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| CMS-SUS-21-001 ; CERN-EP-2022-032 | ||
| Search for direct pair production of supersymmetric partners of $\tau$ leptons in the final state with two hadronically decaying $\tau$ leptons and missing transverse momentum in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 5 July 2022 | ||
| Phys. Rev. D 108 (2023) 012011 | ||
| Abstract: A search for the direct production of a pair of $\tau$ sleptons, the supersymmetric partners of $\tau$ leptons, is presented. Each $\tau$ slepton is assumed to decay to a $\tau$ lepton and the lightest supersymmetric particle (LSP), which is assumed to be stable and to not interact in the detector, leading to an imbalance in the total reconstructed transverse momentum. The search is carried out in events identified as containing two $\tau$ leptons, each decaying to one or more hadrons and a neutrino, and significant transverse momentum imbalance. In addition to scenarios in which the $\tau$ sleptons decay promptly, the search also addresses scenarios in which the $\tau$ sleptons have sufficiently long lifetimes to give rise to nonprompt $\tau$ leptons. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV at the CERN LHC with the CMS detector in 2016-2018, and correspond to an integrated luminosity of 138 fb$^{-1}$. No significant excess is seen with respect to standard model expectations. Upper limits on cross sections for the pair production of $\tau$ sleptons are obtained in the framework of simplified models. In a scenario in which the $\tau$ sleptons are superpartners of left-handed $\tau$ leptons, and each undergoes a prompt decay to a $\tau$ lepton and a nearly massless LSP, $\tau$ slepton masses between 115 and 340 GeV are excluded. In a scenario in which the lifetime of the $\tau$ sleptons corresponds to ${c\tau_{0}} =$ 0.1 mm, where $\tau_{0}$ represents the mean proper lifetime of the $\tau$ slepton, masses between 150 and 220 GeV are excluded. | ||
| Links: e-print arXiv:2207.02254 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Diagram for direct $\tilde{\tau}$ pair production, followed by decay of each $\tilde{\tau}$ to a $\tau$ lepton and an LSP. For models with promptly decaying $\tau$ sleptons, the LSP is assumed to be $\tilde{\chi}^0_1$, the lightest neutralino. For models with long-lived $\tau$ sleptons, it is assumed to be the gravitino, $\tilde{\mathrm{G}}$. |
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Figure 2:
Distributions of ${m_{\mathrm {T2}}}$ (upper left), ${\Sigma {m_{\mathrm {T}}}}$ (upper right), and ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},1}}}$ (lower left) for events passing the selection criteria common to all prompt SRs, and of ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},2}}}$ (lower right) for those passing the criteria common to all displaced SRs. The shaded band indicates the combined statistical and systematic uncertainty in the total SM background prediction. The lower panels show the ratio of the observed event counts to the total background prediction. Signal distributions are shown for benchmark models of $\tilde{\tau}$ pair production that are described in the text. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. |
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Figure 2-a:
Distribution of ${m_{\mathrm {T2}}}$ for events passing the selection criteria common to all prompt SRs. The shaded band indicates the combined statistical and systematic uncertainty in the total SM background prediction. The lower panel shows the ratio of the observed event counts to the total background prediction. Signal distributions are shown for benchmark models of $\tilde{\tau}$ pair production that are described in the text. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. |
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Figure 2-b:
Distribution of ${\Sigma {m_{\mathrm {T}}}}$ for events passing the selection criteria common to all prompt SRs. The shaded band indicates the combined statistical and systematic uncertainty in the total SM background prediction. The lower panel shows the ratio of the observed event counts to the total background prediction. Signal distributions are shown for benchmark models of $\tilde{\tau}$ pair production that are described in the text. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. |
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Figure 2-c:
Distribution of ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},1}}}$ for events passing the selection criteria common to all prompt SRs. The shaded band indicates the combined statistical and systematic uncertainty in the total SM background prediction. The lower panel shows the ratio of the observed event counts to the total background prediction. Signal distributions are shown for benchmark models of $\tilde{\tau}$ pair production that are described in the text. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. |
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Figure 2-d:
Distribution of ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},2}}}$ for events passing the selection criteria common to all displaced SRs. The shaded band indicates the combined statistical and systematic uncertainty in the total SM background prediction. The lower panel shows the ratio of the observed event counts to the total background prediction. Signal distributions are shown for benchmark models of $\tilde{\tau}$ pair production that are described in the text. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. |
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Figure 3:
