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| CMS-EXO-24-005 ; CERN-EP-2026-206 | ||
| Search for scalar leptoquarks produced via muon-quark scattering in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 28 August 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: The first search for TeV-scale scalar leptoquarks (LQs) produced in muon-quark ($ \mu\mathrm{q} $) interactions is presented. It is based on proton-proton collision data recorded at a center-of-mass energy of 13 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Quantum fluctuations inside the proton generate charged-lepton components, enabling the study of lepton-induced processes. In particular, the interaction of a muon from one colliding proton with a quark from the other proton enables the study of resonant production of a single LQ and its subsequent decay. The final state includes one or two muons and a jet that can come from the hadronization of either a light quark (u) or a b quark. The primary observable is the invariant mass of the muon-jet system, whose distribution peaks at the LQ mass. The data are found to be in agreement with the background predictions. Upper limits are set on the product of the LQ production cross section and its decay branching fraction to the $ \mu\mathrm{q} $ final state. The results exclude broad regions in the parameter plane of the LQ mass and the LQ-$ \mu\mathrm{q} $ coupling, improving upon previous CMS searches by extending the coverage for LQs with masses between 1.5 and 3.6 TeV, and couplings between 0.2 and 0.6 for the $ \mathrm{LQ}(\mathrm{u}\mu) $ scenario; and masses above 1.8 TeV, and couplings above 1 for the $ \mathrm{LQ}(\mathrm{b}\mu) $ scenario. | ||
| Links: e-print arXiv:2608.28377 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
An LO Feynman diagram of the lepton-induced LQ production at the LHC. |
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Figure 2:
Comparison of data and background BDT discriminant distributions at the preselection level for the one-muon (left) and two-muon (right) SRs, shown for illustration purposes only. The colored histograms show the simulated background prediction. The error bars are the data statistical uncertainties. The shaded band indicates an uncertainty of one standard deviation in the simulated background, obtained by combining the statistical and normalization-only systematic contributions. The distributions of two simulated signal samples are also shown, corresponding to $ M_{\text{LQ}} = $ 1 or 3 TeV and $ \lambda_{\mathrm{u}\mu} = $ 1. The signal cross section is set to 1\unitpb for visibility. The lower panels show the ratio of the data to the background prediction, with the shaded band indicating the same uncertainty as in the upper panels. |
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Figure 2-a:
Comparison of data and background BDT discriminant distributions at the preselection level for the one-muon (left) and two-muon (right) SRs, shown for illustration purposes only. The colored histograms show the simulated background prediction. The error bars are the data statistical uncertainties. The shaded band indicates an uncertainty of one standard deviation in the simulated background, obtained by combining the statistical and normalization-only systematic contributions. The distributions of two simulated signal samples are also shown, corresponding to $ M_{\text{LQ}} = $ 1 or 3 TeV and $ \lambda_{\mathrm{u}\mu} = $ 1. The signal cross section is set to 1\unitpb for visibility. The lower panels show the ratio of the data to the background prediction, with the shaded band indicating the same uncertainty as in the upper panels. |
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Figure 2-b:
Comparison of data and background BDT discriminant distributions at the preselection level for the one-muon (left) and two-muon (right) SRs, shown for illustration purposes only. The colored histograms show the simulated background prediction. The error bars are the data statistical uncertainties. The shaded band indicates an uncertainty of one standard deviation in the simulated background, obtained by combining the statistical and normalization-only systematic contributions. The distributions of two simulated signal samples are also shown, corresponding to $ M_{\text{LQ}} = $ 1 or 3 TeV and $ \lambda_{\mathrm{u}\mu} = $ 1. The signal cross section is set to 1\unitpb for visibility. The lower panels show the ratio of the data to the background prediction, with the shaded band indicating the same uncertainty as in the upper panels. |
