We present a projected sensitivity study for hadronic mono-Z dark-matter production using CMS Run2015D HTMHT open data corresponding to 2.256382381\invfb, from which 1{,}439{,}523 events satisfy the hadronic mono-Z selection. Backgrounds are modelled with a conditional flow-matching continuous normalizing flow trained on the selected HTMHT events and evaluated on a held-out validation split reweighted to the full selected population. To mitigate artifacts from missing-object features and avoid in-sample scoring bias we apply sentinel imputation for undefined angular features, persist the train/validation split indices, and enforce a minimum reported background yield of 20 events when selecting the working point. A signal-side offline trigger proxy is applied to the simulated signal before scoring. Under this procedure the baseline analysis yields expected significances of 2.89σ, 7.62σ, and 7.41σ for three simplified-model benchmarks. An ablation study that removes the detailed extra-jet kinematics reduces the expected significance by 53--71%, indicating that extra-jet topology carries substantial discriminating power in the hadronic mono-Z channel. These results are projected sensitivities (no unblinding performed); the limitations and reproducibility of the study are discussed in Sections limitations and reproducibility.
Figures & tables
Signal point
Mediator
(mχ,mmed) [ GeV ]
σ [pb]
Nsel
axial_mx10_mv20
axial
(10,20)
1.204
116
axial_mx50_mv200
axial
(50,200)
1.050
487
vector_mx1_mv500
vector
(1,500)
0.544
848
Table 1: Retained dark-matter signal benchmarks. DMsimp_s_spin1 is an s -channel spin-1 mediator; mχ and mmed are the dark-matter and mediator masses. Cross sections are leading-order MadGraph5 values.
Figure 1: Representative closure plots comparing held-out validation data (filled histogram) to samples drawn from the fitted flow (step histogram). Top left: hadronic- Z mass mjj . Top right: ETmiss distribution. Bottom left: event scalar HT . Bottom right: ΔRZjj . The full per-feature closure set is provided in Appendix D .
Figure 2: Additional closure panels for kinematic observables entering the density score. Top left: reconstructed Z transverse momentum pT,Z . Top right: hadronic recoil pT . Bottom left: ETmiss/HT . Bottom right: ∣mjj−mZ∣ . The full per-feature closure set is provided in Appendix D .
Figure 3: Post-fix closure panels for the four undefined extra-jet angular features. Top left: jet1_eta . Top right: jet2_eta . Bottom left: dphi_met_jet1 . Bottom right: dphi_met_jet2 . Each panel shows a distinct sentinel bar at −999 (the “no extra jet” state) plus the physical continuum, both reproduced by the flow.
Figure 4: Validation negative-log-likelihood curves for the baseline (top) and extra-jet-drop ablation (bottom) fits. The red dashed line marks the best epoch selected by early stopping.
Figure 5: Closure panels for the extra-jet pT features jet1_pt (left) and jet2_pt (right), illustrating the residual delta-plus-continuum limitation: the flow smooths the physical pT=0 sentinel spike, undershooting its height while preserving the continuum.
Item
Value
Processed MINIAOD files
444
Total raw events
20,679,437
Selected events (post-selection)
1,439,523
Selection efficiency
6.96%
Table 2: Summary of the processed MINIAOD dataset used for extraction.
Signal point
Mediator benchmark
S
B
Best cut
Signal eff.
ZA
1/B
axial_mx10_mv20
axial, mχ=10GeV , mmed=20GeV
15.76
25.00
77.05
0.250
2.89
0.20
axial_mx50_mv200
axial, mχ=50GeV , mmed=200GeV
46.90
25.00
67.43
0.203
7.62
0.20
vector_mx1_mv500
vector, mχ=1GeV , mmed=500GeV
45.38
25.00
64.97
0.218
7.41
0.20
Table 3: Primary post-fix expected sensitivity for the 32-feature flow-matching model. The signal trigger proxy is applied before scoring; the reported working point requires B≥20 . The final column is the relative Poisson uncertainty on the background yield, 1/B .
Figure 6: Expected-significance scans versus the NLL discriminant threshold for the three benchmark points. Each row pairs the baseline (32-feature) model (left) with the extra-jet-drop ablation (26-feature) model (right) for one signal point: axial mχ=10/mmed=20GeV (top row), axial mχ=50/mmed=200GeV (middle row), and vector mχ=1/mmed=500GeV (bottom row). The green curve marks the B≥20 constrained scan used for the reported working point, the red dashed line the reported optimum, and the grey dotted line the unconstrained optimum.
Baseline ( D=32 )
Ablation ( D=26 )
Signal point
S
B
ZA
S
B
ZA
Rel. drop
axial 10/20
15.76
25.00
2.89
5.98
50.00
0.83
71.3%
axial 50/200
46.90
25.00
7.62
15.16
25.00
2.78
63.5%
vector 1/500
45.38
25.00
7.41
19.13
25.00
3.45
53.5%
Table 4: Effect of dropping the extra-jet kinematic features. The ablation working point is selected with the same B≥20 floor as the baseline.
Figure 7: Signal-versus-background NLL distributions for the baseline (left, D=32 ) and extra-jet-drop ablation (right, D=26 ) models. In the ablation model the axial_mx10_mv20 signal distribution (orange) overlaps almost entirely with the background peak (blue), explaining its collapse to sub- 1σ significance.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Feature
Formula
met_pt
ETmiss=px,miss2+py,miss2
met_phi
atan2(py,miss,px,miss)
min_dphi_met_jets
mini∣Δϕ(MET,jeti)∣
dphi_met_jet1
Δϕ(MET,jet1)
dphi_met_jet2
Δϕ(MET,jet2)
Appendix
Table 5: Feature schema (41 branches) and extraction formulas. Nine columns excluded from training are annotated “(not trained)”.