Event counts and predicted yields in each SR for the SM background before (upper) and after (lower) a maximum likelihood fit to the data under the background-only hypothesis. The yields expected for 3 benchmark models of left-handed $\tilde{\tau}$ pair production assuming prompt $\tilde{\tau}$ decays, and one model of long-lived $\tilde{\tau}$ pair production in the maximally mixed scenario ($\tilde{\tau} _{\text {MM}}$) are overlaid in the pre-fit case. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. The lower panels show the ratio of the observed event counts to the total SM background prediction. The first 29 bins correspond to the prompt SRs, while bins 30 and 31 correspond to the displaced SRs, as labeled in Table 1. |
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Figure 3-a:
Event counts and predicted yields in each SR for the SM background before a maximum likelihood fit to the data under the background-only hypothesis. The yields expected for 3 benchmark models of left-handed $\tilde{\tau}$ pair production assuming prompt $\tilde{\tau}$ decays, and one model of long-lived $\tilde{\tau}$ pair production in the maximally mixed scenario ($\tilde{\tau} _{\text {MM}}$) are overlaid in the pre-fit case. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. The lower panel shows the ratio of the observed event counts to the total SM background prediction. The first 29 bins correspond to the prompt SRs, while bins 30 and 31 correspond to the displaced SRs, as labeled in Table 1. |
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Figure 3-b:
Event counts and predicted yields in each SR for the SM background after a maximum likelihood fit to the data under the background-only hypothesis. The yields expected for 3 benchmark models of left-handed $\tilde{\tau}$ pair production assuming prompt $\tilde{\tau}$ decays, and one model of long-lived $\tilde{\tau}$ pair production in the maximally mixed scenario ($\tilde{\tau} _{\text {MM}}$) are overlaid in the pre-fit case. The numbers in parentheses correspond to the masses of the $\tilde{\tau}$ and LSP in units of GeV for the different signal models. The lower panel shows the ratio of the observed event counts to the total SM background prediction. The first 29 bins correspond to the prompt SRs, while bins 30 and 31 correspond to the displaced SRs, as labeled in Table 1. |
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Figure 4:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the degenerate $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1, 10, 20, and 50 GeV (upper left to lower 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. The red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 4-a:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the degenerate $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 4-b:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the degenerate $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 10 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 4-c:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the degenerate $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 20 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 4-d:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the degenerate $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 50 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 5:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely left-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1, 10, 20, and 50 GeV (upper left to lower 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. The red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 5-a:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely left-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 5-b:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely left-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 10 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 5-c:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely left-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 20 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 5-d:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely left-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 50 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 6:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely right-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1, 10, 20, and 50 GeV (upper left to lower 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. The red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 6-a:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely right-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 1 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 6-b:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely right-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 10 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 6-c:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely right-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 20 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 6-d:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass in the purely right-handed $\tilde{\tau}$ scenario for $\tilde{\chi}^0_1$ masses of 50 GeV. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 7:
Upper limits at 95% CL on the cross section for degenerate (left) and purely left-handed (right) $\tilde{\tau}$ pair production in the $m(\tilde{\tau})$-$m(\tilde{\chi}^0_1)$ plane. The thick black (red) curves show the observed (expected) exclusion limits assuming NLO+NLL predictions for the signal cross sections. The thin black curves represent the variations in the observed limits obtained when these cross sections are varied by their $ \pm 1 $ standard deviation uncertainties. The thin dashed red curves indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. |
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Figure 7-a:
Upper limits at 95% CL on the cross section for degenerate $\tilde{\tau}$ pair production in the $m(\tilde{\tau})$-$m(\tilde{\chi}^0_1)$ plane. The thick black (red) curves show the observed (expected) exclusion limits assuming NLO+NLL predictions for the signal cross sections. The thin black curves represent the variations in the observed limits obtained when these cross sections are varied by their $ \pm 1 $ standard deviation uncertainties. The thin dashed red curves indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. |
