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| CMS-TAU-25-001 ; CERN-EP-2026-243 | ||
| A machine-learning method for the estimation of the background from jets misidentified as hadronic tau lepton decays | ||
| CMS Collaboration | ||
| 9 October 2026 | ||
| Accepted for publication in the Journal of Instrumentation | ||
| Abstract: Backgrounds arising from quark- and gluon-initiated jets misidentified as hadronically decaying tau leptons constitute a major experimental challenge for analyses involving tau leptons. The MUltivariate Fake-Factor INference (MUFFIN) approach, a machine-learning-based method for estimating this background directly from observed events, is presented. Boosted decision tree reweighting is used to learn multidimensional, per-object correction factors directly from observed data, thereby modelling the jet to hadronic tau lepton misidentification probability across the kinematic and topological phase space without relying on low-dimensional parametrisations. Performance studies are presented using proton-proton collision data collected by the CMS experiment at the CERN LHC at $ \sqrt{s}= $ 13.6 TeV, corresponding to an integrated luminosity of 62.4 fb$ ^{-1} $. Compared to low-dimensional parametrisation methods, improved modelling of key kinematic observables is achieved, particularly in regions of high $ p_{\mathrm{T}} $. The improved modelling leads to a reduction of up to 70% in the systematic uncertainty associated with jets being misidentified as hadronically decaying tau leptons. The MUFFIN method provides a robust and scalable method for background estimation in precision measurements and searches for beyond-the-standard-model physics involving tau lepton final states. | ||
| Links: e-print arXiv:2610.13634 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Schematic overview of the DRs, VRs, AR, and SR used in the estimation of the $ \text{jet}\to\tau_\mathrm{h} $ backgrounds. For each process, TFs are derived in dedicated DRs enriched in jets misidentified as $ \tau_\mathrm{h} $ candidates. The performance of the method is assessed in VRs, where available, or through simulation-based studies in cases without an unbiased DR. The prediction is then applied in a common AR, defined by opposite-sign events with one $ \tau_\mathrm{h} $ candidate failing the nominal identification requirement. In the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel, the AR is dominated by QCD multijet events, while in the $ \tau_{\mu}\tau_\mathrm{h} $ channel a combined prediction is constructed from QCD multijet, $ \mathrm{W}+\text{jets} $, and $ \mathrm{t} \overline{\mathrm{t}} $ contributions using relative fractions derived in the AR. The final estimate is obtained in the SR, defined by opposite-sign isolated events passing the nominal $ \tau_\mathrm{h} $ identification requirements. |
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Figure 2:
Schematic overview of the hyperparameter optimisation procedure used to configure the BDT models. For each trial, OPTUNA proposes a hyperparameter set, the model is trained with early stopping, and the evaluation loss is used as the optimisation objective. |
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Figure 3:
Cross-entropy loss (Eq. (5)) versus boosting iteration for all BDT models in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ and $ \tau_{\mu}\tau_\mathrm{h} $ channels, with the loss axis shown on a logarithmic scale. Solid (dashed) lines correspond to the training (evaluation) loss. Cross markers indicate the best (saved) iteration; curves extend up to 10 iterations beyond this point, corresponding to the early stopping window. The lower initial loss of the simulation-only ($ \mathrm{W}+\text{jets} $, $ \mathrm{t} \overline{\mathrm{t}} $) models reflects the binary ($ K= $ 2) classifier setup ($ \ln 2 \approx $ 0.693) compared to the four-class ($ K= $ 4) data channels ($ \ln 4 \approx $ 1.386). |
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Figure 4:
Reliability diagram for the QCD multijet BDT in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel after temperature scaling ($ T^\ast = $ 0.999), shown on the evaluation data set. Each point is placed at the weighted mean confidence of events in the bin (not the geometric bin centre) and shows the event-weight-averaged fraction of correctly classified events (accuracy), with Wilson score 68% confidence intervals using the effective sample size $ n_\text{eff} = (\sum_i w_i)^2 / \sum_i w_i^2 $. The dashed diagonal indicates perfect calibration. The shaded histogram (right axis) shows the weighted confidence-score distribution. The model is well calibrated across the full range, with most events ($ {>}30% $ per bin) at high confidence ($ {>} $ 0.8); the larger uncertainties at low confidence reflect the correspondingly small event counts there. |
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Figure 5:
Distributions of representative observables in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR comparing the MUFFIN prediction (red) and $ F_{\mathrm{F}} $ estimate (blue, dashed) to the target distribution (black markers) for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and decay mode. Vertical bars on the points indicate the statistical uncertainty. The ratio panels display the target-to-prediction ratio, with the corresponding $ \langle|z|\rangle $ values quoted in each panel. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 5-a:
