Optimizing momentum resolution with a new fitting method for silicon-strip detectors

A new fitting method is explored for momentum reconstruction of tracks in a constant magnetic field for a silicon-strip tracker. Substantial increases of momentum resolution respect to standard fit is obtained. The key point is the use of a realistic probability distribution for each hit (heteroscedasticity). Two different methods are used for the fits, the first method introduces an effective variance for each hit, the second method implements the maximum likelihood search. The tracker model is similar to the PAMELA tracker. Each side, of the two sided of the PAMELA detectors, is simulated as momentum reconstruction device. One of the two is similar to silicon micro-strip detectors of large use in running experiments. Two different position reconstructions are used for the standard fits, the $\eta$-algorithm (the best one) and the two-strip center of gravity. The gain obtained in momentum resolution is measured as the virtual magnetic field and the virtual signal-to-noise ratio required by the two standard fits to reach an overlap with the best of two new methods. For the best side, the virtual magnetic field must be increased 1.5 times respect to the real field to reach the overlap and 1.8 for the other. For the high noise side, the increases must be 1.8 and 2.0. The signal-to-noise ratio has similar increases but only for the $\eta$-algorithm. The signal-to-noise ratio has no effect on the fits with the center of gravity. Very important results are obtained if the number N of detecting layers is increased, our methods provide a momentum resolution growing linearly with N, much higher than standard fits that grow as the $\sqrt{N}$.Comment: This article supersedes arXiv:1606.03051, 22 pages and 10 figure

Projective Modules of Finite Type and Monopoles over S2S^2

We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of sections of the corresponding complex rank 1 vector bundle over $S^2$. The canonical connection $\nabla = p \circ d$ is used to compute the topological charges. Transposed projectors gives opposite values for the charges, thus showing that transposition of projectors, although an isomorphism in K-theory, is not the identity map. Also, we construct the partial isometry yielding the equivalence between the tangent projector (which is trivial in K-theory) and the real form of the charge 2 projector.Comment: 15 pages, Late

Scattering Polarization in the Presence of Magnetic and Electric Fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the $Q/I$ profiles and rotation of the plane of polarization in the $U/I$ profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady state and time varying electric fields that surround radiating atoms in Solar atmospheric layers.Comment: 41 pages, 6 figure

Global Analysis of an Expectations Augmented Evolutionary Dynamics

We consider a deterministic evolutionary model where players form expectations about future play. Players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past. We provide a complete characterization of the qualitative dynamics so induced for a two strategies population game, and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectations.evolutionary games, dynamic systems, bounded rationality

Prominence plasma diagnostics through EUV absorption

In this paper we introduce a new diagnostic technique that uses prominence EUV and UV absorption to determine the prominence plasma electron temperature and column emission measure, as well as He/H relative abundance; if a realistic assumption on the geometry of the absorbing plasma can be made, this technique can also yield the absorbing plasma electron density. This technique capitalizes on the absorption properties of Hydrogen and Helium at different wavelength ranges and temperature regimes. Several cases where this technique can be successfully applied are described. This technique works best when prominence plasmas are hotter than 15,000 K and thus it is ideally suited for rapidly heating erupting prominences observed during the initial phases of coronal mass ejections. An example is made using simulated intensities of 4 channels of the SDO/AIA instrument. This technique can be easily applied to existing observations from almost all space missions devoted to the study of the solar atmosphere, which we list.Comment: 17 pages, 4 figures, submitted to Ap