Signal discovery in sparse spectra: a Bayesian analysis

A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely populated spectra. Monte Carlo techniques to evaluate the sensitivity of an experiment are described. As an example, the method is used to calculate the sensitivity of the GERDA experiment to neutrinoless double beta decay.Comment: 15 pages, 5 figure

VHEeP: A very high energy electron-proton collider based on proton-driven plasma wakefield acceleration

Based on current CERN infrastructure, an electron-proton collider is proposed at a centre-of-mass energy of about 9 TeV. A 7 TeV LHC bunch is used as the proton driver to create a plasma wakefield which then accelerates electrons to 3 TeV, these then colliding with the other 7 TeV LHC proton beam. The basic parameters of the collider are presented, which although of very high energy, has integrated luminosities of the order of 1 pb$^{-1}$/year. For such a collider, with a centre-of-mass energy 30 times greater than HERA, parton momentum fractions, $x$, down to about $10^{-8}$ are accessible for $Q^2$ of 1 GeV$^2$ and could lead to effects of saturation or some other breakdown of DGLAP being observed. The total photon-proton cross section can be measured up to very high energies and also at different energies as the possibility of varying the electron beam energy is assumed; this could have synergy with cosmic-ray physics. Other physics which can be pursued at such a collider are contact interaction searches, such as quark and electron substructure, and measurements of the proton structure as well as other more conventional measurements of QCD at high energies and in a new kinematic regime. The events at very low $x$ will lead to electrons and the hadronic final state produced at very low angles and so a novel spectrometer device will be needed to measure these. First ideas of the physics programme of such a collider are given.Comment: 7 pages, 4 figures, presented at the DIS 2015 Workshop, Dalla

Is the bump significant? An axion-search example

Many experiments in physics involve searching for a localized excess over background expectations in an observed spectrum. If the background is known and there is Gaussian noise, the amount of excess of successive observations can be quantified by the runs statistic taking care of the look-elsewhere effect. The distribution of the runs statistic under the background model is known analytically but the computation becomes too expensive for more than about a hundred observations. This work demonstrates a principled high-precision extrapolation from a few dozen up to millions of data points. It is most precise in the interesting regime when an excess is present. The method is verified for benchmark cases and successfully applied to real data from an axion search. The code that implements our method is available at https://github.com/fredRos/runs .Comment: 18 pages, 8 figures. v2 fixes arxiv's parsing of the URL in the abstrac

Modern Logic and Judicial Decision Making: A Sketch of One View

Two hundred years elapsed before the nineteenth century logicians Boole, De Morgan, and others, finally succeeded in formally developing the calculus of reason-ing first suggested by the German mathematician, Leibniz. It is, perhaps, to the credit of the legal profession that less than one century has subsequently elapsed, and already some lawyers and legal writers, along with other scholars, are beginning to explore the relationship between modern logic and law. What is attempted here is to outline the bare bones of one tentative way of looking at the relationship between modern logic and the judicial decision process. From the useful vantage point of a Lasswellian social process framework of analysis, logic and judicial decision making are considered contextually within that total mani-fold of events that we call the world. Thus viewed, the judicial decision making process is just one constituent of the complex unfolding of events through time. We attempt to represent some of the complexities involved in each of these processes and the relationships between them by means of a series of diagrams. By suggesting that we begin with the world as our context, we make no claim to describing it in complete detail. To the contrary, the sketch presented here-we would emphasize the word sketch and the word tentative -is rough, incomplete, and subject to considerable improvement. But one of our purposes will be served if the outline points the way toward cumulative efforts to achieve a comprehensive description of the judicial decision process. In addition to this broad look at logic, judicial decision making, and the world, a more modest aim is to describe, in some detail and with reasonable clarity, one aspect of the relation between logic and judicial decision making