Distributions of representative observables in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR comparing the MUFFIN prediction (red) and $ F_{\mathrm{F}} $ estimate (blue, dashed) to the target distribution (black markers) for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and decay mode. Vertical bars on the points indicate the statistical uncertainty. The ratio panels display the target-to-prediction ratio, with the corresponding $ \langle|z|\rangle $ values quoted in each panel. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 5-b:
Distributions of representative observables in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR comparing the MUFFIN prediction (red) and $ F_{\mathrm{F}} $ estimate (blue, dashed) to the target distribution (black markers) for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and decay mode. Vertical bars on the points indicate the statistical uncertainty. The ratio panels display the target-to-prediction ratio, with the corresponding $ \langle|z|\rangle $ values quoted in each panel. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 5-c:
Distributions of representative observables in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR comparing the MUFFIN prediction (red) and $ F_{\mathrm{F}} $ estimate (blue, dashed) to the target distribution (black markers) for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and decay mode. Vertical bars on the points indicate the statistical uncertainty. The ratio panels display the target-to-prediction ratio, with the corresponding $ \langle|z|\rangle $ values quoted in each panel. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 5-d:
Distributions of representative observables in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR comparing the MUFFIN prediction (red) and $ F_{\mathrm{F}} $ estimate (blue, dashed) to the target distribution (black markers) for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and decay mode. Vertical bars on the points indicate the statistical uncertainty. The ratio panels display the target-to-prediction ratio, with the corresponding $ \langle|z|\rangle $ values quoted in each panel. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 6:
Comparison of the visible mass $ m_{\text{vis}} $ and $ \eta $ distributions in the same $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR with the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions. Vertical bars on the points indicate the statistical uncertainty. The ratio panels highlight residual deviations and the corresponding $ \langle|z|\rangle $ metric values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 6-a:
Comparison of the visible mass $ m_{\text{vis}} $ and $ \eta $ distributions in the same $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR with the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions. Vertical bars on the points indicate the statistical uncertainty. The ratio panels highlight residual deviations and the corresponding $ \langle|z|\rangle $ metric values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 6-b:
Comparison of the visible mass $ m_{\text{vis}} $ and $ \eta $ distributions in the same $ \tau_\mathrm{h}\tau_\mathrm{h} $ AR with the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions. Vertical bars on the points indicate the statistical uncertainty. The ratio panels highlight residual deviations and the corresponding $ \langle|z|\rangle $ metric values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 7:
Validation of the QCD multijet background modelling in the $ \tau_{\mu}\tau_\mathrm{h} $ VR. Predictions from MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) are compared to data for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode. Vertical bars on the points indicate the statistical uncertainty. The lower panels show the data-to-prediction ratio, with $ \langle|z|\rangle $ values indicating the overall level of agreement. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 7-a:
Validation of the QCD multijet background modelling in the $ \tau_{\mu}\tau_\mathrm{h} $ VR. Predictions from MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) are compared to data for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode. Vertical bars on the points indicate the statistical uncertainty. The lower panels show the data-to-prediction ratio, with $ \langle|z|\rangle $ values indicating the overall level of agreement. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 7-b:
Validation of the QCD multijet background modelling in the $ \tau_{\mu}\tau_\mathrm{h} $ VR. Predictions from MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) are compared to data for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode. Vertical bars on the points indicate the statistical uncertainty. The lower panels show the data-to-prediction ratio, with $ \langle|z|\rangle $ values indicating the overall level of agreement. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 7-c:
Validation of the QCD multijet background modelling in the $ \tau_{\mu}\tau_\mathrm{h} $ VR. Predictions from MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) are compared to data for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode. Vertical bars on the points indicate the statistical uncertainty. The lower panels show the data-to-prediction ratio, with $ \langle|z|\rangle $ values indicating the overall level of agreement. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 7-d:
