Optimal Belief Approximation

In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it is to communicate a given approximation. We reproduce and discuss an old proof showing that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. The loss function that is obtained in the derivation is equal to the Kullback-Leibler divergence when normalized. This loss function is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. The correct order ensures that the recipient of a communication is only deprived of the minimal amount of information. We hope that the elementary derivation settles the apparent confusion. For example when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many suggested computational schemes.Comment: made improvements on the proof and the languag

Bayesian decomposition of the Galactic multi-frequency sky using probabilistic autoencoders

All-sky observations of the Milky Way show both Galactic and non-Galactic diffuse emission, for example from interstellar matter or the cosmic microwave background (CMB). The different emitters are partly superimposed in the measurements, partly they obscure each other, and sometimes they dominate within a certain spectral range. The decomposition of the underlying radiative components from spectral data is a signal reconstruction problem and often associated with detailed physical modeling and substantial computational effort. We aim to build an effective and self-instructing algorithm detecting the essential spectral information contained Galactic all-sky data covering spectral bands from $\gamma$-ray to radio waves. Utilizing principles from information theory, we develop a state-of-the-art variational autoencoder specialized on the adaption to Gaussian noise statistics. We first derive a generic generative process that leads from a low-dimensional set of emission features to the observed high-dimensional data. We formulate a posterior distribution of these features using Bayesian methods and approximate this posterior with variational inference. The algorithm efficiently encodes the information of 35 Galactic emission data sets in ten latent feature maps. These contain the essential information required to reconstruct the initial data with high fidelity and are ranked by the algorithm according to their significance for data regeneration. The three most significant feature maps encode astrophysical components: (1) The dense interstellar medium (ISM), (2) the hot and dilute regions of the ISM and (3) the CMB. The machine-assisted and data-driven dimensionality reduction of spectral data is able to uncover the physical features encoding the input data. Our algorithm is able to extract the dense and dilute Galactic regions, as well as the CMB, from the sky brightness values only.Comment: 25 pages, 8 figures, 3 tables. Submitted to Astronomy & Astrophysic

Weakly coupled neutral gauge bosons at future linear colliders

A weakly coupled new neutral gauge boson forms a narrow resonance that is hard to discover directly in e+e- collisions. However, if the gauge boson mass is below the center-of-mass energy, it can be produced through processes where the effective energy is reduced due to initial-state radiation and beamstrahlung. It is shown that at a high-luminosity linear collider, such a gauge boson can be searched for with very high sensitivity, leading to a substantial improvement compared to existing limits from the Tevatron and also extending beyond the expected reach of the LHC in most models. If a new vector boson is discovered either at the Tevatron Run II, the LHC or the linear collider, its properties can be determined at the linear collider with high precision, thus helping to reveal origin of the new boson.Comment: 21 p

On the phenomenology of a Z' coupling only to third-family fermions

The phenomenology of an additional U(1) neutral gauge boson Z' coupled to the third family of fermions is discussed. One might expect such a particle to contribute to processes where taus, b and t quarks are produced. Precision data from LEP1 put severe constraints on the mixing and heavy-boson mass. We find that the effects of such a particle could not be observed at hadronic colliders, be it at the Tevatron or the LHC, because of the QCD background. At LEP2 and future e^+e^- linear colliders, one could instead hope to observe such effects, in particular for b\bar b final states.Comment: 36 pages, LaTeX, including 12 figure

Discovery and Identifictation of Extra Gauge Bosons in e^+e^- -> nu nubar gamma

We examine the sensitivity of the process e+e- -> nu nubar gamma to extra gauge bosons, Z' and W', which arise in various extensions of the standard model. The process is found to be sensitive to W' masses up to several TeV, depending on the model, the center of mass energy, and the assumed integrated luminosity. If extra gauge bosons were discovered first in other experiments, the process could also be used to measure Z' nu nubar and W' couplings. This measurement would provide information that could be used to unravel the underlying theory, complementary to measurements at the Large Hadron Collider.Comment: 45 pages, 17 postscript figures, Latex. Uses RevTex and epsfi

Measuring SUSY Parameters at LEP II Using Chargino Production and Decay

Previously, in the context of the minimal supersymmetric standard model (without {\em a priori} assumptions of parameter unification), we studied the constraints on weak-scale SUSY parameters from chargino production at LEP II, using as observables \mch, \mLSP, the cross section and the leptonic branching fraction. Here, exploiting the high degree of polarization in chargino production, we add to our earlier work the forward-backward asymmetries of the visible hadrons and leptons in chargino decays. For a chargino that is mostly gaugino, the parameter space can now be restricted to a small region; \tanb is constrained, the soft electroweak gaugino and electron sneutrino masses are determined to about 10\%, and the sign of $\mu$ may be determined. Constraints for a chargino that is mostly Higgsino are much weaker, but still disfavor the hypothesis that the chargino is mostly gaugino. For a chargino which is a roughly equal mixture of Higgsino and gaugino, we find intermediate results.Comment: 36 pp., ReVTeX, 15 uuencoded figure

Probing Z' gauge boson with the spin configuration of top quark pair production at future e−e+e^- e^+ linear colliders

We explore the effects of extra neutral gauge boson involved in the supersymmetric E6 model on the spin configuration of the top quark pair produced at the polarized e- e+ collider. Generic mixing terms are considered including kinetic mixing terms as well as mass mixing. In the off-diagonal spin basis of the standard model, we show that the cross sections for the suppressed spin configurations can be enhanced with the effects of the Z' boson through the modification of the spin configuration of produced top quark pair enough to be measured in the Linear Colliders, which provides the way to observe the effects of Z' boson and discriminate the pattern of gauge group decomposition. It is pointed out that the kinetic mixing may dilute the effects of mass mixing terms, and we have to perform the combined analysis.Comment: 19 pages including 5 figures, ReVTe

Discriminating graviton exchange effects from other new physics scenarios in e^+e^- collisions

We study the possibility of uniquely identifying the effects of graviton exchange from other new physics in high energy e^+e^- annihilation into fermion-pairs. For this purpose, we use as basic observable a specific asymmetry among integrated differential distributions, that seems particularly suitable to directly test for such gravitational effects in the data analysis.Comment: 18 pages, including figures; v2: additional references and acknowledgements. To appear in PR

Discovery and Identification of W' Bosons in e gamma to nu q +X

We examine the sensitivity of the process e gamma to nu q +X to W' bosons which arise in various extensions of the standard model. We consider photon spectra from both the Weizsacker Williams process and from a backscattered laser. The process is found to be sensitive to W' masses up to several TeV, depending on the model, the center of mass energy, the integrated luminosity, and assumptions regarding systematic errors. If extra gauge bosons were discovered first in other experiments, the process could also be used to measure W' couplings. This measurement would provide information that could be used to unravel the underlying theory, complementary to measurements at the Large Hadron Collider.Comment: 17 pages, 9 figures, uses Revtex and epsfi