Asymptotic formulae for likelihood-based tests of new physics

Abstract

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.

Lepton Flavour Violation in Tau Decays: Results and Prospects at the LHC

“…A combined fit is performed to the three-muon invariant mass distribution of the most sensitive bins in M 3body × M PID . The result is consistent with the background-only hypothesis, and an upper limit [2] (4) is set on the branching fraction using the CLs method [9,10]. This limit is a factor 2.5 higher than the current best limit [11], set by the Belle experiment.…”

“…From a simultaneous fit to the three BDT bins a signal yield N sig = −7 ± 15 is obtained, and an upper limit [4] B(D 0 → e ± μ ∓ ) < 1.3 × 10 −8 @ 90% C.L. (8) is set on the branching fraction using the CLs method [9,10]. This result improves upon the previous best limit from the Belle experiment [15] by a factor 20.…”

“…An upper limit [1] (2) is set on the τ − → μ − μ + μ − branching fraction using the CLs method [9,10]. Although this limit is not yet competitive with the results from the LHCb [2] and Belle [11] experiments, it demonstrates ATLAS' potential for performing competitive LFV searches using the LHC run 2 data and beyond, and its capabilities to reconstruct and trigger on low-p T muons.…”

A novel approach to the bias-variance problem in bump hunting

“…In this study, I always take the local fit region to have a length of 25σ (25 times the mass resolution) centered on the test-mass value, which includes a ±2.5σ region potentially containing the signal and a 10σ -wide region on either side that is virtually signal free. 3 Each local fit region is transformed such that it spans the interval [−1, 1] with the test mass at zero. 4 Figure 1 shows a Gaussian signal PDF, along with peaking-background structures taken here to be Gaussian distributions with widths of two and three times that of the signal, each projected onto a truncated series of Legendre polynomials.…”

“…Roughly speaking, the ring out must be comparable to the Poisson uncertainty in each mass bin to disfavor building up a signal-like structure in this manner; therefore, including even modes with 10 forbids discovery of signals with S 10 √ B. Furthermore, the extent to which a signal-like structure can be built up by the available even modes will be directly reflected in 3 In principle, the use of a larger fit region can be beneficial if information is known about the form of the background PDF on the larger region; however, if such information is not available, then the use of a larger fit region trades variance for background-model uncertainty. While there are some situations where the use of a larger fit region is preferred, I will not explore this here.…”