Moment Approach to Determining the Orbital Elements of an Astrometric Binary with a Low Signal-to-Noise Ratio
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: 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: 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: 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: 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: Radiative Decays of Ground-State Mesons in the Covariant Quark Model

title: Possible Evidence for a Chiral Axial‐Vector State in the D Meson System
abstract: We reanalyze the D⋅+π− mass spectrum from CLEO II by the VMW method in order to examine the existence of a chiral axial‐vector state, which is predicted in a covariant level‐classification scheme recently proposed, other than normal orbitally‐excited P‐wave states in the D meson system. A result of the present analysis seems to suggest that there exists an extra axial‐vector meson, in addition to the two normal ones, in a similar mass region.

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.