FUMILI-based minimization with constraints using method of elimination of differentials

Vladimir Kurbatov,Victoria Tokareva,Dmitry Tsirkov,I Bobrikov,O Derenovskaya,A Friesen,A Verkheev,V Chudoba

doi:10.1051/epjconf/201920107001

Vladimir Kurbatov, Victoria Tokareva + Show 6 more

Open Access

https://doi.org/10.1051/epjconf/201920107001

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Abstract

Kinematic filtting is one of the popular particle physics problems where constraint minimization is used. The constraints setting additional relations between parameters p can be given in form of equations φ(p1,..., pn) = 0. Often these equations are non-linear and complicated, and thus it is impossible or impractical to eliminate redundant parameters directly. The article covers employing of the minimization approach called a method of elimination of differentials, that is being developed at JINR as an extension to the FUMILI minimizer, and is intended for kinematic filtting in particle physics experiments.

Highlights

Kinematic fitting is one of the popular particle physics problems where constraint minimization is used
In this paper we are going to cover a FUMILI-based framework for kinematic fitting we have developed, which is currently used for data analysis in the ANKE experiment (Jülich, Germany) [4]
The greedy minimization algorithm which is employed in FUMILI was first proposed at JINR by S.N

Summary

Kinematic fitting

A track reconstruction problem in general can be understood as a problem of multidimensional linear regression. For every track j we are looking for a such initial momenta pj that the reconstructed coordinates of detector hits cij( pj), where i is a hit number, would be as close as possible to the registered hit coordinates cij, taking into account the known detector uncertainties δcij. Further we would omit the indices i, j for simplicity, so that c and p would be vectors of all hits and momentum components correspondingly. Where P is a four-momentum of a particle, and MX is a reaction missing mass. Using (2), (3) allows us to narrow down the multidimensional domain of functional (1). A procedure that takes the kinematics constraints. In this paper we are going to cover a FUMILI-based framework for kinematic fitting we have developed, which is currently used for data analysis in the ANKE experiment (Jülich, Germany) [4]

Constrained minimization

Method of elimination of differentials

FUMILI-based realization of the method

Example

Kinematic fitting at ANKE

Conclusion and outlook