Validation of the QCD multijet background modelling in the $ \tau_{\mu}\tau_\mathrm{h} $ VR. Predictions from MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) are compared to data for $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode. Vertical bars on the points indicate the statistical uncertainty. The lower panels show the data-to-prediction ratio, with $ \langle|z|\rangle $ values indicating the overall level of agreement. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 8:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode in the $ \mathrm{W}+\text{jets} $ DR of the $ \tau_{\mu}\tau_\mathrm{h} $ channel, showing MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed). Vertical bars on the points indicate the statistical uncertainty. The ratio panels report the $ \langle|z|\rangle $ values for each method; arrows mark bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 8-a:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode in the $ \mathrm{W}+\text{jets} $ DR of the $ \tau_{\mu}\tau_\mathrm{h} $ channel, showing MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed). Vertical bars on the points indicate the statistical uncertainty. The ratio panels report the $ \langle|z|\rangle $ values for each method; arrows mark bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 8-b:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode in the $ \mathrm{W}+\text{jets} $ DR of the $ \tau_{\mu}\tau_\mathrm{h} $ channel, showing MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed). Vertical bars on the points indicate the statistical uncertainty. The ratio panels report the $ \langle|z|\rangle $ values for each method; arrows mark bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 8-c:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode in the $ \mathrm{W}+\text{jets} $ DR of the $ \tau_{\mu}\tau_\mathrm{h} $ channel, showing MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed). Vertical bars on the points indicate the statistical uncertainty. The ratio panels report the $ \langle|z|\rangle $ values for each method; arrows mark bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 8-d:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode in the $ \mathrm{W}+\text{jets} $ DR of the $ \tau_{\mu}\tau_\mathrm{h} $ channel, showing MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed). Vertical bars on the points indicate the statistical uncertainty. The ratio panels report the $ \langle|z|\rangle $ values for each method; arrows mark bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 9:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) using simulated $ \mathrm{W}+\text{jets} $ events. Vertical bars on the points indicate the statistical uncertainty. Ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 9-a:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) using simulated $ \mathrm{W}+\text{jets} $ events. Vertical bars on the points indicate the statistical uncertainty. Ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 9-b:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) using simulated $ \mathrm{W}+\text{jets} $ events. Vertical bars on the points indicate the statistical uncertainty. Ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 9-c:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) using simulated $ \mathrm{W}+\text{jets} $ events. Vertical bars on the points indicate the statistical uncertainty. Ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 9-d:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) using simulated $ \mathrm{W}+\text{jets} $ events. Vertical bars on the points indicate the statistical uncertainty. Ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 10:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) in simulated $ \mathrm{t} \overline{\mathrm{t}} $ for the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Vertical bars on the points indicate the statistical uncertainty. The ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 10-a:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) in simulated $ \mathrm{t} \overline{\mathrm{t}} $ for the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Vertical bars on the points indicate the statistical uncertainty. The ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 10-b:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) in simulated $ \mathrm{t} \overline{\mathrm{t}} $ for the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Vertical bars on the points indicate the statistical uncertainty. The ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 10-c:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) in simulated $ \mathrm{t} \overline{\mathrm{t}} $ for the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Vertical bars on the points indicate the statistical uncertainty. The ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 10-d:
Comparison of $ p_{\mathrm{T}}^{\tau_\mathrm{h}} $, $ m_{\mathrm{T}}^{\text{total}} $, $ \Delta R $, and $ \tau_\mathrm{h} $ decay mode for MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) in simulated $ \mathrm{t} \overline{\mathrm{t}} $ for the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Vertical bars on the points indicate the statistical uncertainty. The ratio panels show agreement with respect to the simulated target and report the corresponding $ \langle|z|\rangle $ values. Arrows indicate bins outside the plotted range. Overflow is included in the final bin ($ \infty $), where applicable. |
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Figure 11:
Distributions of the visible mass in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ (left) and the $ \tau_{\mu}\tau_\mathrm{h} $ (right) channels in the SRs, as defined in Section 5, of physics analyses targeting Higgs boson decays to $ \tau $ lepton pairs. The MUFFIN method is used to estimate the $ \text{jet}\to\tau_\mathrm{h} $ background contributions. Vertical bars represent the statistical uncertainty on the data points. The lower panels show the ratio of data to the total background prediction, with shaded bands representing the combined statistical and systematic uncertainties from the MUFFIN method. |
