A continuous calibration of the ATLAS flavour-tagging classifiers via optimal transportation maps

TL;DR

This work introduces a continuous calibration of ATLAS flavour-tagging classifiers using optimal transportation maps to align simulated jet-flavour probabilities with data without relying on binning. By modeling the joint density of the DL1r outputs with neural density estimators and conditional normalizing flows, the authors construct a pt-dependent transport map that minimizes changes to the simulation while achieving data–MC closure for b-, c-, and light-flavour jets. The calibration relies on a dilepton tt̄ sample in tt̄ → eμννbb events and uses a background-shape correction from Z+jets regions, with thorough treatment of uncertainties and background contamination. The resulting maps provide a truly continuous, high-dimensional correction framework that preserves jet counts and enables flexible use of flavour-tagging information in ATLAS analyses, including complex charm-tagging strategies and H → cc searches.

Abstract

A calibration of the ATLAS flavour-tagging algorithms using a new calibration procedure based on optimal transportation maps is presented. Simultaneous, continuous corrections to the $b$-jet, $c$-jet, and light-flavour jet classification probabilities from jet-tagging algorithms in simulation are derived for $b$-jets using $t\bar t \to eμννbb$ data. After application of the derived calibration maps, closure between simulation and observation is achieved for jet flavour observables used in ATLAS analyses of Large Hadron Collider (LHC) Run 2 proton-proton collision data. This continuous calibration opens up new possibilities for the future use of jet flavour information in LHC analyses and also serves as a guide for deriving high-dimensional corrections to simulation via transportation maps, an important development for a broad range of inference tasks.

Figures (25)

• Figure 1: Schematic of the optimal calibration maps derived in this study. Only two of the three calibrated log-probabilities are shown. The darkened region around the point of the arrow indicates that there is some uncertainty in the transport mapping. The transport maps are deterministic, so the uncertainty is calculated by deriving transport maps between alternative simulations and the data.
• Figure 2: Comparison of jet observables between the simulation's predictions and observed data, with the predictions separated by process: the selected jets' (a) , (b) $|\eta|$, (c) $D^\mathrm{DL1r}_b$ and (d) $D^\mathrm{DL1r}_c$. Non- distributions were estimated following the procedure in \ref{['sec:nonb_calibration']}; no correction is applied to the simulation for . The uncertainty bands denote the impact of all uncertainties described in \ref{['sec:uncertainties']}.
• Figure 3: Comparison of jet observables between the simulation's predictions and observed data, with the predictions separated by jet flavour: the selected jets' (a) , (b) $|\eta|$, (c) $D^\mathrm{DL1r}_b$ and (d) $D^\mathrm{DL1r}_c$. Non- distributions were estimated following the procedure in \ref{['sec:nonb_calibration']}; no correction is applied to the simulation for . The uncertainty bands denote the impact of all uncertainties described in \ref{['sec:uncertainties']}.
• Figure 4: The predicted purity, $f_\mathrm{sig}(\pt)$, after the event selection, is shown as a function of jet . Both the binned MC ($f_{\text{sig}}^{\text{hist}}$) and neural purity ($f_{\text{sig}}^{\text{NN}}$) estimates are shown, with good agreement observed between the two. The uncertainty bands denote the impact of all uncertainties described in \ref{['sec:uncertainties']}.
• Figure 5: Comparison of binned 1D marginals of $p_\mathrm{sig}$ between the simulation's predictions (MC) and the neural estimates ($p_{sim}$) integrated over jet in the region: (a) $\mathrm{logit}\xspace~p_b\xspace$, (b) $\mathrm{logit}\xspace~p_c\xspace$, and (c) $\mathrm{logit}\xspace~p_u\xspace$. Only statistical uncertainties from the limited size of the sample used to fill the histograms are shown in the error bars.