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CMS-PAS-EXO-19-016
Search for a third-generation leptoquark coupling to a $\tau$ lepton and a b quark through single, pair and nonresonant production at $\sqrt{s}= $ 13 TeV
Abstract: A search is presented for a third-generation leptoquark (LQ) coupling to a $\tau$ lepton and a b quark. Events with $\tau$ leptons plus at least one jet originating from a b quark are considered, targeting the single and pair production of the LQ as well as nonresonant production via $t$-channel LQ exchange. The search is based on proton-proton collision data at a center-of-mass energy of $\sqrt{s}= $ 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 137 fb$^{-1}$. Upper limits are set on the LQ production cross section in the LQ mass range 0.5-2.3 TeV. Lower limits at 95% confidence level on the LQ mass are set in the 1.22-1.96 TeV range and for a coupling strength less than 2.5, depending on the LQ model. Upper limits are also set on the coupling strength of such LQs as a function of their mass. For a representative LQ mass of 2 TeV and a coupling strength of 2.5, an excess with a significance of 3.4 standard deviations above the standard model expectation is observed in the data. Consequently, the observed upper limits on the LQ production cross section are about three times larger than expected for this benchmark.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
Dominant Feynman diagrams of the signal at LO: single (left) and pair LQ production (center), as well as nonresonant production of two $\tau$ leptons via $t$-channel LQ exchange (right).

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Figure 1-a:
Dominant Feynman diagram of single LQ production at LO.

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Figure 1-b:
Dominant Feynman diagram of pair LQ production at LO.

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Figure 1-c:
Dominant Feynman diagram of nonresonant production of two $\tau$ leptons via $t$-channel LQ exchange at LO.

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Figure 2:
The product of acceptance and efficiency for a vector LQ signal in the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ (left) and $\mu\tau_{\mathrm{h}} $ (right) channels of the 0b and $\geq $1b (top), and the 0j categories (bottom) are shown. Vertical bars indicate the statistical uncertainty in the efficiency.

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Figure 2-a:
The product of acceptance and efficiency for a vector LQ signal in the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel of the 0b and $\geq $1b category is shown. Vertical bars indicate the statistical uncertainty in the efficiency.

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Figure 2-b:
The product of acceptance and efficiency for a vector LQ signal in the $\mu\tau_{\mathrm{h}} $ channel of the 0b and $\geq $1b category is shown. Vertical bars indicate the statistical uncertainty in the efficiency.

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Figure 2-c:
The product of acceptance and efficiency for a vector LQ signal in the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel of the 0j category is shown. Vertical bars indicate the statistical uncertainty in the efficiency.

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Figure 2-d:
The product of acceptance and efficiency for a vector LQ signal in the $\mu\tau_{\mathrm{h}} $ channel of the 0j category is shown. Vertical bars indicate the statistical uncertainty in the efficiency.

