Data-Driven, Geometry-Aware Optimal-Transport Calibration of Flavor Tagger

2026-05-02

AI Summary

This work addresses the limitations of existing flavor calibration methods, which provide scale factors or one-dimensional corrections only at discrete operating points and thus fail to support continuous, event-level calibration required by modern multi-output calibrators, leading to information loss in high-precision analyses. The authors formulate flavor calibration as an optimal transport problem on the probability simplex, parameterizing the Brenier map in isometric log-ratio coordinates. By integrating normalizing flows with an expectation–maximization algorithm, the method jointly fits multiple regions using control-sample data to learn flavor-conditional target distributions. Innovatively combining Aitchison geometry with optimal transport theory, the approach introduces a linearized feedback operator to disentangle data-constrained from prior-dominated modes, enabling geometry-aware continuous calibration. Closure tests on simulated data demonstrate significantly improved performance both in dedicated control regions and on independent mixed-validation samples.

Abstract

Flavor-tagging calibrations are often provided either as scale factors measured at a finite set of working points or as binned corrections to a chosen one-dimensional discriminant. However, this approach falls short of providing continuous, event-level calibration across the full multicomponent outputs of modern taggers. This limitation leads to information loss in analyses that demand high-performance flavor tagging, restricting analyses to a limited set of predefined variables. In this work, we propose a geometry-aware framework that formulates flavor-tagger calibration as an optimal transport problem on the probability simplex. The transport maps are parameterized and trained in the isometric log-ratio coordinate system. Because the quadratic Euclidean cost of Brenier transport in this coordinate system is equivalent to the Aitchison distance on the simplex, the learned map induces a minimal deformation under the Aitchison geometry. Furthermore, we extract flavor-conditional target distributions directly from control-region data using an expectation-maximization (EM) technique that simultaneously fits multiple control regions, models each flavor component with a normalizing flow, and estimates the regional mixture fractions. The extracted targets are subsequently used to learn flavor-factorized transport maps. Because the joint estimation of mixture fractions and flexible component densities admits weakly constrained directions, we further introduce a linearized feedback-operator analysis that propagates the fitted composition covariance into the extracted component densities, separating data-constrained modes from those dominated by the composition prior. The simulation-based closure study demonstrates improved closure in dedicated control regions and in independent validation mixtures.

Problem

• flavor tagging
• calibration
• optimal transport
• probability simplex
• event-level

Innovation

• optimal transport
• Aitchison geometry
• normalizing flow
• expectation-maximization
• flavor tagging