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Figure 3:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the one-muon SR: 1$ \mu $0bL (upper left), 1$ \mu $1bL (upper right), 1$ \mu $0bT (lower left), 1$ \mu $1bT (lower right). The upper panel in each frame shows the data distribution and the background component (red line) of the fit obtained using the empirical function. The data are shown as black points, with vertical bars representing the statistical uncertainties computed as Poisson (Garwood) 68% confidence intervals; in bins with no observed events only the upward interval is shown. The light blue (violet) line represents a signal hypothesis with $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 1, while the orange (brown) line represents $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 2. All signals are normalized to the expected upper limit cross section. The horizontal axis shows the $ M_{\mu\mathrm{j}} $ value, while the vertical axis shows the number of events per bin. The lower panel in each plot shows the pulls for each bin, defined as $ (N_{\text{data}} - N_{\text{fit}})/\sqrt{\smash[b]{N_{\text{data}} - \sigma_{\text{fit}}^2}} $, where $ N_{\text{data}} $ denotes the number of observed events, $ N_{\text{fit}} $ the expected number of background events from the fit, and $ \sigma_{\text{fit}} $ the uncertainty in $ N_{\text{fit}} $. |
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Figure 3-a:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the one-muon SR: 1$ \mu $0bL (upper left), 1$ \mu $1bL (upper right), 1$ \mu $0bT (lower left), 1$ \mu $1bT (lower right). The upper panel in each frame shows the data distribution and the background component (red line) of the fit obtained using the empirical function. The data are shown as black points, with vertical bars representing the statistical uncertainties computed as Poisson (Garwood) 68% confidence intervals; in bins with no observed events only the upward interval is shown. The light blue (violet) line represents a signal hypothesis with $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 1, while the orange (brown) line represents $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 2. All signals are normalized to the expected upper limit cross section. The horizontal axis shows the $ M_{\mu\mathrm{j}} $ value, while the vertical axis shows the number of events per bin. The lower panel in each plot shows the pulls for each bin, defined as $ (N_{\text{data}} - N_{\text{fit}})/\sqrt{\smash[b]{N_{\text{data}} - \sigma_{\text{fit}}^2}} $, where $ N_{\text{data}} $ denotes the number of observed events, $ N_{\text{fit}} $ the expected number of background events from the fit, and $ \sigma_{\text{fit}} $ the uncertainty in $ N_{\text{fit}} $. |
png pdf |
Figure 3-b:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the one-muon SR: 1$ \mu $0bL (upper left), 1$ \mu $1bL (upper right), 1$ \mu $0bT (lower left), 1$ \mu $1bT (lower right). The upper panel in each frame shows the data distribution and the background component (red line) of the fit obtained using the empirical function. The data are shown as black points, with vertical bars representing the statistical uncertainties computed as Poisson (Garwood) 68% confidence intervals; in bins with no observed events only the upward interval is shown. The light blue (violet) line represents a signal hypothesis with $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 1, while the orange (brown) line represents $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 2. All signals are normalized to the expected upper limit cross section. The horizontal axis shows the $ M_{\mu\mathrm{j}} $ value, while the vertical axis shows the number of events per bin. The lower panel in each plot shows the pulls for each bin, defined as $ (N_{\text{data}} - N_{\text{fit}})/\sqrt{\smash[b]{N_{\text{data}} - \sigma_{\text{fit}}^2}} $, where $ N_{\text{data}} $ denotes the number of observed events, $ N_{\text{fit}} $ the expected number of background events from the fit, and $ \sigma_{\text{fit}} $ the uncertainty in $ N_{\text{fit}} $. |
png pdf |
Figure 3-c:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the one-muon SR: 1$ \mu $0bL (upper left), 1$ \mu $1bL (upper right), 1$ \mu $0bT (lower left), 1$ \mu $1bT (lower right). The upper panel in each frame shows the data distribution and the background component (red line) of the fit obtained using the empirical function. The data are shown as black points, with vertical bars representing the statistical uncertainties computed as Poisson (Garwood) 68% confidence intervals; in bins with no observed events only the upward interval is shown. The light blue (violet) line represents a signal hypothesis with $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 1, while the orange (brown) line represents $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 2. All signals are normalized to the expected upper limit cross section. The horizontal axis shows the $ M_{\mu\mathrm{j}} $ value, while the vertical axis shows the number of events per bin. The lower panel in each plot shows the pulls for each bin, defined as $ (N_{\text{data}} - N_{\text{fit}})/\sqrt{\smash[b]{N_{\text{data}} - \sigma_{\text{fit}}^2}} $, where $ N_{\text{data}} $ denotes the number of observed events, $ N_{\text{fit}} $ the expected number of background events from the fit, and $ \sigma_{\text{fit}} $ the uncertainty in $ N_{\text{fit}} $. |
png pdf |