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Figure 11-a:
Distributions of the visible mass in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ (left) and the $ \tau_{\mu}\tau_\mathrm{h} $ (right) channels in the SRs, as defined in Section 5, of physics analyses targeting Higgs boson decays to $ \tau $ lepton pairs. The MUFFIN method is used to estimate the $ \text{jet}\to\tau_\mathrm{h} $ background contributions. Vertical bars represent the statistical uncertainty on the data points. The lower panels show the ratio of data to the total background prediction, with shaded bands representing the combined statistical and systematic uncertainties from the MUFFIN method. |
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Figure 11-b:
Distributions of the visible mass in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ (left) and the $ \tau_{\mu}\tau_\mathrm{h} $ (right) channels in the SRs, as defined in Section 5, of physics analyses targeting Higgs boson decays to $ \tau $ lepton pairs. The MUFFIN method is used to estimate the $ \text{jet}\to\tau_\mathrm{h} $ background contributions. Vertical bars represent the statistical uncertainty on the data points. The lower panels show the ratio of data to the total background prediction, with shaded bands representing the combined statistical and systematic uncertainties from the MUFFIN method. |
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Figure 12:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-a:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-b:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-c:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-d:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-e:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 12-f:
The BDT score validation in a $ \mathrm{H}(125)\to\tau\tau C\!P $ VR in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-a:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-b:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-c:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-d:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-e:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
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Figure 13-f:
The BDT score validation in a $ \mathrm{W}+\text{jets} $-enriched VR in the $ \tau_{\mu}\tau_\mathrm{h} $ channel for the Higgs boson enriched, Z boson enriched, and misidentified jet enriched categories. MUFFIN (red) and $ F_{\mathrm{F}} $ (blue, dashed) predictions are compared at the distribution level (left) and through the corresponding non-closure evaluation (right). The statistical uncertainty is indicated by the vertical bars on the data points. In the right panels, the hatched bars indicate the statistical component of the total uncertainty. |
png pdf |
Figure 14:
The STXS-inspired category-by-category yield closure for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ (upper) and $ \tau_{\mu}\tau_\mathrm{h} $ (lower) VR. Points show the ratio of observed to predicted yields per STXS category (non-closure), for the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue) methods, where deviations from unity are interpreted as systematic uncertainties in the $ \text{jet}\to\tau_\mathrm{h} $ background estimate. The right panel shows the total uncertainty per category, with the hatched grey bars indicating the statistical component. Only statistical uncertainties are shown in the left panel; the observed non-closure along with the statistical uncertainty define the systematic uncertainty that would be assigned in a real analysis. |
png pdf |
Figure 14-a:
The STXS-inspired category-by-category yield closure for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ (upper) and $ \tau_{\mu}\tau_\mathrm{h} $ (lower) VR. Points show the ratio of observed to predicted yields per STXS category (non-closure), for the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue) methods, where deviations from unity are interpreted as systematic uncertainties in the $ \text{jet}\to\tau_\mathrm{h} $ background estimate. The right panel shows the total uncertainty per category, with the hatched grey bars indicating the statistical component. Only statistical uncertainties are shown in the left panel; the observed non-closure along with the statistical uncertainty define the systematic uncertainty that would be assigned in a real analysis. |
png pdf |
Figure 14-b:
The STXS-inspired category-by-category yield closure for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ (upper) and $ \tau_{\mu}\tau_\mathrm{h} $ (lower) VR. Points show the ratio of observed to predicted yields per STXS category (non-closure), for the MUFFIN (red) and $ F_{\mathrm{F}} $ (blue) methods, where deviations from unity are interpreted as systematic uncertainties in the $ \text{jet}\to\tau_\mathrm{h} $ background estimate. The right panel shows the total uncertainty per category, with the hatched grey bars indicating the statistical component. Only statistical uncertainties are shown in the left panel; the observed non-closure along with the statistical uncertainty define the systematic uncertainty that would be assigned in a real analysis. |
png pdf |
Figure 15:
