CMS-TOP-22-011

CMS-TOP-22-011 ; CERN-EP-2025-029
Search for charged-lepton flavour violation in top quark interactions with an up-type quark, a muon, and a $\tau$ lepton in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
11 April 2025
Submitted to J. High Energy Phys.
Abstract: A search for charged-lepton flavour violation (CLFV) in top quark (t) production and decay is presented. The search uses proton-proton collision data corresponding to 138 fb $^{-1}$ collected with the CMS experiment at $\sqrt{s}=$ 13 TeV. The signal consists of the production of a single top quark via a CLFV interaction or top quark pair production followed by a CLFV decay. The analysis selects events containing a pair of oppositely charged muon and hadronically decaying $\tau$ lepton and at least three jets, where one has been identified to originate from the fragmentation of a bottom quark. Machine learning classification techniques are used to distinguish signal from standard model background events. The results of this search are consistent with the standard model expectations. The upper limits at 95% confidence level on the branching fraction $\mathcal{B}$ for CLFV top quark decays to a muon, a $\tau$ lepton, and an up or a charm quark are set at $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{u}) <$ (0.040, 0.078, and 0.118) $\times$ 10 $^{-6}$ , and $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{c}) <$ (0.810, 1.710, and 2.052) $\times$ 10 $^{-6}$ for scalar, vector, and tensor-like operators, respectively.
Links: e-print arXiv:2504.08532 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Example Feynman diagrams at leading order for the CLFV production of a single top quark (left and centre) and top quark pair production followed by a CLFV decay (right). Red dots indicate the effective CLFV coupling.
png pdf	Figure 1-a: Example Feynman diagrams at leading order for the CLFV production of a single top quark (left and centre) and top quark pair production followed by a CLFV decay (right). Red dots indicate the effective CLFV coupling.
png pdf	Figure 1-b: Example Feynman diagrams at leading order for the CLFV production of a single top quark (left and centre) and top quark pair production followed by a CLFV decay (right). Red dots indicate the effective CLFV coupling.
png pdf	Figure 1-c: Example Feynman diagrams at leading order for the CLFV production of a single top quark (left and centre) and top quark pair production followed by a CLFV decay (right). Red dots indicate the effective CLFV coupling.
png pdf	Figure 2: Distributions in $p_{\mathrm{T}}$ of the muon (upper left), $\tau_\mathrm{h}$ (upper right), $p_{\mathrm{T}}$ -leading jet (lower left), and $p_{\mathrm{T}}$ -subleading jet (lower right) after all selection steps. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The last bin in each histogram contains the overflow. The color filled histograms show the stacked background contributions. The data are shown as filled points. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 2-a: Distributions in $p_{\mathrm{T}}$ of the muon (upper left), $\tau_\mathrm{h}$ (upper right), $p_{\mathrm{T}}$ -leading jet (lower left), and $p_{\mathrm{T}}$ -subleading jet (lower right) after all selection steps. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The last bin in each histogram contains the overflow. The color filled histograms show the stacked background contributions. The data are shown as filled points. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 2-b: Distributions in $p_{\mathrm{T}}$ of the muon (upper left), $\tau_\mathrm{h}$ (upper right), $p_{\mathrm{T}}$ -leading jet (lower left), and $p_{\mathrm{T}}$ -subleading jet (lower right) after all selection steps. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The last bin in each histogram contains the overflow. The color filled histograms show the stacked background contributions. The data are shown as filled points. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 2-c: Distributions in $p_{\mathrm{T}}$ of the muon (upper left), $\tau_\mathrm{h}$ (upper right), $p_{\mathrm{T}}$ -leading jet (lower left), and $p_{\mathrm{T}}$ -subleading jet (lower right) after all selection steps. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The last bin in each histogram contains the overflow. The color filled histograms show the stacked background contributions. The data are shown as filled points. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 2-d: Distributions in $p_{\mathrm{T}}$ of the muon (upper left), $\tau_\mathrm{h}$ (upper right), $p_{\mathrm{T}}$ -leading jet (lower left), and $p_{\mathrm{T}}$ -subleading jet (lower right) after all selection steps. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The last bin in each histogram contains the overflow. The color filled histograms show the stacked background contributions. The data are shown as filled points. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 3: Distributions in the reconstructed top quark mass (upper left), W boson mass (upper right), and minimum $\chi^2$ (lower) from the top quark reconstruction. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The color filled histograms show the stacked background contributions. The data are shown as filled points. The last bin in each histogram contains the overflow. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 3-a: Distributions in the reconstructed top quark mass (upper left), W boson mass (upper right), and minimum $\chi^2$ (lower) from the top quark reconstruction. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The color filled histograms show the stacked background contributions. The data are shown as filled points. The last bin in each histogram contains the overflow. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 3-b: Distributions in the reconstructed top quark mass (upper left), W boson mass (upper right), and minimum $\chi^2$ (lower) from the top quark reconstruction. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The color filled histograms show the stacked background contributions. The data are shown as filled points. The last bin in each histogram contains the overflow. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 3-c: Distributions in the reconstructed top quark mass (upper left), W boson mass (upper right), and minimum $\chi^2$ (lower) from the top quark reconstruction. The solid and dashed lines show the signal distributions, individually for each type of operator and interaction for the vector Lorentz structure as an example. The signals are normalized to the total number of events in data for visibility. The color filled histograms show the stacked background contributions. The data are shown as filled points. The last bin in each histogram contains the overflow. The shaded band displays the total uncertainty in the predicted SM background, consisting of statistical and systematic uncertainties added in quadrature. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 4: Combined distributions in the DNN score after the profile likelihood fit for all data-taking periods for the vector operators with $\mathrm{t}\mathrm{u}\mu\tau$ (left) and $\mathrm{t}\mathrm{c}\mu\tau$ (right) couplings. The signal distributions are normalized to the total number of events observed in the data. The last bin of each histogram contains the overflow. The hatched bands represent the total post-fit uncertainties in the background predictions, including statistical and systematic sources. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 4-a: Combined distributions in the DNN score after the profile likelihood fit for all data-taking periods for the vector operators with $\mathrm{t}\mathrm{u}\mu\tau$ (left) and $\mathrm{t}\mathrm{c}\mu\tau$ (right) couplings. The signal distributions are normalized to the total number of events observed in the data. The last bin of each histogram contains the overflow. The hatched bands represent the total post-fit uncertainties in the background predictions, including statistical and systematic sources. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 4-b: Combined distributions in the DNN score after the profile likelihood fit for all data-taking periods for the vector operators with $\mathrm{t}\mathrm{u}\mu\tau$ (left) and $\mathrm{t}\mathrm{c}\mu\tau$ (right) couplings. The signal distributions are normalized to the total number of events observed in the data. The last bin of each histogram contains the overflow. The hatched bands represent the total post-fit uncertainties in the background predictions, including statistical and systematic sources. The panels below the distributions show the ratio of data to the background prediction.
png pdf	Figure 5: Exclusion contours for the observed and expected 95% CL upper limits and central probability intervals containing 68% of the expected upper limits for the branching fractions (left) and Wilson coefficients (right) corresponding to the $\mathrm{t}\mathrm{u}\mu\tau$ and $\mathrm{t}\mathrm{c}\mu\tau$ couplings for scalar, vector and tensor Lorentz structures.
png pdf	Figure 5-a: Exclusion contours for the observed and expected 95% CL upper limits and central probability intervals containing 68% of the expected upper limits for the branching fractions (left) and Wilson coefficients (right) corresponding to the $\mathrm{t}\mathrm{u}\mu\tau$ and $\mathrm{t}\mathrm{c}\mu\tau$ couplings for scalar, vector and tensor Lorentz structures.
png pdf	Figure 5-b: Exclusion contours for the observed and expected 95% CL upper limits and central probability intervals containing 68% of the expected upper limits for the branching fractions (left) and Wilson coefficients (right) corresponding to the $\mathrm{t}\mathrm{u}\mu\tau$ and $\mathrm{t}\mathrm{c}\mu\tau$ couplings for scalar, vector and tensor Lorentz structures.