Figure 3-d:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the one-muon SR: 1$ \mu $0bL (upper left), 1$ \mu $1bL (upper right), 1$ \mu $0bT (lower left), 1$ \mu $1bT (lower right). The upper panel in each frame shows the data distribution and the background component (red line) of the fit obtained using the empirical function. The data are shown as black points, with vertical bars representing the statistical uncertainties computed as Poisson (Garwood) 68% confidence intervals; in bins with no observed events only the upward interval is shown. The light blue (violet) line represents a signal hypothesis with $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 1, while the orange (brown) line represents $ M_{\text{LQ}} = $ 2 (4) TeV and $ \lambda_{\mathrm{u}\mu} = $ 2. All signals are normalized to the expected upper limit cross section. The horizontal axis shows the $ M_{\mu\mathrm{j}} $ value, while the vertical axis shows the number of events per bin. The lower panel in each plot shows the pulls for each bin, defined as $ (N_{\text{data}} - N_{\text{fit}})/\sqrt{\smash[b]{N_{\text{data}} - \sigma_{\text{fit}}^2}} $, where $ N_{\text{data}} $ denotes the number of observed events, $ N_{\text{fit}} $ the expected number of background events from the fit, and $ \sigma_{\text{fit}} $ the uncertainty in $ N_{\text{fit}} $. |
png pdf |
Figure 4:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the two-muon SR: 2$ \mu $0bL (upper left), 2$ \mu $1bL (upper right), 2$ \mu $0bT (lower left), 2$ \mu $1bT (lower right). The notations are as in Fig. 3. |
png pdf |
Figure 4-a:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the two-muon SR: 2$ \mu $0bL (upper left), 2$ \mu $1bL (upper right), 2$ \mu $0bT (lower left), 2$ \mu $1bT (lower right). The notations are as in Fig. 3. |
png pdf |
Figure 4-b:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the two-muon SR: 2$ \mu $0bL (upper left), 2$ \mu $1bL (upper right), 2$ \mu $0bT (lower left), 2$ \mu $1bT (lower right). The notations are as in Fig. 3. |
png pdf |
Figure 4-c:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the two-muon SR: 2$ \mu $0bL (upper left), 2$ \mu $1bL (upper right), 2$ \mu $0bT (lower left), 2$ \mu $1bT (lower right). The notations are as in Fig. 3. |
png pdf |
Figure 4-d:
Empirical background function fits to the $ M_{\mu\mathrm{j}} $ invariant mass distributions for all analysis categories within the two-muon SR: 2$ \mu $0bL (upper left), 2$ \mu $1bL (upper right), 2$ \mu $0bT (lower left), 2$ \mu $1bT (lower right). The notations are as in Fig. 3. |
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Figure 5:
Signal efficiency as a function of $ M_{\text{LQ}} $ for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). The black curves are the total efficiency, defined as the sum of the efficiencies of the two SRs. The red and blue curves are the efficiency for the one- and two-muon SRs, respectively. |
png pdf |
Figure 5-a:
Signal efficiency as a function of $ M_{\text{LQ}} $ for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). The black curves are the total efficiency, defined as the sum of the efficiencies of the two SRs. The red and blue curves are the efficiency for the one- and two-muon SRs, respectively. |
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Figure 5-b:
Signal efficiency as a function of $ M_{\text{LQ}} $ for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). The black curves are the total efficiency, defined as the sum of the efficiencies of the two SRs. The red and blue curves are the efficiency for the one- and two-muon SRs, respectively. |
png pdf |
Figure 5-c:
Signal efficiency as a function of $ M_{\text{LQ}} $ for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). The black curves are the total efficiency, defined as the sum of the efficiencies of the two SRs. The red and blue curves are the efficiency for the one- and two-muon SRs, respectively. |
png pdf |
Figure 5-d:
Signal efficiency as a function of $ M_{\text{LQ}} $ for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). The black curves are the total efficiency, defined as the sum of the efficiencies of the two SRs. The red and blue curves are the efficiency for the one- and two-muon SRs, respectively. |
png pdf |
Figure 6:
Expected (dashed black line) and observed (solid black line) 95% CL upper limits on $ \sigma\mathcal{B} $, as a function of $ M_{\text{LQ}} $, for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). Uncertainty bands (68% and 95% CL) around the expected limits, as well as the expected limits for the one-muon (red dashed line) and two-muon (green dashed line) SRs, are also shown. The blue lines show the NLO predictions, with the bands around them representing the scale and PDF uncertainties [21]. |
png pdf |
Figure 6-a:
Expected (dashed black line) and observed (solid black line) 95% CL upper limits on $ \sigma\mathcal{B} $, as a function of $ M_{\text{LQ}} $, for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). Uncertainty bands (68% and 95% CL) around the expected limits, as well as the expected limits for the one-muon (red dashed line) and two-muon (green dashed line) SRs, are also shown. The blue lines show the NLO predictions, with the bands around them representing the scale and PDF uncertainties [21]. |
png pdf |
Figure 6-b:
Expected (dashed black line) and observed (solid black line) 95% CL upper limits on $ \sigma\mathcal{B} $, as a function of $ M_{\text{LQ}} $, for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). Uncertainty bands (68% and 95% CL) around the expected limits, as well as the expected limits for the one-muon (red dashed line) and two-muon (green dashed line) SRs, are also shown. The blue lines show the NLO predictions, with the bands around them representing the scale and PDF uncertainties [21]. |