Closure in the high-$ p_{\mathrm{T}} $ tails of the kinematic distributions for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ QCD multijet-dominated (left) and $ \tau_{\mu}\tau_\mathrm{h} $ $ \mathrm{W}+\text{jets} $ (right) VRs. The dashed lines indicate the statistical component of the uncertainty. The ratio in each bin reflects the non-closure, and the fitted constant (solid horizontal line) is derived by fitting over all events above the $ p_{\mathrm{T}} $ threshold, providing a more statistically robust estimate of the aggregate tail closure than any individual bin. The MUFFIN method achieves significantly improved agreement in both tails, leading to substantially reduced systematic uncertainties for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel and moderate improvements in the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Overflow is included in the final bin ($ \infty $). |
png pdf |
Figure 15-a:
Closure in the high-$ p_{\mathrm{T}} $ tails of the kinematic distributions for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ QCD multijet-dominated (left) and $ \tau_{\mu}\tau_\mathrm{h} $ $ \mathrm{W}+\text{jets} $ (right) VRs. The dashed lines indicate the statistical component of the uncertainty. The ratio in each bin reflects the non-closure, and the fitted constant (solid horizontal line) is derived by fitting over all events above the $ p_{\mathrm{T}} $ threshold, providing a more statistically robust estimate of the aggregate tail closure than any individual bin. The MUFFIN method achieves significantly improved agreement in both tails, leading to substantially reduced systematic uncertainties for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel and moderate improvements in the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Overflow is included in the final bin ($ \infty $). |
png pdf |
Figure 15-b:
Closure in the high-$ p_{\mathrm{T}} $ tails of the kinematic distributions for a $ \tau_\mathrm{h}\tau_\mathrm{h} $ QCD multijet-dominated (left) and $ \tau_{\mu}\tau_\mathrm{h} $ $ \mathrm{W}+\text{jets} $ (right) VRs. The dashed lines indicate the statistical component of the uncertainty. The ratio in each bin reflects the non-closure, and the fitted constant (solid horizontal line) is derived by fitting over all events above the $ p_{\mathrm{T}} $ threshold, providing a more statistically robust estimate of the aggregate tail closure than any individual bin. The MUFFIN method achieves significantly improved agreement in both tails, leading to substantially reduced systematic uncertainties for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ channel and moderate improvements in the $ \tau_{\mu}\tau_\mathrm{h} $ channel. Overflow is included in the final bin ($ \infty $). |
| Tables | |
png pdf |
Table 1:
Online trigger and offline selection requirements applied in the $ \tau_{\mu}\tau_\mathrm{h} $ and $ \tau_\mathrm{h}\tau_\mathrm{h} $ channels. All $ p_{\mathrm{T}} $ values are given in GeVns. Online trigger thresholds are indicated in parentheses. |
png pdf |
Table 2:
Offline selection requirements in the $ \tau_\mathrm{h}\tau_\mathrm{h} $ and $ \tau_{\mu}\tau_\mathrm{h} $ channels. A dash indicates that the requirement is not applied in that channel. |
png pdf |
Table 3:
Total relative uncertainty in the $ \text{jet}\to\tau_\mathrm{h} $ background yield in representative inclusive SR selections for each channel. |
| Summary |
| In this paper, a machine-learning-based alternative to the ``Fake Factor'' (FF) method for estimating backgrounds from jets misidentified as hadronically decaying $ \tau $ leptons ($ \tau_\mathrm{h} $ ) is presented, referred to as MUltivariate Fake-Factor INference (MUFFIN). This method is a generalisation of the previous FF method by replacing low-dimensional transfer factors with multidimensional, per-object reweighting functions learned directly from observed data, while preserving the fully data-driven nature of the background estimation. The method has been developed and validated using CMS data collected in 2022--2023 and is benchmarked against the FF method using a series of closure tests. Across the analysis channels and observables considered, the MUFFIN method has demonstrated improved modelling performance, increased stability in regions sensitive to correlations between multiple variables, and a reduced reliance on additional non-closure corrections. At the same time, the method has provided a more unified and reproducible workflow for background estimation, leading to a reduction of up to 70% in the associated systematic uncertainty. These results indicate that MUFFIN constitutes a robust method for future analyses involving hadronically decaying $ \tau $ leptons. As analyses increasingly exploit fine-grained categorisation and multidimensional phase space information, the method presented here provides a natural framework to improve background modelling precision and to enhance the sensitivity of measurements and searches involving $ \tau_\mathrm{h} $ final states. Looking forward, further improvement in the performance of the MUFFIN method is expected as larger data sets become available. Training on larger, combined data sets therefore offers a natural path to increasing statistical precision while maintaining robustness against changing experimental conditions. The method also does not depend on the specific $ \tau_\mathrm{h} $ identification algorithm and can be readily deployed with future algorithm developments. More broadly, the general nature of the MUFFIN method makes it readily applicable to other data-driven background estimation problems involving misidentified or non-prompt objects, beyond $ \tau_\mathrm{h} $ candidates. |
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