Search for BSM $H \to \tau\tau$ with early Run3 data
HLeprare
CMS Pre-approval 1 / 1
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Search for additional Higgs bosons decaying to a pair of τ leptons with the CMS experiment in pp collisions at $\sqrt{s} = 13.6~\text{TeV}$

HIG-25-006 Pre-approval

Zhiyuan Li1, Xiaohu Sun1, Leyan Li1, Licheng Zhang1, Botao Guo1, Mingxuan Zhang1, Jin Wang1, Zhenyu Dong1

Markus Klute2, Artur Gottmann2, Roger Wolf2

David Colling3, Daniel Winterbottom3, Irene Andreou3

Andrea Cardini4, Aliaksei Raspiareza4, Jacopo Malvaso4

1 Peking University (CN)

2 Karlsruhe Institute of Technology (DE)

3 Imperial College London (UK)

4 Deutsches Elektronen-Synchrotron DESY (DE)

May 1st, 2026 [TODO: Need to update]
  • Introduction
  • Event Selection & Categorization
  • Background Modelling
  • Corrections
  • Neural Network Discriminant
  • Systematic Uncertainties
  • Control Plots
  • Expected Results & Summary
Introduction
Analysis Note Draft
  • Search for additional neutral Higgs bosons $\phi$ in $pp$ collisions at $\sqrt{s}=13.6$ TeV using 62.3 fb$^{-1}$ of early Run 3 data
  • The MSSM Higgs sector, inspired by a 2HDM type II, introduces two Higgs doublets → five physical Higgs bosons: $H^{\pm}$, $h$, $H$, $A$
    • Tree-level properties described by two free parameters: $m_A$ and $\tan\beta$ (ratio of VEVs)
  • BR($H/A \to \tau\tau$) enhanced at high $\tan\beta$ → di-$\tau$ final state is a prime search channel
  • Two production modes: $gg\phi$ (dominant at low $\tan\beta$) and $bb\phi$ (dominant at high $\tan\beta$)
  • Model-independent interpretation: $60 \leq m_\phi \leq 3500$ GeV
  • Study four final states: $\mu\tau_h$, $e\tau_h$, $\tau_h\tau_h$, $e\mu$
  • Hybrid discriminant: PNN score ($m_\phi \leq 1000$ GeV) / $m_{\mathrm{T}}^{\text{tot}}$ ($m_\phi > 1000$ GeV)
  • CMS H→γγ [HIG-20-002] and H→ττ [HIG-21-001] Run 2 analyses indicate local excess ~3σ at $m_\phi$ = 95 and 100 GeV
Decay Channels Pie Chart
ggφ Feynman
(a)
bbφ fusion
(b)
bbφ scattering
(c)
Figure 1: Diagrams for the production of neutral Higgs bosons $\phi$ (left) via gluon fusion, labelled as $gg\phi$, and (middle and right) in association with b quarks, labelled as $bb\phi$ in the text. In the middle diagram, a pair of b quarks is produced from the fusion of two gluons, one from each proton. In the right diagram, a b quark from one proton scatters from a gluon from the other proton. In both cases $\phi$ is radiated off one of the b quarks.
  • CMS $pp$ collisions at $\sqrt{s}=13.6$ TeV, $\mathcal{L}=62.3$ fb$^{-1}$
  • Using HLepRare skimmed samples NanoAODv14
  • Only fully certified data (golden JSON) included
    • 2022preEE (Eras C–D) and 2022postEE (Eras E–G)
    • 2023preBPix (Era C) and 2023postBPix (Era D)
2022 Datasets
2023 Datasets
  • MC simulation used to model most backgrounds
    • DY: $Z \to \tau\tau$ — Drell–Yan (aMC@NLO FxFx, 0/1/2-jet merged)
    • Top quark: $t\bar{t}$ (Powheg) + single top (Powheg, 4FS t-channel & tW)
    • Diboson: $WW/WZ/ZZ$ (Powheg)
    • Other: $W$+jets (aMC@NLO FxFx) + SM Higgs (ggH, VBF, WH, ZH $\to \tau\tau$ Powheg)
  • Fake backgrounds (jet$\to\tau_h$/$\ell$ fakes from QCD multijet, $W$+jets, $t\bar{t}$) are estimated via the data-driven fake factor method
  • All MC yields normalized to best available cross sections × integrated luminosity per era
2022 MC Samples
2023 MC Samples
  • BSM signal: model-independent scalar $\Phi \to \tau\tau$
    • $gg \to \Phi$ — gluon gluon fusion (Powheg, 2HDM-II)
    • $bb \to \Phi$ — $b$-associated production
  • Mass range: 60–3500 GeV, $\sigma \times \mathrm{BR}$ set to 1 pb (model-independent)
  • Signal events generated with Powheg + Pythia8 (TuneCP5) at $\sqrt{s}=13.6$ TeV
  • Two production modes fitted with independent signal strengths, via the other production
    mode is floating
  • SM Higgs ($ggH$, VBF, $WH$, $ZH$, $H \to \tau\tau / bb$) treated as background
ggφ Feynman
(a)
bbφ fusion
(b)
bbφ scattering
(c)
Figure 1: Diagrams for the production of neutral Higgs bosons $\phi$ (a) via gluon fusion, labelled as $gg\phi$, and (b, c) in association with b quarks, labelled as $bb\phi$ in the text. In diagram (b), a pair of b quarks is produced from the fusion of two gluons, one from each proton. In diagram (c), a b quark from one proton scatters from a gluon from the other proton. In both cases $\phi$ is radiated off one of the b quarks.
2022 MC Samples
2023 MC Samples
Event Selection and Categorization
  • Event vertex: selected by maximizing $\Sigma p_{\mathrm{T}}^2$ of associated physics objects
  • Muons & Electrons: standard PF-based IDs with impact parameter cuts ($|d_{xy}|<0.045$ cm, $|d_z|<0.2$ cm); overlap removal $\Delta R> 0.5$ (lep-lep), $> 0.4$ (jet-lep)
  • Hadronic taus ($\tau_h$): reconstructed with hadrons-plus-strips algorithm; identified via DeepTau v2p5 (WPs channel-dependent)
  • Jets & b-tagging: anti-$k_T$ $R=0.4$ with PUPPI pileup mitigation; ParticleNet Medium WP for b-tagging; HF horn mitigation: jet $p_{\mathrm{T}} > 50$ GeV for $2.5 < |\eta| < 3.0$
  • MET: PUPPI MET
Object Identification & Isolation Kinematics
Muon Medium ID, $I_{rel}<0.15$ ($\mu\tau$) / $<0.20$ ($e\mu$) $|\eta|<2.1$ / $<2.4$
Electron MVA WP90 (Isolation included) $| \eta |<2.1$ ($e\tau$) / $<2.4$ ($e\mu$)
$\tau_h$ DeepTau vs jet: Medium
vs e/μ: chan. dependent (Tight/VLoose)		 $| \eta |<2.3$ ($\mu\tau/e\tau$) / $<2.1$ ($\tau\tau$)
Jets anti-$k_T$ $R=0.4$, Tight ID $p_{\mathrm{T}} > 30$ GeV, $| \eta | < 4.7$
b-jets ParticleNet Medium WP $p_{\mathrm{T}} > 20$ GeV, $| \eta | < 2.5$
MET PUPPI MET Type-I corrected —
Table I: Summary of object identification, isolation working points, and kinematic requirements used in the analysis.
  • Trigger & Kinematics: Combines single-lepton, di-$\tau$, and cross triggers. Offline $p_{\mathrm{T}}$ is set strictly above trigger turn-ons (see table for exact bounds).
  • Object & Pair Selection: High-purity ID required (MVA WP90 / Medium / DeepTau). Selected pairs must be oppositely charged (OS), separated by $\Delta R > 0.5$ (0.3 for $e\mu$), and are ranked by highest isolation.
