abstract: We present that there should exist a light strange-scalar meson kappa', in addition to the kappa(800), which has a mass around 1.1-1.2 GeV, a rather narrow width, and couples strongly to kappa(800)sigma(600) (Kpipipi) but weakly to Kpi, based upon the U~(12)-classification scheme of hadrons and BES II data on J/psi -> barK*(892)0K+pi- decay.