Simultaneous least squares fitter based on the Lagrange multiplier method

TL;DR

This paper introduces a least squares fitting method using Lagrange multipliers that accounts for correlations and constraints in high energy physics data analysis, demonstrated on D0-D0bar mixing parameters.

Contribution

The paper presents a novel least squares fitter incorporating Lagrange multipliers for constrained, correlated data analysis in high energy physics.

Findings

Provides unbiased estimators with accurate uncertainties.

Effectively handles correlations and constraints.

Validated through MC simulation on D0-D0bar mixing.

Abstract

We developed a least squares fitter used for extracting expected physics parameters from the correlated experimental data in high energy physics. This fitter considers the correlations among the observables and handles the nonlinearity using linearization during the $\chi^2$ minimization. This method can naturally be extended to the analysis with external inputs. By incorporating with Lagrange multipliers, the fitter includes constraints among the measured observables and the parameters of interest. We applied this fitter to the study of the $D^{0}-\bar{D}^{0}$ mixing parameters as the test-bed based on MC simulation. The test results show that the fitter gives unbiased estimators with correct uncertainties and the approach is credible.