Tables
png pdf	Table 1: The EFT operators considered in this analysis and their definition. The $\varepsilon$ parameter is a fully asymmetric two-dimensional tensor, $\gamma^{\mu}$ are the Dirac matrices, and $\sigma^{\mu\nu}=\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}]$ . Left-handed doublets of leptons and quarks are denoted by $\ell_i$ and $\mathrm{q}_k$ , respectively, where the indices $i$ and $k$ denote the lepton and quark flavours. Right-handed lepton and quark singlets are denoted by $\mathrm{e}_i$ and $\mathrm{u}_k$ , respectively.
png pdf	Table 2: Predicted cross sections for CLFV signal processes are presented together with uncertainties from missing higher orders in matrix element calculations, considering operators with different Lorentz structures using $C_a/\Lambda^2=1\,\text{Te\hspace{-.08em}V}^{-2}$ . The results for $\text{ST CLFV}$ are at LO accuracy and the ones for $\text{TT CLFV}$ are at NNLO+NNLL accuracy for the $\mathrm{t} \overline{\mathrm{t}}$ production with LO accuracy for the CLFV decay.
png pdf	Table 3: Estimated event yields including the background corrections from the ABCD method discussed in Section 5. The numbers shown correspond to observed events before the maximum likelihood fit described in Section 8. Only statistical uncertainties are shown, related to the size of the data sets.
png pdf	Table 4: Input features of the DNN. The angular distance $\Delta R_{ij}$ between two objects $i$ and $j$ is defined as $\Delta R_{ij} = \sqrt{\smash[b]{(\Delta\eta)_{ij}^2+(\Delta\phi)_{ij}^2}}$ , where $\Delta\eta_{ij}$ and $\Delta\phi_{ij}$ are the differences in pseudorapidity and azimuthal angle, respectively.
png pdf	Table 5: The 95% CL observed and expected upper limits on CLFV cross sections, Wilson coefficients $C_{\mathrm{t}\mathrm{q}\mu\tau}$ , and branching fractions for different types of interactions and Lorentz structures. The expected upper limits are shown in parentheses after the observed limits. The central probability intervals containing 68% of the expected upper limits are given in square brackets below the upper limits.