  • Topological Background Suppression (Extra Cuts):
    • $W$+jets ($e\tau_h, \mu\tau_h$): require $m_{\text{T}} \lt 50$ GeV, based on $m_{\text{T}}(e/\mu, p_{\text{T}}^{\text{miss}}) = \sqrt{2p_{\text{T}}^{\ell}p_{\text{T}}^{\text{miss}}[1 - \cos(\Delta\phi)]}$
    • $t\bar{t}$ ($e\mu$): $D_\zeta = p_\zeta^{\text{miss}} - 0.85\,p_\zeta^{\text{vis}} > -35$ GeV (where $p_\zeta^{\text{miss/vis}}$ are projections onto bisector $\hat{\zeta}$)
  • MET Filters: Standard $E_T^{\text{miss}}$ filters recommended by JetMET POG are applied
Dzeta definition
Definition of the $D_{\zeta}$ observable in $e\mu$ channel
$e\tau_h$ $\mu\tau_h$ $\tau_h\tau_h$ $e\mu$
$p_{\mathrm{T}}$ $e > 25(31)$ GeV
$\tau_h > 35$ GeV
depending on trigger		 $\mu > 21(25)$ GeV
$\tau_h > 32$ GeV
depending on trigger		 $\tau_h > 35(40)$ GeV

depending on trigger		 $e > 15(24,31)$ GeV
$\mu > 15(24,25)$ GeV
depending on trigger
$\eta$ $|e| < 2.1, |\tau_h| < 2.3$ $|\mu| < 2.1, |\tau_h| < 2.3$ $|\tau_h| < 2.1$ $|e| < 2.4, |\mu| < 2.4$
DeepTau WP
vs (jet, e, μ)		 (Medium, Tight, VLoose) (Medium, VVLoose, Tight) (Medium, VVLoose, VLoose) —
Lepton ID & Iso MVA WP90 Medium & Iso $< 0.15$ — MVA WP90 $e$ &
Medium $\mu$, $I_{rel} < 0.20$
Trigger Single-$e$ or $e\tau$ cross
or single-$\tau$		 Single-$\mu$ or $\mu\tau$ cross
or single-$\tau$		 Di-$\tau$ or Di-$\tau$+jet
or single-$\tau$		 Single-$e$ or Single-$\mu$
or $e\mu$-cross
$d_z, d_{xy}$ (cm) $\ell$: $|d_{xy}| \lt 0.045, |d_z| \lt 0.2$
$\tau_h$: $|d_z| \lt 0.2$		 $\ell$: $|d_{xy}| \lt 0.045, |d_z| \lt 0.2$
$\tau_h$: $|d_z| \lt 0.2$		 $\ell$: $|d_{xy}| \lt 0.045, |d_z| \lt 0.2$
$\tau_h$: $|d_z| \lt 0.2$		 $\ell$: $|d_{xy}| \lt 0.045, |d_z| \lt 0.2$
$\tau_h$: $|d_z| \lt 0.2$
Extra $m_{\mathrm{T}} < 50$ GeV $m_{\mathrm{T}} < 50$ GeV — $D_\zeta > -35$ GeV
Table II: Event selection summary per channel.
  • Fundamental split by b-jet multiplicity:
    • b-tag ($N_\text{b-jets} \ge 1$): Highly enriched in $bb\phi$ signal events
    • no b-tag ($N_\text{b-jets} = 0$): Dominantly targets $gg\phi$ production
    • $e\tau_h$, $\mu\tau_h$: $m_{\mathrm{T}} \lt 50$ GeV;   $e\mu$: $D_\zeta > -35$ GeV
  • Fit variable strategy (transition at $m_\phi = 1000$ GeV):
    • $m_\phi \leq 1000$ GeV: Fit the PNN score distribution directly
    • $m_\phi > 1000$ GeV: Fit $m_{\mathrm{T}}^{\text{tot}}$ (PNN sensitivity gain is marginal above ~1 TeV)
    • $m_{\mathrm{T}}^{\text{tot}} = \sqrt{m_{\mathrm{T}}^2(\tau_1^{\mathrm{vis}}, p_{\mathrm{T}}^{\text{miss}}) + m_{\mathrm{T}}^2(\tau_2^{\mathrm{vis}}, p_{\mathrm{T}}^{\text{miss}}) + m_{\mathrm{T}}^2(\tau_1^{\mathrm{vis}}, \tau_2^{\mathrm{vis}})}$
  • Low-mass no b-tag sub-binning:
    • Further split into 4 bins using $p_{\mathrm{T}}^{\tau\tau}$ to enhance $gg\phi$ sensitivity:
      $\lt 50$, $[50, 100)$, $[100, 200)$, $\ge 200$ GeV
High-mass categories
High-mass categorization
Low-mass categories
Low-mass categorization
Background Modelling
  • Prompt backgrounds (MC-based):
    • $Z/\gamma^*\to\tau\tau$ (Drell-Yan): dominant in no b-tag
    • $t\bar{t}$: dominant in b-tag categories
    • $Z/\gamma^*\to\ell\ell$ ($\ell=e,\mu$), diboson (WW,WZ,ZZ), single top, $W$+jets, SM $H(125)$
  • Lepton misidentification:
    • $\ell\to\tau_h$ misID: negligible contribution, estimated from MC
    • $e\mu$: $\mu\to e$ misID (from $Z\to\mu\mu$) also MC-based
  • Channel dependencies: Composition varies heavily: $Z\to\tau\tau$ leads in $\mu\tau_h$, $e\tau_h$, $e\mu$ (~40–55%), while fakes dominate $\tau_h\tau_h$ (~80%)
  • Data-driven backgrounds:
    • $\mu\tau_h$, $e\tau_h$, $\tau_h\tau_h$: Fake Factor (FF) method for $j\to\tau_h$ fakes
    • $e\mu$: SS/OS method for QCD multijet estimation
    • Method heritage: background estimation follows closely the related $H\to\tau\tau$ analyses (HIG-19-010, HIG-21-001)
Background Composition mt
Background composition in the $\mu\tau_h$ channel
  • The FF method maps background from jets misidentified as hadronic $\tau$ decays
  • Determination Region (DR): enriched in target fake process, orthogonal to SR
    • W+jets: $m_{\mathrm{T}}^{e/\mu} > 50$ GeV and $N_{b\text{-jets}}=0$
    • QCD:
      • $e\tau_h$ and $\mu\tau_h$: same-sign taus, $m_{\mathrm{T}}^{e/\mu} < 50$ and $I_{\text{rel}}>0.05$
      • $\tau_h\tau_h$: same-sign taus
    • $t\bar{t}$: $m_{\mathrm{T}}^{e/\mu} > 50$ GeV and $N_{b\text{-jets}}>0$
  • $F_F$ weighted by estimated AR fraction:
    $F_F = \displaystyle\sum_{i} w_i \cdot F_F^i = F_F^{t\bar{t}} \times f_{t\bar{t}} + F_F^{\mathrm{QCD}} \times f_{\mathrm{QCD}} + F_F^{\mathrm{W+jets}} \times f_{\mathrm{W+jets}}$
  • For $\tau_h\tau_h$: QCD dominant, only $F_{\text{QCD}}$ measured
  • Application Region (AR): SR selection but $\tau_h$ passes VVVLoose and fails Medium DeepTau WP
  • Genuine $\tau$ decays from MC subtracted
FF method diagram FF workflow: DR → AR → SR
AR fraction μτh nob 2022postEE $w_i$ in AR ($\mu\tau_h$, no b-tag, 2022postEE,more in backup)
  • In each DR the $F_F$ are binned in $N_{\text{pre b-jets}}$ and $p_{\mathrm{T}}^{\text{jet}}/p_{\mathrm{T}}^{\tau_h}$ and fit to $p_{\mathrm{T}}^{\tau_h}$
    • QCD, W+jets: 2 $N_{\text{pre b-jets}}$ bins $(0, \geq1)$ × 3 $p_{\mathrm{T}}^{\text{jet}}/p_{\mathrm{T}}^{\tau_h}$ bins
    • $t\bar{t}$: 3 $p_{\mathrm{T}}^{\text{jet}}/p_{\mathrm{T}}^{\tau_h}$ bins only (derived from MC)
    • Fitted using Landau + first-order polynomial
  • High-$p_{\mathrm{T}}$ tail: binned values used where statistics are limited ($p_T > 140$ GeV)
    • If frac. error of [140, 200] < 0.5 and [200, ∞] < 0.5 → take binned values [140, 200, ∞]
    • If frac. error of [140, 200] > 0.5 and [200, ∞] < 0.5 → take binned value [200, ∞]
    • Else use fit for all $p_T$
