Hadronic Mono-Z Dark Matter Sensitivity with Flow Matching on CMS Open Data

Hitesh Rasineni; Bhavishya Chebrolu

hep-exAug 21, 2026

Hadronic Mono-Z Dark Matter Sensitivity with Flow Matching on CMS Open Data

Authors: Hitesh Rasineni, Bhavishya Chebrolu

Organizations: VIT-AP University, Amaravati, India · VIT-AP University, Amaravati, 522241, India · Mohan Babu University, Tirupati, India · Mohan Babu University, Tirupati, 517102, India

Abstract

We present a projected sensitivity study for hadronic mono- $Z$ dark-matter production using CMS Run~~2015D 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 2.89 $σ$ , 7.62 $σ$ , and 7.41 $σ$ 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	$(m_{\chi},\,m_{\mathrm{med}})$ [ GeV ]	$\sigma$ [pb]	$N_{\mathrm{sel}}$
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;

m_{\chi}

and

m_{\mathrm{med}}

are the dark-matter and mediator masses. Cross sections are leading-order MadGraph5 values.

Panel of Figure 1 — 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 $m_{jj}$ . Top right: $E_{\mathrm{T}}^{\mathrm{miss}}$ distribution. Bottom left: event scalar $H_{T}$ . Bottom right: $\Delta R_{Zjj}$ . The full per-feature closure set is provided in Appendix D .

Panel of Figure 2 — Figure 2: Additional closure panels for kinematic observables entering the density score. Top left: reconstructed $Z$ transverse momentum $p_{T,Z}$ . Top right: hadronic recoil $p_{T}$ . Bottom left: $E_{\mathrm{T}}^{\mathrm{miss}}/\sqrt{H_{T}}$ . Bottom right: $|m_{jj}-m_{Z}|$ . The full per-feature closure set is provided in Appendix D .

Panel of Figure 3 — 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.

Panel of Figure 4 — 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.

Panel of Figure 5 — Figure 5: Closure panels for the extra-jet $p_{T}$ features jet1_pt (left) and jet2_pt (right), illustrating the residual delta-plus-continuum limitation: the flow smooths the physical $p_{T}=0$ 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.	$Z_{A}$	$1/\sqrt{B}$
axial_mx10_mv20	axial, $m_{\chi}=10~\text{GeV}$ , $m_{\mathrm{med}}=20~\text{GeV}$	15.76	25.00	77.05	0.250	2.89	0.20
axial_mx50_mv200	axial, $m_{\chi}=50~\text{GeV}$ , $m_{\mathrm{med}}=200~\text{GeV}$	46.90	25.00	67.43	0.203	7.62	0.20
vector_mx1_mv500	vector, $m_{\chi}=1~\text{GeV}$ , $m_{\mathrm{med}}=500~\text{GeV}$	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\geq 20

. The final column is the relative Poisson uncertainty on the background yield,

1/\sqrt{B}

Panel of Figure 6 — 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 $m_{\chi}=10/m_{\mathrm{med}}=20~\text{GeV}$ (top row), axial $m_{\chi}=50/m_{\mathrm{med}}=200~\text{GeV}$ (middle row), and vector $m_{\chi}=1/m_{\mathrm{med}}=500~\text{GeV}$ (bottom row). The green curve marks the $B\geq 20$ 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	$S$	$B$	$Z_{A}$	$S$	$B$	$Z_{A}$	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\geq 20

floor as the baseline.

Panel of Figure 7 — 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- $1\sigma$ significance.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix


Feature	Formula
met_pt	$E_{\mathrm{T}}^{\mathrm{miss}}=\sqrt{p_{x,\text{miss}}^{2}+p_{y,\text{miss}}^{2}}$
met_phi	$\mathrm{atan2}(p_{y,\text{miss}},p_{x,\text{miss}})$
min_dphi_met_jets	$\min_{i}\,\|\Delta\phi(\mathrm{MET},\mathrm{jet}_{i})\|$
dphi_met_jet1	$\Delta\phi(\mathrm{MET},\mathrm{jet}_{1})$
dphi_met_jet2	$\Delta\phi(\mathrm{MET},\mathrm{jet}_{2})$

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 $\geq$ 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.

Panel of Figure 8 — Figure 8: Baseline closure plots for the missing-momentum observables and the undefined extra-jet angular features.

Panel of Figure 9 — Figure 9: Baseline closure plots for the MET-to-scale ratios and angular proximity summary.

Panel of Figure 10 — Figure 10: Baseline closure plots for the hadronic- $Z$ mass window observables and reconstructed $Z$ kinematics.

Panel of Figure 11 — Figure 11: Baseline closure plots for the reconstructed $Z$ direction, dijet geometry, and recoil decomposition.

Panel of Figure 12 — Figure 12: Baseline closure plots for the recoil components and leading $Z$ -daughter jet kinematics.

Panel of Figure 13 — Figure 13: Baseline closure plots for the $Z$ -daughter and extra-jet $p_{T}$ observables.

Panel of Figure 14 — Figure 14: Baseline closure plots for the jet-multiplicity observables.

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Mono-Z Dark Matter Search with Neural Spline Flows Using CMS Run 2015D Open Data

Hitesh Rasineni, Bhavishya Chebrolu

VIT-AP University, Amaravati, India · 1VIT-AP University, Amaravati, 522241, India · Mohan Babu University, Tirupati, India+1

High-Energy Physics

Open paper AskPDF arXiv

We report a search for dark matter (DM) produced in association with a leptonically decaying

Z

boson at

\sqrt{s}=13

TeV using CMS Run 2015D open data corresponding to an integrated luminosity of

2.32\,\mathrm{fb}^{-1}

together with simplified-model Monte Carlo simulation. Events are selected in the mono-

Z\rightarrow\ell^+\ell^-

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

\mathrm{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-

\mathrm{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.

Abstract

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