Improving the moment approach for astrometric binaries: possible application to Cygnus X-1
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: 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: 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: Possible altitudinal, latitudinal, and directional dependence of the relativistic Sagnac effect in Chern-Simons modified gravity
abstract: 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: Triangular solution to the general relativistic three-body problem for general masses
abstract: Continuing work initiated in an earlier publication [Ichita, Yamada and Asada,  (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that a triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if it has the relativistic corrections to each side length. This post-Newtonian configuration for three finite masses is not always equilateral and it recovers previous results for the restricted three-body problem when one mass goes to zero. For the same masses and angular velocity, the post-Newtonian triangular configuration is always smaller than the Newtonian one.

title: Collinear solution to the general relativistic three-body problem
abstract: The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence, it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L{sub 1}, L{sub 2}, and L{sub 3} are also evaluated.

title: Radiative Decays of Ground-State Mesons in the Covariant Quark Model

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: Radiative Decays of q bar q Chiral States in the U~(12)-Scheme
abstract: The radiative transitions between ground-states (GS) of light q bar q mesons are investigated in the U~(12)-scheme. In this scheme the rich decay-spectra are offered even in transition between GS due to the appearance of chiral states. As a result the radiative decay widths of the ordinary V -> P gamma process are well reproduced, and furthermore, the predicted width of b_{1}(1235) -> pi gamma process (Gamma_{theor}=229 keV), by assigning b_{1}(1235) as a member of the {}^{3}S_{1} chiral states A^{(E)}, is in good agreement with experimental one (Gamma_{exp} =230 +- 60 keV). From this results it is indicated that b_{1}(1235) meson, classified as {}^{1}P_{1} state in conventional non-relativistic (NR) classification scheme, is a good candidate of chiral state in the U~(12)-scheme. The other radiative transition widths of some chiral states are also predicted. Accordingly the predicted values given here, will provide useful insights in their search at BES.