  • $\tau_h\tau_h$: only QCD $F_F$ measured (QCD fraction $\sim$100% in AR); done for leading $\tau_h$, subleading jet fakes added using MC
QCD FF μτh
QCD FF in $\mu\tau_h$
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
QCD FF eτh
QCD FF in $e\tau_h$
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
W FF μτh
W+jets FF in $\mu\tau_h$
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
W FF eτh
W+jets FF in $e\tau_h$
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
ttbar FF μτh
$t\bar{t}$ FF in $\mu\tau_h$
($N_{\text{pre b-jets}}\geq 1, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
ttbar FF eτh
$t\bar{t}$ FF in $e\tau_h$
($N_{\text{pre b-jets}}\geq 1, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
  • A DR closure correction is determined in each region
    • Non-closures observed in $E_{\mathrm{T}}^{\text{miss}}$ and $\eta^{\tau}$
    • Corrections fitted using polynomials
  • From alternate DRs a DR→AR correction is also calculated
  • No obvious non-closure observed in $t\bar{t}$ DR
  • $\tau_h\tau_h$: only $\eta^{\tau_h}$ correction applied (no $E_T^{\text{miss}}$ correction needed)
QCD closure eτ MET
QCD $E_T^{\text{miss}}$ ($e\tau_h$)
QCD closure eτ eta
QCD $\eta^{\tau}$ ($e\tau_h$)
QCD closure μτ MET
QCD $E_T^{\text{miss}}$ ($\mu\tau_h$)
QCD closure μτ eta
QCD $\eta^{\tau}$ ($\mu\tau_h$)
DR closure corrections (2022postEE representative)
  • DR closure validation: data vs background estimation in the FF derivation regions (Good agreement validates the FF method)
  • Representative $\mu\tau_h$ plots shown (2022postEE, $N_{\text{pre b-jets}}=0$)
  • Full set of closure plots for all channels in backup
$E_T^{\text{miss}}$
$\eta_{\mu}$
$\eta_{\tau_h}$
$p_T^{\tau_h}$
QCD DR
$E_T^{\text{miss}}$
$\eta_{\mu}$
$\eta_{\tau_h}$
$p_T^{\tau_h}$
W+jets DR
$\mu\tau_h$ closure plots (2022postEE)
  • QCD multijet: dominant misID background in $e\mu$, where both leptons are mimicked by hadronic jets; non-QCD fakes (W/Z+jets, $t\bar{t}$) estimated from MC
  • Based on the strategy developed in HIG-19-010 and HIG-21-001
  • QCD background estimated from sideband with SS $e\mu$ pair
  • OS/SS extrapolation factor: $R_{\text{OS/SS}}(\Delta R) = \dfrac{N_{\text{anti-iso}\;\mu}^{\text{OS}}(\Delta R)}{N_{\text{anti-iso}\;\mu}^{\text{SS}}(\Delta R)}$
  • Determination region: nominal electron and anti-isolated muon ($0.20 < I_{\text{rel}}^{\mu} < 0.50$)
  • Dependence of OS/SS on $\Delta R(e,\mu)$ fitted with 2nd ~ 4th order polynomial
2022postEE OS/SS factor in no b-tag region
2022postEE OS/SS factor in b-tag region
  • OS/SS scale factors depend not only on $\Delta R(e,\mu)$ and jet multiplicity, but also on $p_T^{e}$ and $p_T^{\mu}$
  • Residual 2D correction $C_{p_T}(p_T^{e},\, p_T^{\mu})$ derived in the anti-isolated $\mu$ control region
  • Apply the $\Delta R$-dependent factors to SS events, then adjust the 2D QCD distribution to match OS data
  • Final QCD estimate: $N_{\text{QCD}}^{\text{OS,SR}} = R \times C_{p_T}(p_T^{e},\, p_T^{\mu}) \times \big(N_{\text{data}}^{\text{SS}} - N_{\text{prompt,MC}}^{\text{SS}}\big)$
  • 2D weights derived independently for each data-taking era
(a) 2022preEE
(b) 2022postEE
(c) 2023preBPix
(d) 2023postBPix
Corrections of the QCD OS/SS scale factors determined in the region with an anti-isolated muon as a function of the $p_T$ of the electron and the muon, using data collected in 2022preEE(a), 2022postEE(b), 2023preBPix(c), 2023postBPix(d)
  • Closure tests in the $\text{DR}_{\text{OS}}$ control region: isolated $e$ + anti-isolated $\mu$ (OS), with 2D $p_T$ correction applied
  • Representative $e\mu$ plots shown (2022postEE); good data-MC agreement validates the QCD estimation
$\Delta R(e,\mu)$
$E_T^{\text{miss}}$
$p_T^{e}$
$p_T^{\mu}$
$\Delta R(e,\mu)$
$E_T^{\text{miss}}$
$p_T^{e}$
$p_T^{\mu}$
Corrections
  • Pileup reweighting:
    • Minimum-bias cross section 69.2 mb ± 4.6% [TWiki]
  • Electron corrections: [EGamma]
    • ID/isolation scale factors (tag-and-probe)
    • Energy scale and smearing ($p_T$-dependent)
  • Muon corrections: [MuonPOG]
    • ID/isolation scale factors (tag-and-probe)
  • $\tau_h$ corrections: [TauPOG]
    • DeepTau v2.5 ID SF (genuine $\tau_h$, per WP)
    • $e \to \tau_h$, $\mu \to \tau_h$ mis-ID rate corrections
    • Energy scale: decay-mode dependent (DM 0, 1, 10, 11)
  • Jet corrections: [JERC]
    • JES: $p_{\mathrm{T}}$, $\eta$, pileup dependent
    • JER: Hybrid smearing to match data resolution
  • b-tagging SF: [BTV Wiki]
    • Method 1a event reweighting (flavor, $p_T$, $\eta$)
    • Efficiency maps: DY, $t\bar{t}$, ggH, bbH
  • DY reweighting: [HLepRare]
    • $Z$ $p_T$-mass reweighting + MET recoil correction
  • Trigger SF: [HLepRare]
    • Dedicated SFs calculated with OR logic
    • Per-leg tag-and-probe
  • Top $p_T$ reweighting (for $t\bar{t}$ MC)
  • Jet-fake $\tau_h$ residual corrections
  • $Z$ $p_T$-mass reweighting for DY+jets MC [HLepRare] [Dennis Roy, 22 Oct 2025]
  • Ratio of (Data − non-DY MC) / DY MC in $\mu\mu$ region over reco-level $p_{T,\ell\ell}$
  • Normalized — should not affect overall DY normalization
  • Fit splits into 3 regions with floating boundaries; ~8–10 uncorrelated shape uncertainties
Before $Z$ $p_T$ reweighting [NLO CR Z→μμ]
After $Z$ $p_T$ reweighting [NLO CR Z→μμ]
  • Bosonic recoil correction derived from $Z \to \mu\mu$ final state, binned by $N_{\text{jet}}$ and $p_{T,\ell\ell}$ [HLepRare] [Dennis Roy, 22 Oct 2025]
  • Quantile mapping & Rescaling applied to $U_{\parallel}$, $U_{\perp}$ to recompute PUPPI MET
  • Derived after nominal $Z$ $p_T$ reweighting
  • Corrections from $Z \to \mu\mu$; validation & uncertainties from $Z \to ee$