Summary

A search for charged-lepton flavour violation (CLFV) in the top quark sector has been presented. The search uses data corresponding to an integrated luminosity of 138 fb

$^{-1}$ collected by the CMS experiment during 2016--2018 in proton-proton (pp) collisions at

$\sqrt{s}=$ 13 TeV. Interactions of a top quark with a muon, a

$\tau$ lepton, and an up-type quark u or c are considered, where the scale of new physics responsible for CLFV is assumed to be larger than the energy of pp collisions at the LHC. The signal extraction is performed using measured distributions in a multiclass discriminator obtained with a deep neural network. No significant deviation is observed from the standard model background prediction. Upper limits on the signal cross sections are set at 95% confidence level (CL). The limits are interpreted in terms of CLFV branching fractions (

$\mathcal{B}$ ) of the top quark, resulting in

$\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{u}) <$ (0.040, 0.078, and 0.118)

$\times$ 10

$^{-6}$ , and

$\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{c}) <$ (0.810, 1.710, and 2.052)

$\times$ 10

$^{-6}$ at 95% CL for scalar, vector, and tensor-like operators, respectively. This search complements previous CMS results involving

$\mathrm{e}\mu$ CLFV interactions [12,13] and results in more stringent upper limits on Wilson coefficients in an effective field theory by approximately a factor of two compared to the latest experimental results involving

$\mu\tau$ CLFV interactions [11].