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Figure 3:
Postfit distributions of ${{S_\mathrm {T}^\text {MET}}} $ for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The last bin includes the overflow. The e$\mu$ (top) and ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ (bottom) channels in the 0b (left) and $\geq $1b (right) category are shown. The fitted signal distributions for the total scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. They include the single and pair LQ production, as well as the nonresonant production of a $\tau $ lepton pair. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 3-a:
Postfit distribution of ${{S_\mathrm {T}^\text {MET}}} $ for the e$\mu$ channel in the 0b category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The last bin includes the overflow. The fitted signal distributions for the total scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. They include the single and pair LQ production, as well as the nonresonant production of a $\tau $ lepton pair. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 3-b:
Postfit distribution of ${{S_\mathrm {T}^\text {MET}}} $ for the e$\mu$ channel in the $\geq $1b category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The last bin includes the overflow. The fitted signal distributions for the total scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. They include the single and pair LQ production, as well as the nonresonant production of a $\tau $ lepton pair. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 3-c:
Postfit distribution of ${{S_\mathrm {T}^\text {MET}}} $ for the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel in the 0b category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The last bin includes the overflow. The fitted signal distributions for the total scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. They include the single and pair LQ production, as well as the nonresonant production of a $\tau $ lepton pair. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 3-d:
Postfit distribution of ${{S_\mathrm {T}^\text {MET}}} $ for the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel in the $\geq $1b category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The last bin includes the overflow. The fitted signal distributions for the total scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. They include the single and pair LQ production, as well as the nonresonant production of a $\tau $ lepton pair. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 4:
Postfit distributions of $\chi $ for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The e$\mu$ (top) and ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ (bottom) channels in the 400 GeV $ < {{m_\text {vis}}} < $ 600 GeV (left) and ${{m_\text {vis}}} > $ 600 GeV (right) category are shown. The fitted nonresonant signal for the scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 4-a:
Postfit distributions of $\chi $ for the e$\mu$ channel in the 400 GeV $ < {{m_\text {vis}}} < $ 600 GeV category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The fitted nonresonant signal for the scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 4-b:
Postfit distributions of $\chi $ for the e$\mu$ channel in the ${{m_\text {vis}}} > $ 600 GeV category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The fitted nonresonant signal for the scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 4-c:
Postfit distributions of $\chi $ for the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel in the 400 GeV $ < {{m_\text {vis}}} < $ 600 GeV category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The fitted nonresonant signal for the scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 4-d:
Postfit distributions of $\chi $ for the ${{\tau_{\mathrm{h}}\tau_{\mathrm{h}}}} $ channel in the ${{m_\text {vis}}} > $ 600 GeV category, for the combined 2016-2018 dataset after a simultaneous fit of the scalar LQ signal to the data in each data-taking period. The fitted nonresonant signal for the scalar (solid red) and vector LQ model (dashed red) with a mass of 2000 GeV and a coupling strength of $\lambda = $ 2.5 are overlaid to illustrate the sensitivity. The lower panel shows the ratio between the observed data and background from the S+B fit (black). The hatched uncertainty bands include the total postfit uncertainties in the background.

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Figure 5:
Histograms of ${{\log_{10}[S(S{+}B)]}}$ counting events in all bins, assuming a vector LQ with ${{m_{{{\mathrm {LQ}}}}}} = $ 1400 GeV and $\lambda = $ 1.0 (left), or ${{m_{{{\mathrm {LQ}}}}}} = $ 2000 GeV and $\lambda = $ 2.5 (right). The ${{\log_{10}[S(S{+}B)]}}$ is computed per bin of the postfit $\chi $ and ${{S_\mathrm {T}^\text {MET}}} $ distributions, using an S+B fit model. The total LQ signal strength (single, pair and nonresonant) is fitted simultaneously. The lower panel shows the ratio of the observed data to the expected background from the S+B fit. The expected background is grouped by jet categories in stacked histograms.

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Figure 5-a:
Histograms of ${{\log_{10}[S(S{+}B)]}}$ counting events in all bins, assuming a vector LQ with ${{m_{{{\mathrm {LQ}}}}}} = $ 1400 GeV and $\lambda = $ 1.0. The ${{\log_{10}[S(S{+}B)]}}$ is computed per bin of the postfit $\chi $ and ${{S_\mathrm {T}^\text {MET}}} $ distributions, using an S+B fit model. The total LQ signal strength (single, pair and nonresonant) is fitted simultaneously. The lower panel shows the ratio of the observed data to the expected background from the S+B fit. The expected background is grouped by jet categories in stacked histograms.

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Figure 5-b:
Histograms of ${{\log_{10}[S(S{+}B)]}}$ counting events in all bins, assuming a vector LQ with ${{m_{{{\mathrm {LQ}}}}}} = $ 2000 GeV and $\lambda = $ 2.5. The ${{\log_{10}[S(S{+}B)]}}$ is computed per bin of the postfit $\chi $ and ${{S_\mathrm {T}^\text {MET}}} $ distributions, using an S+B fit model. The total LQ signal strength (single, pair and nonresonant) is fitted simultaneously. The lower panel shows the ratio of the observed data to the expected background from the S+B fit. The expected background is grouped by jet categories in stacked histograms.