  • Applied to $Z/\gamma^*$+jets, $W$+jets, and Higgs signal
Before recoil correction [NLO CR Z→μμ]
After recoil correction [NLO CR Z→μμ]
  • All triggers combined via OR logic per channel [HLepRare]
    • $\mu\tau_h$: single $\mu$ (IsoMu24) OR $\mu\tau$ cross (Mu20Tau27)
    • $e\tau_h$: single $e$ (Ele30) OR $e\tau$ cross (Ele24Tau30)
    • $\tau_h\tau_h$: di-$\tau$ (DoubleTau35) OR di-$\tau$ + jet (DoubleTau30 + Jet60)
    • $e\mu$: 4 triggers — IsoMu24, Ele30, Mu8Ele23, Mu23Ele12
  • For 2-trigger channels ($\mu\tau_h$, $e\tau_h$, $\tau_h\tau_h$), taking single $\mu$ OR $\mu\tau$ cross as example:
    $\begin{aligned} \text{OR_eff}_{i} &= \text{passSingle} \times \text{single_}\mu^{\text{eff}}_{i} \\ &\quad - \text{passCross} \times \text{passSingle} \times \min(\text{single_}\mu^{\text{eff}}_{i},\; \mu\text{_leg}^{\text{eff}}_{i}) \times \tau\text{_leg}^{\text{eff}}_{i} \\ &\quad + \text{passCross} \times \mu\text{_leg}^{\text{eff}}_{i} \times \tau\text{_leg}^{\text{eff}}_{i} \end{aligned}$
  • For $e\mu$ channel (4 triggers), simplified via inclusion-exclusion (see Backup S61–S62):
    $\varepsilon_{\text{union}} = \varepsilon(\mu{>}24) + \varepsilon(e{>}30) + \varepsilon(\mu{>}15,\,e{>}23) - \varepsilon(\mu{>}24,\,e{>}23) - \varepsilon(\mu{>}15,\,e{>}30)$
  • Per-leg efficiencies measured via tag-and-probe following EGM POG / MUO POG recommendations
  • Uncertainties: decorrelated across eras; lepton-leg unc. fully correlated with single-lepton trigger unc.
  • Electron leg SF measured via EGamma tag-and-probe: 4-fit average ± RMS as SF and uncertainty
  • Tag-and-probe using HLT_Ele23_Ele12_CaloIdL_TrackIdL_IsoVL as recommended
  • $p_T$ bins: [15, 20, 25, 50, 100, 200, ∞]; $|\eta|$ bins optimized for offline selection
  • For more measurement details, see EGM POG presentation: [Leyan Li, 11/21 2025] [EGM gitlab issue]
  • For Combined OR SF validations, see Backup S65.
HLT SF vs pT 2022
SF vs $p_T$ (2022postEE)
HLT SF vs eta 2022
SF vs $|\eta|$ (2022postEE)
HLT SF vs pT 2023
SF vs $p_T$ (2023)
HLT SF vs eta 2023
SF vs $|\eta|$ (2023)
  • Efficiency extracted on the Z peak using standard MUO POG tag-and-probe
  • Since HLT_Mu8_TrkIsoVVL is highly prescaled, the alternative cross-trigger
    HLT_Mu17_TrkIsoVVL_Mu8_TrkIsoVVL_DZ_Mass8 is used as recommended
  • Probe selection: TightID && LoosePFIso
  • Systematics: tag isolation, fit mass range & binning, alternative background
  • For more measurement details, see [Full plots]
SF vs $p_T$ (2022postEE)
SF vs $|\eta|$ (2022postEE)
SF vs $p_T$ (2023preBPix)
SF vs $|\eta|$ (2023preBPix)
Neural Network Discriminant
  • A PNN introduces mass hypothesis $m_\Phi$ as an explicit network input, replacing many separate classifiers across mass points [arXiv:1601.07913]
  • The model learns $f_\theta(\mathbf{x}, m_\Phi)$ — conditioned on both event features $\mathbf{x}$ and mass $m_\Phi$
  • Signal events paired with their true mass; background events randomly assigned mass → smooth interpolation across full mass range
  • Architecture: [550, 2550, 550] fully-connected layers
    • LeakyReLU ($\alpha\!=\!0.1$), Dropout (0.5), BatchNorm, $L_2$ reg ($\lambda\!=\!5\!\times\!10^{-3}$)
    • SGD + Nesterov momentum; Sparse categorical cross-entropy
    • Early stopping mechanism and dynamic LR decay
PNN Reference
Left: Individual networks each trained at a single fixed parameter $\theta$ (suboptimal, non-smooth interpolation).Right: A unified network trained with input features and $\theta$, learning smooth interpolation across several values of $\theta$ [arXiv:1601.07913]
Our PNN Architecture
Kinematic features + $m_\Phi$ → [550, 2550, 550] → Softmax(S, T, F)
  • Training datasets: ggH + bbH signals (unified single-signal-node) + all SR backgrounds (MC + data-driven fakes with weights)
    • Unified training improves limits and avoids prohibitive template scaling; ggH/bbH separated as independent POIs at fit stage (see Backup S66)
  • Variable selection: 44 candidates → ~25 best variables per channel, selected based on:
    • Separation power: rank variables by $\langle S^2 \rangle$ (following TMVA)
    • Decorrelation: remove highly correlated pairs with $|r_{ij}| > 0.85$
    • Same candidate set for all 4 channels; channel-specific ranking optimizes final selection
    $\langle S^2 \rangle = \frac{1}{2}\int\frac{(\hat{y}_S - \hat{y}_B)^2}{\hat{y}_S + \hat{y}_B}\,dy$
    $r_{ij} = \frac{\sum_k w_k (x_i^{(k)} - \bar{x}_i)(x_j^{(k)} - \bar{x}_j)}{\sqrt{\sum_k w_k (x_i^{(k)} - \bar{x}_i)^2} \sqrt{\sum_k w_k (x_j^{(k)} - \bar{x}_j)^2}}$
Category Representative Variables Main Discrimination Target
Mass $m_\mathrm{T}^\mathrm{tot}$, $m_\mathrm{vis}$, $m_{\tau\tau}$, $m_\mathrm{T}^{\ell_1}$, $m_\mathrm{T}^{\ell_2}$ Resonance scale; $W$+jets / $t\bar{t}$ rejection
Momentum $p_\mathrm{T}^{\ell_1}$, $p_\mathrm{T}^{\ell_2}$, $p_\mathrm{T}^{\tau\tau}$, $p_\mathrm{T}^\mathrm{vis}$, MET, $D_\zeta$ Boost of the system; recoil and MET topology
Angular $\Delta R(\ell_1,\ell_2)$, $\Delta\phi(\ell_1,\ell_2)$, $\Delta\eta(\ell_1,\ell_2)$, $\phi_\mathrm{MET}$ Event geometry; reducible bkg separation
FastMTT $m_\mathrm{fastmtt}$, $p_\mathrm{T}^\mathrm{fastmtt}$, $\eta^\mathrm{fastmtt}$, $\phi^\mathrm{fastmtt}$ Improved parent-boson kinematics
b-tag / Jet leading b-jet kinematics, $p_T^{b_1}/p_T^{\mathrm{fastmtt}}$, $\Delta\eta(b_1,\tau\tau)$ $gg\phi$ vs $bb\phi$ topology; top rejection
Mass hypothesis $m_\Phi$ (explicit network input) Continuous parameterization across signal masses
Table 2: Representative categories of PNN input variables. The full feature set includes channel-dependent variations and composite observables.