References
1	R. J. Gaitskell	Direct detection of dark matter	Ann. Rev. Nucl. Part. Sci. 54 (2004) 315
2	V. Trimble	Existence and nature of dark matter in the universe	Ann. Rev. Astron. Astrophys. 25 (1987) 425
3	T. A. Porter, R. P. Johnson, and P. W. Graham	Dark matter searches with astroparticle data	Ann. Rev. Astron. Astrophys. 49 (2011) 155	1104.2836
4	G. Bertone, D. Hooper, and J. Silk	Particle dark matter: evidence, candidates and constraints	Phys. Rept. 405 (2005) 279	hep-ph/0404175
5	A. D. Sakharov	Violation of ${CP}$ invariance, ${C}$ asymmetry, and baryon asymmetry of the universe	Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32
6	R. Davis, Jr., D. S. Harmer, and K. C. Hoffman	Search for neutrinos from the sun	PRL 20 (1968) 1205
7	L. Calibbi and G. Signorelli	Charged lepton flavour violation: An experimental and theoretical introduction	Riv. Nuovo Cim. 41 (2018) 71	1709.00294
8	HFLAV Collaboration	Averages of b-hadron, c-hadron, and $\tau$ -lepton properties as of 2021	PRD 107 (2023) 052008	2206.07501
9	T. J. Kim et al.	Correlation between ${R_{\mathrm{D}^{(\ast)}}}$ and top quark FCNC decays in leptoquark models	JHEP 07 (2019) 025	1812.08484
10	LHCb Collaboration	Measurement of the ratios of branching fractions $\mathcal{R}({\mathrm{D}^{*}})$ and $\mathcal{R}({\mathrm{D^0}})$	PRL 131 (2023) 111802	2302.02886
11	ATLAS Collaboration	Search for charged-lepton-flavor violating ${\mu\tau\mathrm{q}\mathrm{t}}$ interactions in top-quark production and decay in ${\mathrm{p}\mathrm{p}}$ collisions at $\sqrt{s}=$ 13 TeV with the ATLAS detector at the LHC	PRD 110 (2024) 012014	2403.06742
12	CMS Collaboration	Search for charged-lepton flavor violation in top quark production and decay in ${\mathrm{p}\mathrm{p}}$ collisions at $\sqrt{s}=$ 13 TeV	JHEP 06 (2022) 082	CMS-TOP-19-006 2201.07859
13	CMS Collaboration	Search for charged-lepton flavor violation in the production and decay of top quarks using trilepton final states in proton-proton collisions at $\sqrt{s}=$ 13 TeV	PRD 111 (2025) 012009	CMS-TOP-22-005 2312.03199
14	J. A. Aguilar-Saavedra et al.	Interpreting top-quark LHC measurements in the standard-model effective field theory	LHC TOP Working Group Public Note CERN-LPCC-2018-01, 2018	1802.07237
15	B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek	Dimension-six terms in the standard model Lagrangian	JHEP 10 (2010) 085	1008.4884
16	CMS Collaboration	HEPData record for this analysis	link
17	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $\sqrt{s}=$ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
18	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
19	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
20	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
21	J. Alwall et al.	The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations	JHEP 07 (2014) 079	1405.0301
22	A. Dedes et al.	\textscSmeftFR---Feynman rules generator for the standard model effective field theory	Comput. Phys. Commun. 247 (2020) 106931	1904.03204
23	M. Czakon and A. Mitov	\textsctop++: a program for the calculation of the top-pair cross-section at hadron colliders	Comput. Phys. Commun. 185 (2014) 2930	1112.5675
24	J. Kile and A. Soni	Model-independent constraints on lepton-flavor-violating decays of the top quark	PRD 78 (2008) 094008	0807.4199
25	J. A. Aguilar-Saavedra	Effective four-fermion operators in top physics: A roadmap	NPB 843 (2011) 638	1008.3562
26	I. Brivio	SMEFTsim 3.0---a practical guide	JHEP 04 (2021) 073	2012.11343
27	CMS Collaboration	Measurements of $\mathrm{t} \overline{\mathrm{t}}$ differential cross sections in proton-proton collisions at $\sqrt{s}=$ 13 TeV using events containing two leptons	JHEP 02 (2019) 149	CMS-TOP-17-014 1811.06625
28	CMS Collaboration	Measurement of normalized differential $\mathrm{t} \overline{\mathrm{t}}$ cross sections in the dilepton channel from ${\mathrm{p}\mathrm{p}}$ collisions at $\sqrt{s}=$ 13 TeV	JHEP 04 (2018) 060	CMS-TOP-16-007 1708.07638
