sFit: a method for background subtraction in maximum likelihood fit

TL;DR

sFit is a novel statistical method that enables background subtraction directly within maximum likelihood fits without needing separate background models or simulations, improving the accuracy of parameter estimation.

Contribution

It extends the sPlot technique to create a background-free likelihood function, allowing unbiased parameter estimation in the presence of background.

Findings

Enables background subtraction without sideband or simulation.

Provides unbiased estimates of fit parameters.

Integrates with maximum likelihood fitting procedures.

Abstract

This paper presents a statistical method to subtract background in maximum likelihood fit, without relying on any separate sideband or simulation for background modeling. The method, called sFit, is an extension to the sPlot technique originally developed to reconstruct true distribution for each date component. The sWeights defined for the sPlot technique allow to construct a modified likelihood function using only the signal probability density function and events in the signal region. Contribution of background events in the signal region to the likelihood function cancels out on a statistical basis. Maximizing this likelihood function leads to unbiased estimates of the fit parameters in the signal probability density function.