  • 3-class softmax output: S (Signal), T (True bkg), F (Fake bkg)
    • Background split into genuine $\tau$/lepton (T) vs misidentified (F) for improved modeling
    • Ratio-type variables: explicit denominator protection; NaN/inf events removed
  • Multiple formulas tested: $S$, $\dfrac{S}{S+F}$, $\dfrac{S}{S+T}$, $\dfrac{S}{T}$, $\dfrac{S}{F}$, etc.
    • No visible performance difference
  • Final discriminant:
    $\text{PNN}_{\text{score}} = S$
    • Raw signal node probability used directly for simplicity
PNN score distribution at 250 GeV
PNN score at $m_\Phi = 250$ GeV ($e\mu$ channel):
signal peaks near 1, background near 0
  • Two dedicated models: Low-mass (60–250 GeV) and High-mass (300–3500 GeV)
    • Mass normalized to [0,1]: $m_{\text{scaled}} = (m - m_{\min})/(m_{\max} - m_{\min})$; background events randomly assigned mass from signal mass points
    • Low-mass PNN serves as nominal discriminant for 60–250 GeV
    • High-mass PNN trained to extend PNN coverage to 300–3500 GeV; systematic comparison with $m_T^{\text{tot}}$ shows PNN advantage diminishes at high mass — score degenerates (S→1, B→0), reducing shape fit to counting experiment
    • Final strategy: PNN score for $m_\Phi \le 1$ TeV, $m_T^{\text{tot}}$ for $m_\Phi > 1$ TeV (see Backup S47)
  • Inference: for each mass $M$, PNN score evaluated at $m_\Phi = M$ for all data & MC
    • Even events → odd model, odd events → even model → full statistics
  • The scores from even and odd models, applied to the same even event number events, show no significant deviation and overfitting
(a) PNN score at 100 GeV
(b) PNN score at 160 GeV
(c) PNN score at 200 GeV
PNN scores calculated with even and odd models, applied on even event number events. Shown for $\mu\tau$ channel and $gg\phi$ signal. The ratio of background prediction is shown in the bottom pad.
Systematic Uncertainties
  • Tau ID efficiency & TES: [TauPOG]
    • Statistical: decorrelated by DM and by year
    • Systematic: 3-way split (fully corr. / corr. across years but not DM / fully decorr.)
  • Trigger efficiency: [HLepRare]
    • OR logic (single lepton + cross triggers)
    • Lepton leg corr. with single lepton; tau leg uncorr.
    • All decorrelated between years
  • Electron energy scale: [EGamma]
    • Scale + resolution from EGamma POG; fully corr. between eras
  • Jet energy scale: [JES]
    • Reduced grouping: 11 nuisances/era
    • Propagated to MET
  • Jet energy resolution: [JER]
    • Uncorr. between years; propagated to MET
  • $l \to \tau_h$ fake energy scale:
    • 1.0% for muons; 0.5–6.6% for electrons
    • Uncorr. between years
  • MET recoil corrections: [HLepRare]
    • Response and resolution varied; uncorr. between eras
  • Top $p_T$ reweighting:
    • 0 to 2× correction; fully corr. between eras
  • DY mass, $p_T$ reweighting: [HLepRare]
    • 10 NLO fit parameters; fully uncorr. from each other
  • Fake-factor shape uncertainties: [HIG-19-010] [HIG-21-001]
    • $\tau_h\tau_h$ / $\mu\tau_h$ / $e\tau_h$: FF stat., closure, non-closure, process subtraction
    • $e\mu$: OS/SS stat., 2D $p_T$ weight correction, data-driven stat. (see Backup 72)
  • Bin-by-bin: autoMCStats (Barlow-Beeston lite)
  • Luminosity: [LumiPOG]
    • 2022: 34.7 fb$^{-1}$ (1.4%); 2023: 27.6 fb$^{-1}$ (1.3%)
    • Combined: 62.3 fb$^{-1}$ (~1.0%); partially correlated (2 nuisances)
  • Electron, muon ID efficiency:
    • 2% per lepton; fully correlated between years
  • Lepton to tau fake rate: [TauPOG]
    • $\eta$-dependent; negligible shape → lnN
    • Uncorrelated between eras
  • b-tagging efficiency: [BTV]
    • btagSFbc (b/c): 1 corr. + 1 decorr. across years
    • btagSFlight: 1 corr. + 1 decorr. across years
    • Decorrelated per channel (phase-space dependent)
  • Background normalization: [SM Xsec]
    • DY: scale 1.1% + PDF 1.0%
    • $t\bar{t}$: scale 3.6% + PDF 2.5% [ttbar]
    • Diboson: scale 2.4% + PDF 0.1%
    • W+jets: scale 5.4% + PDF 0.2%
    • $e\mu$ QCD: $r_{\text{b-tag}}$ non-closure unc., uncorr. across years
  • SM Higgs theory: [LHCHXSWG]
    • ggH: scale 6.7%, PDF+$\alpha_s$ 3.2%
    • VBF: scale 0.5%, PDF+$\alpha_s$ 2.1%
    • BR($H\to\tau\tau$): 1.7% (h.o.) + 0.99% ($m_q$) + 0.62% ($\alpha_s$) [CERN YR4]
Control Plots
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
mTtot 2022EE nob mTtot 2022postEE nob mTtot 2023 nob mTtot 2023BPix nob mTtot 2022EE btag mTtot 2022postEE btag mTtot 2023 btag mTtot 2023BPix btag
mTtot 2022EE nob mTtot 2022postEE nob mTtot 2023 nob mTtot 2023BPix nob mTtot 2022EE btag mTtot 2022postEE btag mTtot 2023 btag mTtot 2023BPix btag
mTtot 2022EE nob mTtot 2022postEE nob mTtot 2023 nob mTtot 2023BPix nob mTtot 2022EE btag mTtot 2022postEE btag mTtot 2023 btag mTtot 2023BPix btag
mTtot 2022EE nob mTtot 2022postEE nob mTtot 2023 nob mTtot 2023BPix nob mTtot 2022EE btag mTtot 2022postEE btag mTtot 2023 btag mTtot 2023BPix btag
PNN100 2022postEE nob1 PNN100 2023 nob1 PNN200 2022postEE nob1 PNN200 2023 nob1 PNN100 2022postEE btag PNN100 2023 btag PNN200 2022postEE btag PNN200 2023 btag
PNN100 2022postEE nob1 PNN100 2023 nob1 PNN200 2022postEE nob1 PNN200 2023 nob1 PNN100 2022postEE btag PNN100 2023 btag PNN200 2022postEE btag PNN200 2023 btag
PNN100 2022postEE nob1 PNN100 2023 nob1 PNN200 2022postEE nob1 PNN200 2023 nob1 PNN100 2022postEE btag PNN100 2023 btag PNN200 2022postEE btag PNN200 2023 btag
PNN100 2022postEE nob1 PNN100 2023 nob1 PNN200 2022postEE nob1 PNN200 2023 nob1 PNN100 2022postEE btag PNN100 2023 btag PNN200 2022postEE btag PNN200 2023 btag
Expected Results
  • Simultaneous binned maximum-likelihood fit across all channels, categories, and control regions
  • Shape uncertainties: template morphing; normalization: log-normal constraints; finite MC: automatic bin-by-bin statistical terms
  • 95% CL upper limits on $\sigma \times \mathcal{B}(\phi \to \tau\tau)$ via $CL_s$ method [CMS:COMBINE2024]
  • Hybrid discriminant strategy:
    • $m_\phi \le 1000$ GeV: PNN score (evaluated at each mass hypothesis)
    • $m_\phi > 1000$ GeV: $m_{\mathrm{T}}^{\text{tot}}$
  • Transition at 1000 GeV: PNN gain decreases at high mass; $m_{\mathrm{T}}^{\text{tot}}$ provides robust and competitive performance
  • Independent signal-strength parameters for gg$\phi$ and bb$\phi$ in dedicated fits
  • Blinded analysis: all results shown are expected limits from Asimov dataset
  • Expected 95% CL upper limits on $\sigma(\text{gg}\phi/\text{bb}\phi) \times \mathcal{B}(\phi \to \tau\tau)$, combined 2022 + 2023
  • Exclusion limits range from a few pb at low Higgs boson masses to $\sim 0.9$ fb at the highest Higgs boson masses
Limit ggH Limit bbH
ggH Limits by Channel
Expected upper limits on gg$\phi$ production for individual final states
bbH Limits by Channel
Expected upper limits on bb$\phi$ production for individual final states
  • The model-independent expected limits for HIG-21-001 are calculated based on their provided datacards.
