Abstract (data abstract)

This paper presents a search for a new $Z'$ vector gauge boson with the ATLAS experiment at the Large Hadron Collider using $pp$ collision data collected at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 139 fb$^{-1}$.The new gauge boson $Z'$ is predicted by $L_{\mu}-L_{\tau}$ models to address observed phenomena that can not be explained by the Standard Model.The search examines the four-muon (4$\mu$) final state, using a deep learning neural network classifier to separate the $Z'$ signal from the Standard Model background events.The di-muon invariant masses in the $4\mu$ events are used to extract the $Z'$ resonance signature.No significant excess of events is observed over the predicted background.Upper limits at a 95% confidence level on the $Z'$ production cross-section times the decay branching fraction of $pp \rightarrow Z'\mu\mu \rightarrow 4\mu$ are set from 0.31 to 4.3 fb for the $Z'$ mass ranging from 5 to 81 GeV.The corresponding common coupling strengths, $g_{Z'}$, of the $Z'$ boson to the second and third generation leptons above 0.003 -- 0.2 have been excluded.

Table 1

Data from Table 1

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Summary of the chosen $Z'$ hypotheses and corresponding coupling, width, and cross-section (calculated at LO accuracy in QCD) at each...
Table 2

Data from Table 2

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The $Z'$ signal event selection efficiencies compared to the events passing the previous cut level for several representative mass points....
Table 3

Data from Table 3

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The selected 4$\mu$ events in data and the estimated backgrounds and their combined statistical and systematic uncertainties.
Table 4

Data from Figure 2 (a)

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Distributions of $p_{T}^{Z_1}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data...
Table 5

Data from Figure 2 (b)

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Distributions of $p_{T}^{Z_2}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data...
Table 6

Data from Figure 2 (c)

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Distributions of the mass difference of the $Z_1$ and $Z_2$ candidates. Small background contributions are denoted as "other backgrounds", including...
Table 7

Data from Figure 3 (a)

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The pDNN output discriminant variable distributions for low mass with a signal sample at 35 GeV and 51 GeV, respectively.
Table 8

Data from Figure 3 (b)

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The pDNN output discriminant variable distributions for high mass with a signal sample at 35 GeV and 51 GeV, respectively.
Table 9

Data from Figure 4 (a)

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Mass spectra of $m_{Z2}$ for the pDNN-selected events with a signal sample at 15 GeV.
Table 10

Data from Figure 4 (b)

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Mass spectra of $m_{Z1}$ for the pDNN-selected events with a signal sample at 51 GeV.
Table 11

Data from Figure 5

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The $p_0$-value scan across the Z' mass signal regions.
Table 12

Data from Figure 6 (a)

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95% CL upper limits (expected and observed) on the cross-sections times branching fraction. The discontinuity at 42 GeV represents the...
Table 13

Data from Figure 6 (b)

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95% CL upper limits (expected and observed) on the coupling parameter. The discontinuity at 42 GeV represents the border of...
Table 14

Data from Figure 8 in the auxiliary material

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The parameterized mass resolution $\sigma_{m_{\mu\mu}}$ as a function of $m_{Z'}$ using fully simulated $Z' \rightarrow \mu^+\mu^-$ events.
Table 15

Data from Figure 12 (a) in the auxiliary material

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The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major...
Table 16

Data from Figure 12 (b) in the auxiliary material

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The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major...
Table 17

Data from Figure 12 (c) in the auxiliary material

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The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major...
Table 18

Data from Figure 12 (d) in the auxiliary material

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The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major...
Table 19

Data from Figure 13 (a) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons...
Table 20

Data from Figure 13 (b) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons...
Table 21

Data from Figure 13 (c) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons...
Table 22

Data from Figure 13 (d) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons...
Table 23

Data from Figure 14 (a) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two...
Table 24

Data from Figure 14 (b) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two...
Table 25

Data from Figure 14 (c) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two...
Table 26

Data from Figure 14 (d) in the auxiliary material

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Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two...
Table 27

Data from Figure 15 (a) in the auxiliary material

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Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution...
Table 28

Data from Figure 15 (b) in the auxiliary material

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Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution...
Table 29

Data from Figure 15 (c) in the auxiliary material

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Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution...

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