Post-Newtonian effects of planetary gravity on the perihelion shift
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: Marginally stable circular orbit of a test body in spherically symmetric and static spacetimes
abstract: We study a marginally stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. It turns out that the metric components are separable from the constants of motion along geodesics. We show also that a metric component $g_{rr}$ with a radial coordinate $r$ does not affect MSCOs. This suggests that, as a test of gravity, any ISCO measurement may be put into the same category as gravitational redshift experiments. MSCOs for exact solutions to the Einstein's equation are also mentioned.

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: Improving the moment approach for astrometric binaries: possible application to Cygnus X-1
abstract: A moment approach for orbital determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). Through avoiding a direct use of the time-consuming Kepler equation, temporalinformationistakenintoaccount toincrease theaccuracy ofstatistical moments. As numerical tests, 100 realizations are done and the mean value and the standard deviation are also evaluated. For a semimajor axis, the difference between the mean of the recovered values and the true value decreases to less than a tenth in the case of 10000 observed points. Therefore, the present approach works better than the previous one for orbital determinations when one has a large number of observed points. The present approach is thus applicable to CygX-1.

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: Possible evidence for a chiral particle D1**chi, axial vector in the D meson system
abstract: In the covariant level-classification scheme of hadrons proposed recently, the existence of "chiral particles", scalar and axial-vector mesons as the partners of the ground-state pseudo-scalar and vector mesons, respectively, were predicted in the D and B meson systems, realizing a linear representation of chiral symmetry. In this work we reanalyze the D* pi mass spectra obtained through the Upsilon (4S) and Z0 decays to show a possibility for the D_1chi.

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.

title: Meson spectra and wave functions in a covariant version of the linear-plus-Coulomb potential quark model
abstract: We examine mass spectra and wave functions of nn, cc and bb meson systems in the covariant oscillator quark model with the four-dimensional color-Coulomb interaction and find that these spectra are described well. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model.

title: A Novel View of Exotic Hadrons and the Covariant Ũ(12)‐Classification Scheme
abstract: I classify exotic hadrons into two types, “genuine” and “hidden” exotics, and propose that the “hidden” exotics would be interpreted as “chiralons” in the Ũ(12)SF×O(3,1)L‐classification scheme of hadrons. Based upon this conjecture I investigate the mass spectrum of 1S, 1P, and 2S states for the cc system by use of a phenomenological mass formula with the spin‐dependent interactions and present possible assignments for exotic neutral charmonium‐like states which were recently discovered. It is also mentioned that some JPC‐exotic states predicted in this scheme might correspond to those found in a recent lattice QCD calculation of the charmonium spectrum.

title: A Universal Spring and Baryon Regge Trajectories
abstract: In the covariant oscillator quark model (COQM) the squared-mass spectra of cvnfined meson and baryon systems are described by harmonic oscillators. In this work we propose a hypothesis of universal spring in COQM, which predicts the respective values of oscillator quanta in terms of constituent quark masses and a spring constant. In the previous work we have examined the universality within the meson system. In this work we shall examine the universality, further, in the baryon system by comparing the predicted orbital Regge trajectories in the respective flavor channels with experiments. The spring constants in the meson and baryon systems are related mutually by a color factor obtained through heuristic arguments. It seems to us that our universality is realized experimentally for the light-quark baryons, while for the heavy-flavored baryons the experimental knowledge is too poor to lead to any definite conclusions.