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Figure 6:
The observed and expected upper limit on the total cross section of a scalar LQ signal with $\lambda =$ 1 (left) and 2.5 (right) at 95% CL. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-a:
The observed and expected upper limit on the total cross section of a scalar LQ signal with $\lambda =$ 1 at 95% CL. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-b:
The observed and expected upper limit on the total cross section of a scalar LQ signal with $\lambda =$ 2.5 at 95% CL. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7:
The observed and expected upper limit on the total cross section of a vector LQ signal with $\lambda =$ 1 (left) and 2.5 (right) at 95% CL. The top (bottom) row assumes a nonminimal coupling of $\kappa =$ 1 (0). The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7-a:
The observed and expected upper limit on the total cross section of a vector LQ signal with $\lambda =$ 1 at 95% CL, assuming a nonminimal coupling of $\kappa =$ 1. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7-b:
The observed and expected upper limit on the total cross section of a vector LQ signal with $\lambda =$ 2.5 at 95% CL, assuming a nonminimal coupling of $\kappa =$ 1. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7-c:
The observed and expected upper limit on the total cross section of a vector LQ signal with $\lambda =$ 1 at 95% CL, assuming a nonminimal coupling of $\kappa =$ 0. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7-d:
The observed and expected upper limit on the total cross section of a vector LQ signal with $\lambda =$ 2.5 at 95% CL, assuming a nonminimal coupling of $\kappa =$ 0. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 8:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a scalar LQ. All years and all channels in each category are combined. The limits derived for the single (green), pair (red), nonresonant (orange) and total LQ production (black) are shown. The hatched bands around the expected limit lines correspond to the regions containing 68% of the distribution of limits expected under the background-only hypothesis.

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Figure 9:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a vector LQ model with $\kappa =$ 0 (left) and $\kappa =$ 1 (right). All years and all channels in each category are combined. The limits derived for the single (green), pair (red), nonresonant (orange) and total LQ production (black) are shown. The hatched bands around the expected limit lines correspond to the regions containing 68% of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.

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Figure 9-a:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a vector LQ model with $\kappa =$ 0. All years and all channels in each category are combined. The limits derived for the single (green), pair (red), nonresonant (orange) and total LQ production (black) are shown. The hatched bands around the expected limit lines correspond to the regions containing 68% of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.

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Figure 9-b:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a vector LQ model with $\kappa =$ 1. All years and all channels in each category are combined. The limits derived for the single (green), pair (red), nonresonant (orange) and total LQ production (black) are shown. The hatched bands around the expected limit lines correspond to the regions containing 68% of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.
Tables

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Table 1:
The sources of uncertainty considered, categorized as to whether they affect the normalization or shape of the distributions. "s.d.'' refers to the standard deviation of the input variable.

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Table 2:
Best-fit LQ cross sections $\sigma $ for various masses and coupling strengths $\lambda $, and the corresponding significance $z$ (given in standard deviations) for different production modes individually, as well as their combination.
Summary
This note has reported a search for a third-generation leptoquark (LQ) decaying to a $\tau$ lepton and a b quark. Events with $\tau$ leptons and one jet originating from a b quark were considered, targeting the single and pair production of the LQ, as well as the nonresonant production with the LQ in the $t$ channel. The search used proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector corresponding to an integrated luminosity of 137 fb$^{-1}$. Upper limits have been set on the third-generation scalar LQ production cross section as a function of the LQ mass, and results were compared with theoretical predictions to obtain lower limits on the LQ mass. At 95% confidence level, third-generation LQ decaying to a $\tau$ lepton and a b quark with unit coupling are excluded for masses below 1.25 TeV for a scalar model, and below 1.53 (1.86) GeV for a vector model with non-minimal coupling $\kappa=$ 0 (1), while at $\lambda=$ 2.5 the lower limits are 1.37 TeV for a scalar model, and 1.86 (1.96) GeV for a vector model with $\kappa=$ 0 (1). Upper limits are also set on the coupling strength of such LQs as a function of their mass.

