Asymptotic formulae for likelihood-based tests of new physics

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.Comment: fixed typo in equations 75 & 7

Trial factors for the look elsewhere effect in high energy physics

When searching for a new resonance somewhere in a possible mass range, the significance of observing a local excess of events must take into account the probability of observing such an excess anywhere in the range. This is the so called "look elsewhere effect". The effect can be quantified in terms of a trial factor, which is the ratio between the probability of observing the excess at some fixed mass point, to the probability of observing it anywhere in the range. We propose a simple and fast procedure for estimating the trial factor, based on earlier results by Davies. We show that asymptotically, the trial factor grows linearly with the (fixed mass) significance

Testing minimal lepton flavor violation with extra vector-like leptons at the LHC

Models of minimal lepton flavor violation where the seesaw scale is higher than the relevant flavor scale predict that all lepton flavor violation is proportional to the charged lepton Yukawa matrix. If extra vector-like leptons are within the reach of the LHC, it will be possible to test the resulting predictions in ATLAS/CMS.Comment: 19 pages, 8 figure

Estimating the "look elsewhere effect" when searching for a signal

The "look elsewhere effect" refers to a common situation where one searchesfor a signal in some space of parameters-for example, a resonance search withunknown mass, or a search for astrophysical point sources with unknown locationin the sky. Since Wilks' theorem does not apply in such cases, one usually hasto resort to computationally expansive Monte-Carlo simulations in order tocorrectly estimate the significance of a given observation. Recent results fromthe theory of random fields provide powerful tools which may be used toalleviate this difficulty, in a wide range of applications. We review thoseresults and discuss their implementation in problems of practical interest