A Poisson likelihood approach to fake lepton estimation with the matrix method

Abstract

Many high-energy physics analyses require the presence of leptons from W , Z, or H boson decay. For these analyses, signatures that mimic such leptons present a 'fake lepton' background that must be estimated. Since the magnitude of this background depends strongly upon details of the detector response, it can be difficult to estimate with simulation. One data-driven approach is the 'matrix method', in which two categories of leptons are defined ('loose' and 'tight'), with the tight category being a subset of the loose category. Using the populations of leptons in each category in the analysis sample, and the efficiencies for both real and fake leptons in the loose category to satisfy the criteria for the tight category, the fake background yield can be estimated. This paper describes a Poisson likelihood implementation of the matrix method, which provides a more precise, reliable, and robust estimate of the fake background yield compared to an analytic solution. This implementation also provides a reliable estimate of the background for cases in which the analysis selection permits more loose leptons than tight leptons, potentially allowing for greater selection efficiency.

Reformulation of a likelihood approach to fake-lepton estimation in the framework of Bayesian inference

“…In the following, a maximum likelihood approach is described, as motivated and explained in more detail in Ref. [2]. The motivation for this method and the Bayesian derivation is mentioned afterwards.…”

“…The likelihood matrix method as derived in Ref. [2] describes leptons passing the loose criteria to be subsequently divided into two orthogonal groups, referred to as tight and non-tight.…”

“…(3.2) and Eq. (3.3) can be defined in the tight and the loose region, there are two different corresponding parameterisations for a maximum-likelihood approach [2].…”

“…In order to simplify the fit, the uncertainties on the efficiencies are assumed to be negligible compared to the Poissonian uncertainties 3 , so the efficiencies are parameterised as δ distributions in Ref. [2]. The likelihood from Eq.…”

“…Motivated by limitations of the matrix method, in particular the possibility that the predicted fake-lepton event yields can be negative, a maximum-likelihood approach was proposed in Ref. [2]. In this paper, this improved method is reformulated in Bayesian reasoning, the equality of both approaches is shown and both formulations are implemented in the Bayesian Analysis Toolkit (BAT) [3], a multi-purpose software package for Bayesian inference.…”