Effect of SUSY phases on the Bd0−Bˉd0B^0_d - \bar{B}^0_d mixing in the minimal supergravity model

We investigate the effect of SUSY phases ($\theta_A$ and $\theta_\mu$) on the $B^0_d - \bar{B}^0_d$ mixing in the minimal supergravity model. It is known that the complex phase $\theta_A$ $=$ arg($A$) ($A$ is the universal coefficient of the trilinear scalar couplings) is essentially unconstrained by the electric dipole moment experiment, while the phase $\theta_\mu$ $=$ arg($\mu$) ($\mu$ is the supersymmetric Higgsino mass) is strongly constrained to zero. We found that $\theta_A$ does not affect the phase of the $B^0_d - \bar{B}^0_d$ mixing matrix element $M_{12}(B)$ by numerical analysis of the renormalization group equations. This means that the measurement of the $B^0_d - \bar{B}^0_d$ mixing at the future B-factory could give the direct information on the parameters of the CKM matrix even in the framework of the minimal supergravity model with the SUSY phase $\theta_A$.Comment: 12 pages, 3 figure

Suppression of the neutralino relic density with supersymmetric CP violation

We study pair annihilations of the neutralino dark matter in the minimal supersymmetric standard model with CP violation. We consider the case that the higgsino mass and the trilinear scalar couplings have CP-violating phases of order unity, taking a scenario that the scalar fermions in the first two generations are much heavier than those in the third generation to avoid a severe constraint from experimental limits on electric dipole moments. It is found that, when the lightest neutralino ($\chi$) is bino-like, the cross sections of the $W$-boson pair production $\chi\chi$ $\to$ $W^+W^-$ and the lightest Higgs boson pair production $\chi\chi$ $\to$ $H^0_2 H^0_2$ for nonrelativistic neutralinos can be significantly enhanced by the phase of the higgsino mass. The relic density of the neutralino can be considerably suppressed by this effect. However, even this suppression is not enough to make bino-like dark matter consistent with a cosmological constraint. We also discuss the effect of CP violation on the positron flux from neutralino pair annihilations in the galactic halo.Comment: 37 pages, 16 figures. Numerical erros are corrected in the new versio

A trajectory mechanics approach for the study of wave propagation in an anisotropic elastic medium

We derive equations describing the path and traveltime of a coherent elastic wave propagating in an anisotropic medium, generalizing expressions from conventional high-frequency asymptotic ray theory. The methodology is valid across a broad range of frequencies and allows for subwavelength variations in the material properties of the medium. The primary difference from current ray methods is the retention of a term that is neglected in the derivation of the eikonal equation. The additional term contains spatial derivatives of the properties of the medium and of the amplitude field, and its presence couples the equations governing the evolution of the amplitude and phase along the trajectory. The magnitude of this term provides a measure of the validity of expressions based upon high-frequency asymptotic methods, such as the eikonal equation, when modelling wave propagation dominated by a band of frequencies. In calculations involving a layer with gradational boundaries, we find that asymptotic estimates do deviate from those of our frequency-dependent approach when the width of the layer boundaries become sufficiently narrow. For example, for a layer with boundaries that vary over tens of meters, the term neglected by a high-frequency asymptotic approximation is significant for frequencies around 10 Hz. The visible differences in the paths of the rays that traverse the layer substantiate this conclusion. For a velocity model derived from an observed well log, the majority of the trajectories calculated using the extended approach, accounting for the frequency-dependence of the rays, are noticeably different from those produced by the eikonal equation. A suite of paths from a source to a specified receiver, calculated for a range of frequencies between 10 and 100 Hz, define a region of sensitivity to velocity variations and may be used for an augmented form of tomographic imaging