  • The limits shown in the comparisons are the original expected limits without any luminosity scaling, evaluated at their absolute integrated luminosities.
  • Expanded the mass scan from 30 to 42 points by computing additional expected limits for [65, 70, 75, 85, 90, 95, 105, 110, 115, 135, 450, 1100] GeV.
  • For both gg$\phi$ and bb$\phi$ productions, the PNN technique applied in the $< 1$ TeV range effectively improves upon the $m_{\mathrm{T}}^{\text{tot}}$ performance, generally outperforming the HIG-21-001 limits:
    • gg$\phi$: improvements are seen across the entire 60–1000 GeV range.
    • bb$\phi$: improvements are slightly smaller but remain superior in the 60–600 GeV range, except for the 80–120 GeV region where a background peak is naturally expected due to the dominant DY background.
ggH Run3 vs Run2 bbH Run3 vs Run2
ggH 100 GeV Impacts
30 leading impacts for the gg$\phi$ production mode at $m_{\phi} = 100$ GeV fitted by PNN score
bbH 100 GeV Impacts
30 leading impacts for the bb$\phi$ production mode at $m_{\phi} = 100$ GeV fitted by PNN score
  • Presented BSM $H \to \tau\tau$ analysis on early Run 3 data (62.3 fb$^{-1}$ at $\sqrt{s} = 13.6$ TeV): model-independent search for additional neutral Higgs bosons in the $\tau_h\tau_h$, $\mu\tau_h$, $e\tau_h$, and $e\mu$ final states over $m_\phi = 60$–$3500$ GeV, targeting both gg$\phi$ and bb$\phi$ production
  • Two-regime strategy: PNN-score templates for $m_\phi \le 1000$ GeV; $m_{\mathrm{T}}^{\text{tot}}$ templates for $m_\phi > 1000$ GeV. A common boundary at $m_\phi = 1000$ GeV selected from a dedicated Run 3 strategy comparison
  • Expected upper limits on $\sigma \times \mathcal{B}(\phi \to \tau\tau)$ derived with full treatment of systematic uncertainties for both production modes
  • The PNN technique in the $m_\phi \lt 1$ TeV range resolves the known limitation of $m_{\mathrm{T}}^{\text{tot}}$ being suboptimal at low mass [HIG-21-001], providing improved or comparable sensitivity for both gg$\phi$ and bb$\phi$ productions under absolute luminosity
Status: Analysis is blinded. All POG sign-offs obtained (BTV in progress). Pre-approval questionnaire completed. We are seeking permission to unblind & pre-approval of the analysis.
Backup
  • PNN extended to cover full $60$–$3500$ GeV range (two models: low-mass + high-mass)
  • Compare expected upper limits: PNN score vs $m_{\mathrm{T}}^{\text{tot}}$ in the $300$–$3500$ GeV region
  • PNN advantage decreases with mass, becomes marginal around $1000$ GeV → chosen as common boundary
ggH PNN vs mTtot
All-channel combined expected upper-limit comparison in the high-mass region between fits using PNN score and fits using $m_{\mathrm{T}}^{\text{tot}}$ for $gg\phi$
bbH PNN vs mTtot
All-channel combined expected upper-limit comparison in the high-mass region between fits using PNN score and fits using $m_{\mathrm{T}}^{\text{tot}}$ for $bb\phi$
  • Expected limits are derived from the PNN score for $60 \le m_{\phi} \le 1000$ GeV, and from $m_{\mathrm{T}}^{\text{tot}}$ for $m_{\phi} > 1000$ GeV
  • Evaluated on a finer mass grid than HIG-21-001 (union of both sets): 60, 80, 100, 120, 125, 130, 140, 160, 180, 200, 250, 300, 350, 400, 500, 600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000, 2300, 2600, 2900, 3200, 3500 GeV
ggH HIG-21-001 vs This Analysis
bbH HIG-21-001 vs This Analysis
The bb/gg$\phi$ All-channel combined expected upper limits results with full systematics at 95% confidence level of HIG-21-001 and this analysis
Channel Trigger type Trigger threshold (GeV) Offline $p_{\mathrm{T}}$ (GeV)
$\tau_h\tau_h$ di-$\tau$ $\tau(35),\tau(35)$ $\tau(40),\tau(40)$
di-$\tau$+jet $\tau(30),\tau(30)$, jet(60) $\tau(35),\tau(35)$, jet(60)
$\mu\tau_h$ single-$\mu$ $\mu(24)$ $\mu(25)$
$\mu\tau$ cross $\mu(20),\tau(27)$ $\mu(21),\tau(32)$
$e\tau_h$ single-$e$ $e(30)$ $e(31)$
$e\tau$ cross $e(24),\tau(30)$ $e(25),\tau(35)$
$e\mu$ single-$e$/single-$\mu$ $e(30)$/$\mu(24)$ $e(31)$/$\mu(25)$
$e\mu$ cross $e(12)\mu(23)$ / $e(23)\mu(8)$ $e(15)\mu(24)$ / $e(24)\mu(15)$
Table III: Trigger and offline $p_{\mathrm{T}}$ thresholds per channel (2022–2023).