png pdf |
Figure 6-c:
Expected (dashed black line) and observed (solid black line) 95% CL upper limits on $ \sigma\mathcal{B} $, as a function of $ M_{\text{LQ}} $, for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). Uncertainty bands (68% and 95% CL) around the expected limits, as well as the expected limits for the one-muon (red dashed line) and two-muon (green dashed line) SRs, are also shown. The blue lines show the NLO predictions, with the bands around them representing the scale and PDF uncertainties [21]. |
png pdf |
Figure 6-d:
Expected (dashed black line) and observed (solid black line) 95% CL upper limits on $ \sigma\mathcal{B} $, as a function of $ M_{\text{LQ}} $, for $ \lambda_{\mathrm{u}\mu} = $ 1 (upper left), $ \lambda_{\mathrm{u}\mu} = $ 2 (upper right), $ \lambda_{\mathrm{b}\mu} = $ 1 (lower left), and $ \lambda_{\mathrm{b}\mu} = $ 2 (lower right). Uncertainty bands (68% and 95% CL) around the expected limits, as well as the expected limits for the one-muon (red dashed line) and two-muon (green dashed line) SRs, are also shown. The blue lines show the NLO predictions, with the bands around them representing the scale and PDF uncertainties [21]. |
png pdf |
Figure 7:
95% CL exclusion regions in the ($ M_{\text{LQ}} $, $ \lambda $) plane, for the $ \mathrm{LQ}(\mathrm{u}\mu) $ (left) and $ \mathrm{LQ}(\mathrm{b}\mu) $ (right) scenarios. For each production mode, shown in a different color, the dashed contour indicates the expected exclusion and the shaded area the observed one, as illustrated by the black keys in the legend. The cyan area shows the region excluded by the lepton-induced single LQ production considered in this analysis. The red and magenta areas show the regions excluded by previous CMS searches targeting the pair production [23,24] and the nonresonant production [25] modes, respectively. The nonresonant production constraint is available only for the $ \mathrm{LQ}(\mathrm{u}\mu) $ scenario. |
png pdf |
Figure 7-a:
95% CL exclusion regions in the ($ M_{\text{LQ}} $, $ \lambda $) plane, for the $ \mathrm{LQ}(\mathrm{u}\mu) $ (left) and $ \mathrm{LQ}(\mathrm{b}\mu) $ (right) scenarios. For each production mode, shown in a different color, the dashed contour indicates the expected exclusion and the shaded area the observed one, as illustrated by the black keys in the legend. The cyan area shows the region excluded by the lepton-induced single LQ production considered in this analysis. The red and magenta areas show the regions excluded by previous CMS searches targeting the pair production [23,24] and the nonresonant production [25] modes, respectively. The nonresonant production constraint is available only for the $ \mathrm{LQ}(\mathrm{u}\mu) $ scenario. |
png pdf |
Figure 7-b:
95% CL exclusion regions in the ($ M_{\text{LQ}} $, $ \lambda $) plane, for the $ \mathrm{LQ}(\mathrm{u}\mu) $ (left) and $ \mathrm{LQ}(\mathrm{b}\mu) $ (right) scenarios. For each production mode, shown in a different color, the dashed contour indicates the expected exclusion and the shaded area the observed one, as illustrated by the black keys in the legend. The cyan area shows the region excluded by the lepton-induced single LQ production considered in this analysis. The red and magenta areas show the regions excluded by previous CMS searches targeting the pair production [23,24] and the nonresonant production [25] modes, respectively. The nonresonant production constraint is available only for the $ \mathrm{LQ}(\mathrm{u}\mu) $ scenario. |
| Tables | |
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Table 1:
Preselections for the one- and two-muon SRs. |
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Table 2:
Final category selection for the SRs. The preselection requirements of Table \reftab:Signal Region are applied in all categories. |
| Summary |
| A search for scalar leptoquarks (LQs) coupled to muons, using proton-proton collision data at $ \sqrt{s} = $ 13 TeV collected by the CMS experiment at the LHC and corresponding to an integrated luminosity of 138 fb$ ^{-1} $, has been presented. The final state includes one or two muons ($ \mu $) and a jet that can come from the hadronization of either a light quark (u) or a b quark. The analysis extends the search for LQs coupled to muons by exploiting a new production mechanism that leverages the charged-lepton content of protons arising from quantum fluctuations. This mechanism enables the study of lepton-induced processes and resonant single LQ production and decay at the LHC. The data are found to be in agreement with the background predictions. Upper limits on the product of the LQ production cross section and branching fraction to the muon-quark final state are derived. These limits exclude LQs with masses between 1.5 and 3.6 TeV, and couplings between 0.2 and 0.6 for the $ \mathrm{LQ}(\mathrm{u}\mu) $ scenario; and masses above 1.8 TeV, and couplings above 1 for the $ \mathrm{LQ}(\mathrm{b}\mu) $ scenario. These results extend the mass and coupling ranges probed by previous searches in other production modes. |
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