29	CMS Collaboration	Measurement of differential cross sections for top quark pair production using the lepton+jets final state in proton-proton collisions at 13 TeV	PRD 95 (2017) 092001	CMS-TOP-16-008 1610.04191
30	M. Czakon et al.	Top-pair production at the LHC through NNLO QCD and NLO EW	JHEP 10 (2017) 186	1705.04105
31	CMS Collaboration	Measurement of differential $\mathrm{t} \overline{\mathrm{t}}$ production cross sections in the full kinematic range using lepton+jets events from proton-proton collisions at $\sqrt{s}=$ 13 TeV	PRD 104 (2021) 092013	CMS-TOP-20-001 2108.02803
32	P. Nason	A new method for combining NLO QCD with shower Monte Carlo algorithms	JHEP 11 (2004) 040	hep-ph/0409146
33	S. Frixione, P. Nason, and C. Oleari	Matching NLO QCD computations with parton shower simulations: the POWHEG method	JHEP 11 (2007) 070	0709.2092
34	S. Alioli, P. Nason, C. Oleari, and E. Re	A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG \textscbox	JHEP 06 (2010) 043	1002.2581
35	E. Re	Single-top ${\mathrm{W}\mathrm{t}}$ -channel production matched with parton showers using the POWHEG method	EPJC 71 (2011) 1547	1009.2450
36	M. Aliev et al.	\textschathor: Hadronic top and heavy quarks cross section calculator	Comput. Phys. Commun. 182 (2011) 1034	1007.1327
37	P. Kant et al.	\textschathor for single top-quark production: Updated predictions and uncertainty estimates for single top-quark production in hadronic collisions	Comput. Phys. Commun. 191 (2015) 74	1406.4403
38	N. Kidonakis	Two-loop soft anomalous dimensions for single top quark associated production with a $\mathrm{W^-}$ or $\mathrm{H}^{-}$	PRD 82 (2010) 054018	1005.4451
39	N. Kidonakis	NNLL threshold resummation for top-pair and single-top production	Phys. Part. Nucl. 45 (2014) 714	1210.7813
40	J. Alwall et al.	Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions	EPJC 53 (2008) 473	0706.2569
41	T. Sjöstrand et al.	An introduction to PYTHIA8.2	Comput. Phys. Commun. 191 (2015) 159	1410.3012
42	NNPDF Collaboration	Parton distributions from high-precision collider data	EPJC 77 (2017) 663	1706.00428
43	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
44	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
45	CMS Collaboration	Measurement of the inelastic proton-proton cross section at $\sqrt{s}=$ 13 TeV	JHEP 07 (2018) 161	CMS-FSQ-15-005 1802.02613
46	CMS Collaboration	Particle-flow reconstruction and global event description with the CMS detector	JINST 12 (2017) P10003	CMS-PRF-14-001 1706.04965
47	CMS Collaboration	Technical proposal for the Phase-II upgrade of the Compact Muon Solenoid	CMS Technical Proposal CERN-LHCC-2015-010, CMS-TDR-15-02, 2015 link
48	CMS Collaboration	Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC	JINST 16 (2021) P05014	CMS-EGM-17-001 2012.06888
49	M. Cacciari, G. P. Salam, and G. Soyez	The anti- $k_{\mathrm{T}}$ jet clustering algorithm	JHEP 04 (2008) 063	0802.1189
50	M. Cacciari, G. P. Salam, and G. Soyez	FASTJET user manual	EPJC 72 (2012) 1896	1111.6097
51	M. Cacciari and G. P. Salam	Dispelling the ${N^3}$ myth for the $k_{\mathrm{T}}$ jet-finder	PLB 641 (2006) 57	hep-ph/0512210
52	CMS Collaboration	Jet energy scale and resolution in the CMS experiment in ${\mathrm{p}\mathrm{p}}$ collisions at 8 TeV	JINST 12 (2017) P02014	CMS-JME-13-004 1607.03663
53	CMS Collaboration	Identification of heavy-flavour jets with the CMS detector in ${\mathrm{p}\mathrm{p}}$ collisions at 13 TeV	JINST 13 (2018) P05011	CMS-BTV-16-002 1712.07158
54	E. Bols et al.	Jet flavour classification using DeepJet	JINST 15 (2020) P12012	2008.10519
55	CMS Collaboration	Performance of the DeepJet b tagging algorithm using 41.9 fb $^{-1}$ of data from proton-proton collisions at 13 TeV with \mboxPhase 1 CMS detector	CMS Detector Performance Note CMS-DP-2018-058, 2018 CDS
