Spin correlations in polarizations of P-wave charmonia χcJ\chi_{cJ} and impact on J/ψJ/\psi polarization

Based on a general form of the effective vertex functions for the decays of P-wave charmonia \chicj, angular distribution formulas for the subsequent decays \chicj\rightarrow \jpsi \gamma and \jpsi \to \mu^+\mu^- are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of \jpsi and muon in the cascade decay \chicj\to\jpsi\gamma\to\mu^+\mu^-\gamma. The \chicj polarization observables are expressed in terms of rational functions of the spin density matrix elements of \chicj production. Generalized rotation-invariant relations for arbitrary integer-spin particles are also derived and their expressions in terms of observable angular distribution parameters are given in the $\chi_{c1}$ and $\chi_{c2}$. To complement our previous direct-\jpsi polarization result, we also discuss the impact on the observable prompt-\jpsi polarization. As an illustrative application of our angular distribution formulas, we present the angular distributions in terms of the tree-level spin density matrix elements of $\chi_{c1}$ and $\chi_{c2}$ production in several different frames at the Large Hadron Collider. Moreover, a reweighting method is also proposed to determine the entire set of the production spin density matrix elements of the $\chi_{c2}$, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.Comment: Version published in PRD, 23 pages, 18 figure

Propagation of Gevrey regularity for solutions of Landau equations

By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian molecules and hard potential

Gevrey Regularity for Solution of the Spatially Homogeneous Landau Equation

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case

Real-time image difference detection using a polarization rotation spacial light modulator

An image difference detection system is described, of the type wherein two created image representations such as transparencies representing the images to be compared lie coplanar, while light passes through the two transparencies and is formed into coincident images at the image plane for comparison. The two transparencies are formed by portions of a polarization-rotation spatial light modulator display such as a multi-pixel liquid crystal display or a magnetooptical rotation type display. In a system where light passing through the two transparencies is polarized in transverse directions to enable the use of a Wollaston prism to bring the images into coincidence, a liquid crystal display can be used which is devoid of polarizing sheets that would interfere with transverse polarizing of the light passing through the two transparencies

Real-time optical multiple object recognition and tracking system and method

The invention relates to an apparatus and associated methods for the optical recognition and tracking of multiple objects in real time. Multiple point spatial filters are employed that pre-define the objects to be recognized at run-time. The system takes the basic technology of a Vander Lugt filter and adds a hololens. The technique replaces time, space and cost-intensive digital techniques. In place of multiple objects, the system can also recognize multiple orientations of a single object. This later capability has potential for space applications where space and weight are at a premium

Analytic smoothness effect of solutions for spatially homogeneous Landau equation

In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under rather weak assumptions on the initial datum.Comment: 16 page