  • Offline $p_{\mathrm{T}}$: 1 GeV above trigger threshold for $e/\mu$ (minimum 15 GeV)
  • Offline $p_{\mathrm{T}}$: 5 GeV above trigger threshold for $\tau_h$ (minimum 30 GeV)
  • Trigger objects matched offline within $\Delta R < 0.5$
e mu $e\mu$
e tau_h $e\tau_h$
mu tau_h $\mu\tau_h$
tau_h tau_h $\tau_h\tau_h$

  • Fractions of QCD, W+jets, and $t\bar{t}$ in the AR as a function of $m_{\mathrm{T}}^{\text{tot}}$, used as weights $f_k$ in the combined $F_F$
μτh nob fraction $\mu\tau_h$ — no b-tag
μτh btag fraction $\mu\tau_h$ — b-tag
eτh nob fraction $e\tau_h$ — no b-tag
eτh btag fraction $e\tau_h$ — b-tag
QCD 2022postEE
QCD (2022postEE)
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
QCD 2023preBPix
QCD (2023preBPix)
($N_{\text{pre b-jets}}=0, p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$)
QCD (2022postEE, $N_{\text{pre b-jets}}=0$)
W+jets (2022postEE, $N_{\text{pre b-jets}}=0$)
$t\bar{t}$ (2022postEE, $N_{\text{pre b-jets}}\ge 1$)
QCD (2023preBPix)
W+jets (2023preBPix)
$t\bar{t}$ (2023preBPix)
All plots shown for lowest $p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$ bin
QCD (2022postEE, $N_{\text{pre b-jets}}=0$)
W+jets (2022postEE, $N_{\text{pre b-jets}}=0$)
$t\bar{t}$ (2022postEE, $N_{\text{pre b-jets}}\ge 1$)
QCD (2023preBPix)
W+jets (2023preBPix)
$t\bar{t}$ (2023preBPix)
All plots shown for lowest $p_T^{\text{jet}}/p_T^{\tau_h} < 1.25$ bin
2022preEE
2022postEE
2023preBPix
2023postBPix
Only $\eta^{\tau_h}$ correction applied in $\tau_h\tau_h$ channel (no $E_T^{\text{miss}}$ correction needed)
$E_T^{\text{miss}}$ 2022preEE
$E_T^{\text{miss}}$ 2022postEE
$E_T^{\text{miss}}$ 2023preBPix
$E_T^{\text{miss}}$ 2023postBPix
$\eta^{\tau_h}$ 2022preEE
$\eta^{\tau_h}$ 2022postEE
$\eta^{\tau_h}$ 2023preBPix
$\eta^{\tau_h}$ 2023postBPix
$E_T^{\text{miss}}$ 2022preEE
$E_T^{\text{miss}}$ 2022postEE
$E_T^{\text{miss}}$ 2023preBPix
$E_T^{\text{miss}}$ 2023postBPix
$\eta^{\tau_h}$ 2022preEE
$\eta^{\tau_h}$ 2022postEE
$\eta^{\tau_h}$ 2023preBPix
$\eta^{\tau_h}$ 2023postBPix
$E_T^{\text{miss}}$
$\eta$ (leading $\tau_h$)
$\eta$ (sub-leading $\tau_h$)
$p_T$ (sub-leading $\tau_h$)
2022postEE
$E_T^{\text{miss}}$
$\eta$ (leading $\tau_h$)
$\eta$ (sub-leading $\tau_h$)
$p_T$ (sub-leading $\tau_h$)
2023preBPix
QCD: $E_T^{\text{miss}}$
QCD: $\eta_e$
QCD: $\eta_{\tau_h}$
QCD: $p_T^{\tau_h}$
QCD DR
W: $E_T^{\text{miss}}$
W: $\eta_e$
W: $\eta_{\tau_h}$
W: $p_T^{\tau_h}$
W+jets DR
QCD: $E_T^{\text{miss}}$
QCD: $\eta_e$
QCD: $\eta_{\tau_h}$
QCD: $p_T^{\tau_h}$
QCD DR
W: $E_T^{\text{miss}}$
W: $\eta_e$
W: $\eta_{\tau_h}$
W: $p_T^{\tau_h}$
W+jets DR
$\mu\tau_h$: $E_T^{\text{miss}}$
$\mu\tau_h$: $\eta_\mu$
$\mu\tau_h$: $\eta_{\tau_h}$
$\mu\tau_h$: $p_T^{\tau_h}$
$\mu\tau_h$ $t\bar{t}$ DR
$e\tau_h$: $E_T^{\text{miss}}$
$e\tau_h$: $\eta_e$
$e\tau_h$: $\eta_{\tau_h}$
$e\tau_h$: $p_T^{\tau_h}$
$e\tau_h$ $t\bar{t}$ DR
  • Both 2022 and 2023 Data and MC events are required to pass the following $E_T^{\text{miss}}$ filters recommended by the JetMET POG [TWiki]:
    • Primary vertex filter (Data, MC)
    • Beam halo filter (Data, MC)
    • ECAL TP filter (Data, MC)
    • Bad PF Muon Filter (Data, MC)
    • Bad PF Muon Dz Filter (Data, MC)
    • HF noisy hits filter (Data, MC)
    • ee badSC noise filter (Data, MC)
    • ECAL bad calibration filter update (Data, MC)
  • Notation — We make following notation to simply the derivation:
    • $T_1 = \text{Mu24}$: $\mu: p_T > 24$ (single muon trigger)
    • $T_2 = \text{Ele30}$: $e: p_T > 30$ (single electron trigger)
    • $T_3 = \text{Mu8Ele23}$: $\mu: p_T > 8$, $e: p_T > 23$ (dilepton trigger)
    • $T_4 = \text{Mu23Ele12}$: $\mu: p_T > 23$, $e: p_T > 12$ (dilepton trigger)
  • Subset relations — Due to the $p_T$ threshold, we have:
    1. $\mu > 24 \subset \mu > 23 \subset \mu > 8$ (so $T_1 \subset T_4 \subset T_3$ for muon legs)
    2. $e > 30 \subset e > 23 \subset e > 12$ (so $T_2 \subset T_3 \subset T_4$ for electron legs)
    3. $T_1 \cap T_2 \subset T_3 \cap T_4$, and $T_1 \cap T_2 = T_1 \cap T_2 \cap T_3 \cap T_4$ (four-fold intersection $\equiv T_1T_2$ double intersection).
    Considering the lepton ID and isolation, this subset relation is still valid. This is becasue the single-lepton triggers $\text{Mu24}$ and $\text{Ele30}$ use tighter identification and isolation criteria than the dilepton triggers $\text{Mu8Ele23}$ and $\text{Mu23Ele12}$.
  • Inclusion-exclusion — The total union efficiency for the OR combination of four triggers is:
    \begin{equation*} \begin{split} \varepsilon_{\rm union} =& \underbrace{(\varepsilon_1+\varepsilon_2+\varepsilon_3+\varepsilon_4)}_{\text{Single-trigger terms}} - \underbrace{(\varepsilon_{12}+\varepsilon_{13}+\varepsilon_{14} +\varepsilon_{23}+\varepsilon_{24}+\varepsilon_{34})}_{\text{Pairwise intersections (6 terms)}} \\ &+ \underbrace{(\varepsilon_{123}+\varepsilon_{124}+\varepsilon_{134}+\varepsilon_{234})}_{\text{Triple intersections (4 terms)}} - \underbrace{\varepsilon_{1234}}_{\text{Four-fold intersection (1 term)}} \end{split} \end{equation*}
    Where: $\varepsilon_i$ = efficiency of trigger $i$ firing alone; $\varepsilon_{ij}$ = triggers $i,j$ firing simultaneously; $\varepsilon_{ijk}$ = triggers $i,j,k$ simultaneously; $\varepsilon_{1234}$ = all four triggers simultaneously.