The observed data agree with the standard model expectation within 2 standard deviations below a coupling strength of $\lambda=$ 1.5. For a representative LQ mass of 2 TeV and a coupling strength of 2.5, an excess with a significance of 3.4 standard deviations above the standard model expectation is observed in the data. Consequently, the observed upper limits on the LQ production cross section are about three times larger than expected for this benchmark.
Additional Figures

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Additional Figure 1:
The expected upper limit on the cross section of a scalar LQ signal at 95% CL. Shown are pair (top left), nonresonant (top right), and single production with $\lambda =$ 1 (bottom left) and $\lambda =$ 2.5 (bottom right). The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 1-a:
The expected upper limit on the cross section of a scalar LQ signal at 95% CL. Shown is pair production. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 1-b:
The expected upper limit on the cross section of a scalar LQ signal at 95% CL. Shown is nonresonant production. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 1-c:
The expected upper limit on the cross section of a scalar LQ signal at 95% CL. Shown is single production with $\lambda =$ 1. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 1-d:
The expected upper limit on the cross section of a scalar LQ signal at 95% CL. Shown is single production with $\lambda =$ 2.5. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 2:
The expected upper limit on the cross section of a vector LQ signal with $\kappa =$ 1 at 95% CL. Shown are pair (top left), nonresonant (top right), and single production with $\lambda =$ 1 (bottom left) and $\lambda =$ 2.5 (bottom right). The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 2-a:
The expected upper limit on the cross section of a vector LQ signal with $\kappa =$ 1 at 95% CL. Shown is pair production. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 2-b:
The expected upper limit on the cross section of a vector LQ signal with $\kappa =$ 1 at 95% CL. Shown is nonresonant production. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 2-c:
The expected upper limit on the cross section of a vector LQ signal with $\kappa =$ 1 at 95% CL. Shown is single production with $\lambda =$ 1. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 2-d:
The expected upper limit on the cross section of a vector LQ signal with $\kappa =$ 1 at 95% CL. Shown is single production with $\lambda =$ 2.5. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Additional Figure 3:
The expected upper limit on the total LQ production cross section at 95% CL comparing each production mode as a separate signal to illustrate their respective sensitivity and contribution to the total sensitivity: single (green), pair (red), nonresonant (orange) and total LQ production (black). All years and all channels in each category are combined. Shown are the scalar (top) and vector LQ model (bottom, $\kappa =$ 1) for $\lambda =$ 1 (left) and $\lambda =$ 2.5 (right).

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Additional Figure 3-a:
The expected upper limit on the total LQ production cross section at 95% CL comparing each production mode as a separate signal to illustrate their respective sensitivity and contribution to the total sensitivity: single (green), pair (red), nonresonant (orange) and total LQ production (black). All years and all channels in each category are combined. Shown is the scalar LQ model for $\lambda =$ 1.

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Additional Figure 3-b:
The expected upper limit on the total LQ production cross section at 95% CL comparing each production mode as a separate signal to illustrate their respective sensitivity and contribution to the total sensitivity: single (green), pair (red), nonresonant (orange) and total LQ production (black). All years and all channels in each category are combined. Shown is the scalar LQ model for $\lambda =$ 2.5.

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Additional Figure 3-c:
The expected upper limit on the total LQ production cross section at 95% CL comparing each production mode as a separate signal to illustrate their respective sensitivity and contribution to the total sensitivity: single (green), pair (red), nonresonant (orange) and total LQ production (black). All years and all channels in each category are combined. Shown is the vector LQ model ($\kappa =$ 1) for $\lambda =$ 1.

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Additional Figure 3-d:
The expected upper limit on the total LQ production cross section at 95% CL comparing each production mode as a separate signal to illustrate their respective sensitivity and contribution to the total sensitivity: single (green), pair (red), nonresonant (orange) and total LQ production (black). All years and all channels in each category are combined. Shown is the vector LQ model ($\kappa =$ 1) for $\lambda =$ 2.5.

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Additional Figure 4:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a scalar (left) and vector LQ model (right) determined from a nonresonant LQ signal only. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.

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Additional Figure 4-a:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a scalar LQ model determined from a nonresonant LQ signal only. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.

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Additional Figure 4-b:
The observed and expected upper limit at 95% CL on the coupling strength $\lambda $ of a vector LQ model determined from a nonresonant LQ signal only. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The region with blue shading shows the parameter space preferred by one of the models proposed to explain anomalies observed in B physics.
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