Some aspects of global Lambda polarization in heavy-ion collisions

Large orbital angular momentum can be generated in non-central heavy-ion collisions, and part of it is expected to be converted into final particle's polarization due to the spin-orbit coupling. Within the framework of A Multi-Phase Transport (AMPT) model, we studied the vorticity-induced polarization of $\Lambda$ hyperons at the midrapidity region $|\eta|<1$ in Au-Au collisions at energies $\sqrt{s_{NN}}=7.7\sim200$ GeV. Our results show that the global polarization decreases with the collisional energies and is consistent with the recent STAR measurements. This behavior can be understood by less asymmetry of participant matter in the midrapidity region due to faster expansion of fireball at higher energies. As another evidence, we discuss how much the angular momentum is deposited in different rapidity region. The result supports our asymmetry argument.Comment: 6 pages, 4 figures, CPOD 2017 proceedin

B→SB\to S Transition Form Factors in the PQCD approach

Under two different scenarios for the light scalar mesons, we investigate the transition form factors of $B(B_s)$ mesons decay into a scalar meson in the perturbative QCD approach. In the large recoiling region, the form factors are dominated by the short-distance dynamics and can be calculated using perturbation theory. We adopt the dipole parametrization to recast the $q^2$ dependence of the form factors. Since the decay constants defined by the scalar current are large, our predictions on the $B\to S$ form factors are much larger than the $B\to P$ transitions, especially in the second scenario. Contributions from various light-cone distribution amplitudes (LCDAs) are elaborated and we find that the twist-3 LCDAs provide more than a half contributions to the form factors. The two terms of the twist-2 LCDAs give destructive contributions in the first scenario while they give constructive contributions in the second scenario. With the form factors, we also predict the decay width and branching ratios of the semileptonic $B\to Sl\bar\nu$ and $B\to Sl^+l^-$ decays. The branching ratios of $B\to Sl\bar\nu$ channels are found to have the order of $10^{-4}$ while those of $B\to Sl^+l^-$ have the order of $10^{-7}$. These predictions can be tested by the future experiments.Comment: 20 pages, 31 figure

Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.Comment: 24 page