56	CMS Collaboration	Performance of reconstruction and identification of $\tau$ leptons decaying to hadrons and $\nu_{\!\tau}$ in ${\mathrm{p}\mathrm{p}}$ collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P10005	CMS-TAU-16-003 1809.02816
57	CMS Collaboration	Identification of hadronic tau lepton decays using a deep neural network	JINST 17 (2022) P07023	CMS-TAU-20-001 2201.08458
58	CMS Collaboration	Performance of missing transverse momentum reconstruction in proton-proton collisions at $\sqrt{s}=$ 13 TeV using the CMS detector	JINST 14 (2019) P07004	CMS-JME-17-001 1903.06078
59	CMS Collaboration	Measurement of the inclusive W and Z production cross sections in ${\mathrm{p}\mathrm{p}}$ collisions at $\sqrt{s}=$ 7 TeV with the CMS experiment	JHEP 10 (2011) 132	CMS-EWK-10-005 1107.4789
60	CDF Collaboration	Measurement of $\sigma\mathcal{B}({\mathrm{W}\to\mathrm{e}\nu})$ and $\sigma\mathcal{B}({\mathrm{Z^0}\to\mathrm{e}^+\mathrm{e}^-})$ in ${\overline{\mathrm{p}}\mathrm{p}}$ collisions at $\sqrt{s}=$ 1800 GeV	PRD 44 (1991) 29
61	F. Chollet et al.	\textsckeras	Software available from \urlhttps://keras.io, 2015
62	M. Abadi et al.	\textscTensorFlow: Large-scale machine learning on heterogeneous systems	Software available from \urlhttp://tensorflow.org, 2015 link
63	D. P. Kingma and J. Ba	\textscadam: a method for stochastic optimization	in Proc. 3rd Int. Conf. on Learning Representations (): San Diego CA, USA, May 7--9,, 2015 ICLR 201 (2015) 5	1412.6980
64	A. F. Agarap	Deep learning using rectified linear units (ReLU)		1803.08375
65	J. S. Conway	Incorporating nuisance parameters in likelihoods for multisource spectra	in orkshop on Statistical Issues Related to Discovery Claims in Search Experiments and Unfolding (PHYSTAT ): Geneva, Switzerland, January 17--20,, 2011 Proc. 2011 (2011) W	1103.0354
66	CMS Collaboration	Precision luminosity measurement in proton-proton collisions at $\sqrt{s}=$ 13 TeV in 2015 and 2016 at CMS	EPJC 81 (2021) 800	CMS-LUM-17-003 2104.01927
67	CMS Collaboration	CMS luminosity measurement for the 2017 data-taking period at $\sqrt{s}=$ 13 TeV	CMS Physics Analysis Summary, 2018 CMS-PAS-LUM-17-004	CMS-PAS-LUM-17-004
68	CMS Collaboration	CMS luminosity measurement for the 2018 data-taking period at $\sqrt{s}=$ 13 TeV	CMS Physics Analysis Summary, 2019 CMS-PAS-LUM-18-002	CMS-PAS-LUM-18-002
69	CMS Collaboration	Observation of ${\gamma\gamma\to\tau\tau}$ in proton-proton collisions and limits on the anomalous electromagnetic moments of the $\tau$ lepton	Rep. Prog. Phys. 87 (2024) 107801	CMS-SMP-23-005 2406.03975
70	CMS Collaboration	Strategies and performance of the CMS silicon tracker alignment during LHC \mboxRun 2	NIM A 1037 (2022) 166795	CMS-TRK-20-001 2111.08757
71	J. Butterworth et al.	PDF4LHC recommendations for LHC \mboxRun 2	JPG 43 (2016) 023001	1510.03865
72	CMS Collaboration	Investigations of the impact of the parton shower tuning in PYTHIA8 in the modelling of $\mathrm{t} \overline{\mathrm{t}}$ at $\sqrt{s}=$ 8 and 13 TeV	CMS Physics Analysis Summary, 2016 CMS-PAS-TOP-16-021	CMS-PAS-TOP-16-021
73	T. Junk	Confidence level computation for combining searches with small statistics	NIM A 434 (1999) 435	hep-ex/9902006
74	A. L. Read	Presentation of search results: The $\text{CL}_\text{s}$ technique	JPG 28 (2002) 2693
75	G. Cowan, K. Cranmer, E. Gross, and O. Vitells	Asymptotic formulae for likelihood-based tests of new physics	EPJC 71 (2011) 1554	1007.1727
76	CMS Collaboration	The CMS statistical analysis and combination tool: \textsccombine	Comput. Softw. Big Sci. 8 (2024) 19	CMS-CAT-23-001 2404.06614
77	W. Verkerke and D. Kirkby	The \textscRooFit toolkit for data modeling	in th International Conference on Computing in High Energy and Nuclear Physics (CHEP ): La Jolla CA, United States, March 24--28, . . . [eConf C0303241 MOLT007], 2003 Proc. 1 (2003) 3	physics/0306116
78	L. Moneta et al.	The \textscRooStats project	in th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT ): Jaipur, India, February 22--27, . . . [PoS (ACAT) 057], 2010 Proc. 1 (2010) 3	1009.1003