Stage
Events
Efficiency
Raw events processed
20,679,437
100%
Pass ≥ 1 HLT path
18,875,596
91.3%
Pass offline hadronic mono- Z selection
1,439,523
6.96%
Appendix
Table 6: Data-side cutflow for the CMS Run 2015D HTMHT open dataset.
Figure 8: Baseline closure plots for the missing-momentum observables and the undefined extra-jet angular features.
Figure 9: Baseline closure plots for the MET-to-scale ratios and angular proximity summary.
Figure 10: Baseline closure plots for the hadronic- Z mass window observables and reconstructed Z kinematics.
Figure 11: Baseline closure plots for the reconstructed Z direction, dijet geometry, and recoil decomposition.
Figure 12: Baseline closure plots for the recoil components and leading Z -daughter jet kinematics.
Figure 13: Baseline closure plots for the Z -daughter and extra-jet pT observables.
Figure 14: Baseline closure plots for the jet-multiplicity observables.
We report a search for dark matter (DM) produced in association with a leptonically decaying Z boson at s=13 TeV using CMS Run 2015D open data corresponding to an integrated luminosity of 2.32fb−1 together with simplified-model Monte Carlo simulation. Events are selected in the mono-Z→ℓ+ℓ− final state in both the μμ and ee channels. Forty kinematic observables are extracted from MINIAOD and MINIAODSIM, cleaned with physics-motivated selections, and reduced to a 37-dimensional feature vector. Five Neural Spline Flows are trained independently to model Standard Model background and mediator-specific DM signal densities. The per-event test statistic is constructed from the log-likelihood ratio between the signal and background density estimates, providing sensitivity across the full kinematic phase space without requiring a hard upper MET threshold. A simultaneous profile-likelihood fit combining the two channels yields observed (expected) 95% confidence level upper limits on the signal-strength parameter of μ<0.0177 (0.0018) for the scalar mediator, μ<0.0362 (0.0039) for the vector mediator, and μ<0.0498 (0.0069) for the axial-vector mediator. The observed limits are weaker than expected because of a residual high-MET background-modeling discrepancy rather than evidence for a DM signal. To our knowledge, this is the first application of Neural Spline Flow likelihood-ratio scoring to a mono-Z dark matter search using CMS Run 2015D open data simultaneously in the μμ and ee channels.
Hitesh Rasineni, Bhavishya Chebrolu
VIT-AP University, Amaravati, India · 1VIT-AP University, Amaravati, 522241, India · Mohan Babu University, Tirupati, India +1
We present an unsupervised search for anomalous dijet events in proton--proton collision data using neural spline flow density estimation. A normalizing flow model is trained on a high-dimensional feature space comprising jet, dijet, and event-level observables to learn the dominant Standard Model background directly from data, without assuming a specific signal hypothesis. Events assigned low likelihood under the learned density are identified as potential anomalous events. Using this approach on a CMS Open Data dijet sample, we investigate extreme events in the tail of the anomaly-score distribution and perform an extensive validation and robustness study. This study includes feature-level statistical comparisons, mass decorrelation tests, permutation-based null tests, and evaluations of training stability. The selected anomalous events exhibit notable departures from the background-only expectation, primarily in jet-substructure observables, while remaining stable under several known sources of bias in unsupervised learning. The identified anomalies are distributed across the kinematic phase space and do not exhibit a narrow structure in the dijet invariant-mass spectrum. Instead, they show correlated deviations across multiple observables, consistent with a multivariate difference in jet substructure and event topology rather than a localized resonance. While no claim of new physics is made, this study demonstrates that neural spline flow-based density estimation can be sensitive to rare, structured deviations in collider data and may provide a model-independent exploratory tool for searches for physics beyond the Standard Model at the LHC.
Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it. A raw anomaly score has no calibrated meaning, a model that scans many regions inflates the look-elsewhere effect, and the asymptotic significances the field relies on are blind to the background mismodelling that anomaly detectors are especially prone to. We propose a calibration layer, built on conformal prediction, that turns any anomaly score into a defensible significance with distribution-free, finite-sample guarantees. Conformal prediction converts scores into valid local p-values, weighted and Mondrian variants repair the sideband-to-signal-region exchangeability failures that resonant searches suffer, and a Gross-Vitells step carries the result through to a look-elsewhere-aware global significance. The layer does two things at once. It exposes miscalibration that the standard pipeline cannot see, and it corrects it without retraining the detector. On public LHC Olympics data, a classifier develops a substructure-mass correlation that makes sideband-calibrated background p-values anti-conservative. Taken at face value, this manufactures a ∼46σ excess from background sculpting alone, which the label-free weighted correction removes, restoring an honest null. When run as a blind wide-mass bump hunt, the standard asymptotic and unweighted procedures fabricate ≳10σ excesses and ≈5σ excesses even in signal-free windows, while the conformal layer raises no false alarms and its global false-positive rate is verified on background-only pseudoexperiments. The result is an auditable, detector-agnostic path from an uncalibrated score to a trials-factor-aware significance, ready to be folded into experimental anomaly searches.
Jack Y. Araz, Michael Spannowsky
Department of Physics and Astronomy, University College London, London, WC1E 6B, UK · Department of Engineering, City St. George’s, University of London, London, EC1V 0HB, UK · Institute for Theoretical Physics, Campus Süd, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany +1