Isolating the chiral magnetic effect from backgrounds by pair invariant mass

Topological gluon configurations in quantum chromodynamics induce quark chirality imbalance in local domains, which can result in the chiral magnetic effect (CME)--an electric charge separation along a strong magnetic field. Experimental searches for the CME in relativistic heavy ion collisions via the charge-dependent azimuthal correlator ($\Delta\gamma$) suffer from large backgrounds arising from particle correlations (e.g. due to resonance decays) coupled with the elliptic anisotropy. We propose differential measurements of the $\Delta\gamma$ as a function of the pair invariant mass ($m_{\rm inv}$), by restricting to high $m_{\rm inv}$ thus relatively background free, and by studying the $m_{\rm inv}$ dependence to separate the possible CME signal from backgrounds. We demonstrate by model studies the feasibility and effectiveness of such measurements for the CME search.Comment: 16 preprint pages 5 figures. v2: added a test with a broad "instanton/sphaleron" peak, and added clarifying texts; v3: added event-shape engineering (and two new figures) and expanded discussions on the low invariant mass region; v4: repeated cautionary discussions in introduction and conclusion sections, published versio

M\"obius and Laguerre geometry of Dupin Hypersurfaces

In this paper we show that a Dupin hypersurface with constant M\"{o}bius curvatures is M\"{o}bius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al on the classification of Dupin hypersurfaces.Comment: 45 pages. arXiv admin note: text overlap with arXiv:math/0512090 by other author

Conditional Log-Laplace Functionals of Immigration Superprocesses with Dependent Spatial Motion

A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A representation of its conditional log-Laplace functionals is established, which gives the uniqueness of the solution and hence its Markov property. Some properties of the superprocess including an ergodic theorem are also obtained