  • Step 1 — Replace $\varepsilon_1 \sim \varepsilon_4$ with physical leg criteria:
    \[ \varepsilon_1+\varepsilon_2+\varepsilon_3+\varepsilon_4 = \varepsilon(\mu{>}24) + \varepsilon(e{>}30) + \varepsilon(\mu{>}8, e{>}23) + \varepsilon(\mu{>}24,e{>}12) \]
  • Step 2 — Eliminate redundancy via subset inclusion:
    \begin{align*} &\varepsilon_{12}+\varepsilon_{13}+\varepsilon_{14}+\varepsilon_{23}+\varepsilon_{24}+\varepsilon_{34} \\ &= \varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}23) + \varepsilon(\mu{>}24,e{>}12) + \varepsilon(\mu{>}8,e{>}30) + \varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}23) \\ &= 2\varepsilon(\mu{>}24,e{>}30) + 2\varepsilon(\mu{>}24,e{>}23) + \varepsilon(\mu{>}24,e{>}12) + \varepsilon(\mu{>}8,e{>}30) \end{align*}
  • Step 3 — Collapse triple intersections to core double intersections:
    \begin{align*} \varepsilon_{123}+\varepsilon_{124}+\varepsilon_{134}+\varepsilon_{234} &= \varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}23) + \varepsilon(\mu{>}24,e{>}30) \\ &= 3\varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}23) \end{align*}
  • Step 4 — By global subset inclusion ($T_1\cap T_2 \subset T_3\cap T_4$): $\varepsilon_{1234} = \varepsilon(\mu{>}24,e{>}30)$
    \begin{align*} \varepsilon_{\rm union} &= \left[\varepsilon(\mu{>}24) + \varepsilon(e{>}30) + \varepsilon_3 + \varepsilon(\mu{>}24,e{>}12)\right] \\ &- \left[2\varepsilon(\mu{>}24,e{>}30) + 2\varepsilon(\mu{>}24,e{>}23) + \varepsilon(\mu{>}24,e{>}12) + \varepsilon(\mu{>}8,e{>}30)\right] \\ &+ \left[3\varepsilon(\mu{>}24,e{>}30) + \varepsilon(\mu{>}24,e{>}23)\right] - \varepsilon(\mu{>}24,e{>}30) \end{align*}
  • Cancel redundant terms to obtain the minimal formula:
    $\varepsilon_{\rm union} = \varepsilon(\mu{>}24) + \varepsilon(e{>}30) + \varepsilon(\mu {>} 8, e{>}23) - \varepsilon(\mu{>}24,e{>}23) - \varepsilon(\mu{>}8,e{>}30)$
  • Comply with the offline lepton $p_T > 15$ GeV requirement, the final formula becomes:
    $\varepsilon_{\rm union} = \varepsilon(\mu{>}24) + \varepsilon(e{>}30) + \varepsilon(\mu {>} 15, e{>}23) - \varepsilon(\mu{>}24,e{>}23) - \varepsilon(\mu{>}15,e{>}30)$
  • Combined Trigger OR scale factors are calculated on the fly in the analysis framework
  • Evaluates combinatorial behavior of single vs. cross trigger efficiencies across $p_T$ and $\eta$
OR SF vs $p_T^e$ (2022postEE)
OR SF vs $p_T^{\mu}$ (2022postEE)
OR SF vs $p_T^e$ (2023preBPix)
OR SF vs $p_T^{\mu}$ (2023preBPix)
OR SF vs $\eta$ ($e$ bins, 22postEE)
OR SF vs $\eta$ ($\mu$ bins, 22postEE)
OR SF vs $\eta$ ($e$ bins, 23preBPix)
OR SF vs $\eta$ ($\mu$ bins, 23preBPix)
  • Separate ggH-only and bbH-only models tested → slightly inferior expected limits
  • Dual models → double templates across 40+ mass × 4 channels × 4 eras × 2 regions → operationally prohibitive
  • 3-class softmax effectively binary-like: bkg → score~0, signal → score~1
  • Dedicated b-jet variables ($p_T^{b_1}/p_T^{\text{fastmtt}}$, $\Delta\eta(b_1,\tau\tau)$) adaptively leverage region-dependent features
  • At fit stage, ggH and bbH are fully separated via generator-level flags (independent POI)
$e\mu$
$e\tau_h$
$\mu\tau_h$
$\tau_h\tau_h$
PNN score at $m_\Phi = 250$ GeV: ggH and bbH achieve comparable discrimination
  • At high mass, PNN score degenerates: signal concentrates near ~1, background near ~0 → few effective bins
  • $m_T^{\text{tot}}$ retains shape power: signal and background peaks naturally well-separated
  • Final strategy: PNN for 60–1000 GeV, $m_T^{\text{tot}}$ for 1000–3500 GeV
$m_T^{\text{tot}}$ at 250 GeV
$m_T^{\text{tot}}$ at 1000 GeV
$m_T^{\text{tot}}$ at 3500 GeV
PNN score at 250 GeV
PNN score at 1000 GeV
PNN score at 3500 GeV
  • Loss function: Sparse categorical cross-entropy (3-class: True bkg / Fake bkg / Signal)
    • Weighted by per-event sample weights (MC × SF × lumi); negative weights preserved
  • Accuracy metrics: unweighted and weighted sparse_categorical_accuracy
    • Weighted accuracy accounts for physical cross-section differences among processes
  • Early stopping: monitor val_loss, patience = 170 epochs
    • Best model saved by ModelCheckpoint on val_weighted_sparse_categorical_accuracy
  • Dynamic LR decay: ReduceLROnPlateau (factor = 0.99, patience = 25) + per-epoch schedule (×0.995), floor at $10^{-6}$
  • Optimizer: SGD + Nesterov momentum (0.9), initial LR = 0.1
Loss
Accuracy
Weighted Accuracy
Learning Rate
TensorBoard diagnostics — $e\mu$ low-mass model example
Signal Correlation Matrix
Correlation matrix of the PNN input variables of the ggH signal (60–250 GeV all mass points) sample for the low-mass model ($e\mu$ channel).
Background Correlation Matrix
Correlation matrix of the PNN input variables of the background sample for the low-mass model ($e\mu$ channel).
  • Theory uncertainties for bb process known to affect the $N_{\text{bjet}}$ distributions → different predictions for NoBtag and Btag categories
  • We estimate theory uncertainties due to: Hdamp variations, QCD ($\mu_R$, $\mu_F$) scale variations, and PDF variations
    • Other contributions e.g. parton shower uncertainties sub-dominant so neglected
  • Hdamp and QCD scale uncertainties added linearly as recommended in YR4
  • Hdamp + QCD scale uncertainties range between ~1.5–5%; PDF uncertainty ~1–2%
  • We also compare predictions to Madgraph5_aMC@NLO but find good agreement with POWHEG — no additional uncertainty introduced
bbH signal theory uncertainties
  • $j \to \tau_h$ fakes ($\tau_h\tau_h$, $\mu\tau_h$, $e\tau_h$):
    • FF statistical unc. — from fitted functions, split no-btag / btag; per $N_{\text{jets}}$/$p_T^{\text{jet}}$ bin; uncorr. across years
    • Closure correction stat. unc. — split no-btag / btag; per $N_{\text{jets}}$ bin; uncorr. across years
    • Non-closure corrections: applied 2× for up, not applied for down
    • W+jets subtraction ($\mu\tau_h$/$e\tau_h$): varied ±50%; fully corr. across years
    • $t\bar{t}$ subtraction ($\mu\tau_h$/$e\tau_h$): varied ±50%; fully corr. across years
    • W+jets / QCD FF ($\mu\tau_h$/$e\tau_h$): unc. from subtraction of other processes
  • $e\mu$ QCD fakes (OS/SS method):
    • OS/SS scale factor stat. unc.: from fitted functions, ~10–30% in no-btag regions; separate unc. per no-btag/$\Delta R(e,\mu)$ bin; uncorr. across years
    • 2D $p_T$ weight correction syst.: ~20% up/down in no-btag regions; covers residual $p_T(e/\mu)$ correlation mismodeling
      • Validated via closure tests in anti-iso muon region
    • Data-driven stat. unc.: ~10%; from limited statistics in data control regions used for fake estimation
  • The exact mass points simulated are:
[60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 160, 180, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1400, 1600, 1800, 2000, 2300, 2600, 2900, 3200, 3500] GeV
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
m_fastmtt nob met nob pt_1 nob pt_2 nob m_fastmtt btag met btag pt_1 btag pt_2 btag
ggH 1000 GeV PNN Impacts
30 leading impacts for the gg$\phi$ production mode at $m_{\phi} = 1000$ GeV fitted by PNN score
bbH 1000 GeV PNN Impacts
30 leading impacts for the bb$\phi$ production mode at $m_{\phi} = 1000$ GeV fitted by PNN score
ggH 1000 GeV mTtot Impacts
30 leading impacts for the gg$\phi$ production mode at $m_{\phi} = 1000$ GeV fitted by $m_{\mathrm{T}}^{\text{tot}}$
bbH 1000 GeV mTtot Impacts
30 leading impacts for the bb$\phi$ production mode at $m_{\phi} = 1000$ GeV fitted by $m_{\mathrm{T}}^{\text{tot}}$