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Figure 7-b:
Upper limits at 95% CL on the cross section for purely left-handed $\tilde{\tau}$ pair production in the $m(\tilde{\tau})$-$m(\tilde{\chi}^0_1)$ plane. The thick black (red) curves show the observed (expected) exclusion limits assuming NLO+NLL predictions for the signal cross sections. The thin black curves represent the variations in the observed limits obtained when these cross sections are varied by their $ \pm 1 $ standard deviation uncertainties. The thin dashed red curves indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. |
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Figure 8:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 0.01, 0.05, 0.1, 0.5, 1, and 2.5 mm (upper left to lower 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. The red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-a:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 0.01 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-b:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 0.05 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-c:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 0.1 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-d:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 0.5 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-e:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 1 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
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Figure 8-f:
Expected and observed 95% CL cross section upper limits as functions of the $\tilde{\tau}$ mass for long-lived $\tilde{\tau}$ in the maximally mixed scenario for an LSP mass of 1 GeV, and for ${c\tau _{0}}$ values of 2.5 mm. 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 red line and thin shaded band indicate the NLO+NLL prediction for the signal production cross section calculated with Resummino [29], and its uncertainty. |
| Tables | |
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Table 1:
Ranges of ${\Sigma {m_{\mathrm {T}}}}, {m_{\mathrm {T2}}}$, and ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},1}}}$ used to define the prompt SRs for the $ {N_{\text {j}}} =$ 0 and $ {N_{\text {j}}} \geq $ 1 event categories, and ranges of ${{p_{\mathrm {T}}} ^{\tau _{\mathrm {h},2}}}$ used to define the displaced SRs. |
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Table 2:
Uncertainties in the analysis affecting signal and the SM backgrounds. The numbers indicate the percentage effect of propagating $ \pm $ 1-standard deviation variations of the respective sources of uncertainty on the predicted signal and background yields, prior to a fit to the data. The ranges shown for signal refer to a representative benchmark model of ${\tilde{\tau} _{\mathrm {L}}}$ pair production with $m({\tilde{\tau} _{\mathrm {L}}}) = $ 150 GeV, $m(\tilde{\chi}^0_1) = $ 1 GeV. |
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Table 3:
Predicted SM background yields, observed event counts, and predicted signal yields for two benchmark models with a $\tilde{\tau}$ mass of 150 GeV and an LSP mass of 1 GeV, in all prompt and displaced SRs as labeled in Table 1. For the prompt signal model shown, we assume left-handed $\tilde{\tau}$ pair production, while for the displaced signal model we assume a maximally mixed scenario and $c\tau _{0}(\tilde{\tau})=$ 0.5 mm. The uncertainties listed are the sum in quadrature of the statistical and systematic components. For any estimate with no events in the data sideband, embedded, or simulation sample corresponding to a given SR selection, we provide the one standard deviation upper bound evaluated for that estimate. |
| Summary |
| A search for direct $\tau$ slepton ($\tilde{\tau}$) pair production has been performed in proton-proton collisions at a center-of-mass energy of 13 TeV in events with two hadronically decaying $\tau$ leptons and significant missing transverse momentum. The data used for this search correspond to an integrated luminosity of 138 fb$^{-1}$ collected in 2016--2018 with the CMS detector. Both prompt and displaced decays of the $\tau$ slepton are studied. Thirty-one different search regions are used in the analysis, based on kinematic observables that exploit expected differences between signal and background. No significant excess of events above the expected standard model background has been observed. Upper limits have been set on the cross section for direct $\tilde{\tau}$ pair production for simplified models in which each $\tilde{\tau}$ decays to a $\tau$ lepton and the lightest supersymmetric particle (LSP). For purely left-handed $\tilde{\tau}$ pair production with prompt decays, $\tilde{\tau}$ masses between 115 and 340 GeV are excluded at 95% confidence level for the case of a nearly massless LSP, while for the degenerate production of left- and right-handed $\tilde{\tau}$ pairs, $\tilde{\tau}$ masses up to 400 GeV are excluded under the same hypothesis. The limits observed are the most stringent obtained thus far in the case of direct $\tilde{\tau}$ pair production with prompt $\tilde{\tau}$ decays, for both the purely left-handed and degenerate production scenarios. They represent a considerable improvement in sensitivity with respect to the previous CMS search reported in Ref. [38]. In the context of long-lived $\tau$ sleptons, final states with displaced $\tau_{\mathrm{h}}$candidates are investigated for the first time. In a scenario with $c\tau(\tilde{\tau})=$ 0.1 mm, where $\tau_{0}$ denotes the mean proper lifetime of the $\tilde{\tau}$, masses between 150 and 220 GeV are excluded for the case that the LSP is nearly massless. |
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