Searches for physics beyond the standard model with the M T 2 variable in hadronic final states with and without disappearing tracks in proton-proton collisions at s = 13 Te

Abstract

Two related searches for phenomena beyond the standard model (BSM) are performed using events with hadronic jets and significant transverse momentum imbalance. The results are based on a sample of proton-proton collisions at a center-of-mass energy of $13\text{Te}$ , collected by the CMS experiment at the LHC in 2016-2018 and corresponding to an integrated luminosity of 137 ${\text{fb}}^{-1}$ . The first search is inclusive, based on signal regions defined by the hadronic energy in the event, the jet multiplicity, the number of jets identified as originating from bottom quarks, and the value of the kinematic variable $M_{T2}$ for events with at least two jets. For events with exactly one jet, the transverse momentum of the jet is used instead. The second search looks in addition for disappearing tracks produced by BSM long-lived charged particles that decay within the volume of the tracking detector. No excess event yield is observed above the predicted standard model background. This is used to constrain a range of BSM models that predict the following: the pair production of gluinos and squarks in the context of supersymmetry models conserving R-parity, with or without intermediate long-lived charginos produced in the decay chain; the resonant production of a colored scalar state decaying to a massive Dirac fermion and a quark; or the pair production of scalar and vector leptoquarks each decaying to a neutrino and a top, bottom, or light-flavor quark. In most of the cases, the results obtained are the most stringent constraints to date.

Fig. 1

Distributions of the $M_{\mathrm{T}2}$ variable in data and simulation for the single-lepton control region, after normalizing the simulation to data in bins of $H_{\mathrm{T}}$, $N_{\mathrm{j}}$, and $N_{\text{b}}$, for events with no b-tagged jets (left), and events with at least one b-tagged jet (right). The hatched bands on the top panels show the MC statistical uncertainty, while the solid gray bands in the ratio plots show the systematic uncertainty in the $M_{\mathrm{T}2}$ shape. The bins have different widths, denoted by the horizontal bars

Fig. 2

(Left) Ratio $R^{\mathrm{SF}/\mathrm{DF}}$ in data as a function of $N_{\mathrm{j}}$. The solid black line enclosed by the red dashed lines corresponds to a value of $1.06\pm 0.15$ that is observed to be stable with respect to event kinematic variables, while the two dashed black lines denote the statistical uncertainty in the $R^{\mathrm{SF}/\mathrm{DF}}$ value. (Right) The shape of the $M_{\mathrm{T}2}$ distribution in $\text{Z}\to \mathrm{\nu }\overline{\mathrm{\nu }}$ simulation compared to the one obtained from the $\text{Z}\to {\ell }^{+}{\ell }^{-}$ data control sample, in a region with $1200<H_{\mathrm{T}}<1500$ $\text{Ge}$ and $N_{\mathrm{j}}\ge 2$, inclusive in $N_{\text{b}}$. The solid gray band on the ratio plot shows the systematic uncertainty in the $M_{\mathrm{T}2}$ shape. The bins have different widths, denoted by the horizontal bars

Fig. 3

Validation of the R&S multijet background prediction in control regions in data selected with $\Delta {\varphi }_{\text{min}}<0.3$. Electroweak backgrounds (LL and $\text{Z}\to \mathrm{\nu }\overline{\mathrm{\nu }}$) are estimated from data. In regions where the amount of data is insufficient to estimate the electroweak backgrounds, the corresponding yields are taken directly from simulation. The bins on the horizontal axis correspond to the ($H_{\mathrm{T}}$, $N_{\mathrm{j}}$, $N_{\text{b}}$) topological regions. The gray band on the ratio plot represents the total uncertainty in the prediction

Fig. 4

Validation of the background prediction method in (upper) 2016 and (lower) 2017–2018 data with $100<M_{\mathrm{T}2}<200\text{Ge}$, for the disappearing tracks search. The red histograms represent the predicted backgrounds, while the black markers are the observed data counts. The cyan bands represent the statistical uncertainty in the prediction. The gray bands represent the total uncertainty in the prediction. The labels on the x axes are explained in Tables 24 and 25 of Appendix B.2. Regions whose predictions use the same measurement of $f_{\text{short}}$ are grouped by the vertical dashed lines. Bins with no entry in the ratio have zero predicted background

Fig. 5

(Upper) Comparison of the estimated (pre-fit) background and observed data events in each topological region. The hatched bands represent the full uncertainty in the background estimate. The monojet regions ($N_{\mathrm{j}}=1$) are identified by the labels “1j, 0b” and “1j, 1b”, and are binned in jet $p_{\mathrm{T}}$. The multijet regions are shown for each $H_{\mathrm{T}}$ region separately, and are labeled accordingly. The notations j, b are short for $N_{\mathrm{j}}$, $N_{\text{b}}$. (Lower) Same for individual $M_{\mathrm{T}2}$ search bins in the medium-$H_{\mathrm{T}}$ region. On the x axis, the $M_{\mathrm{T}2}$ binning is shown in units of GeV

Fig. 6

Comparison of the estimated (pre-fit) background and observed data events in (upper) each of the 2016 search regions, and in (lower) each of the 2017–2018 search regions, in the search for disappearing tracks. The red histogram represents the predicted background, while the black markers are the observed data counts. The cyan band represents the statistical uncertainty in the prediction. The gray band represents the total uncertainty. The labels on the x axes are explained in Tables 24 and 25 of Appendix B.2. Regions whose predictions use the same measurement of $f_{\text{short}}$ are grouped by the vertical dashed lines. Bins with no entry in the ratio have zero pre-fit predicted background

Fig. 7

(Upper) Diagrams for three scenarios of direct gluino pair production where each gluino undergoes a three-body decay to light-flavor (u, d, s, c) quarks, with different decay modes. For mixed-decay scenarios, we assume equal branching fraction for each decay mode. (Upper middle) Diagrams for the direct gluino pair production where gluinos decay to bottom and top quarks. (Lower middle) Diagrams for the direct pair production of light-flavor, bottom, and top squark pairs. (Lower) Diagrams for three alternate scenarios of direct top squark pair production with different decay modes. For mixed-decay scenarios, we assume equal branching fraction for each decay mode

Fig. 8

Diagram for the mono-$\varphi$ model, where a colored scalar $\varphi$ is resonantly produced, and it decays to an invisible massive Dirac fermion $\psi$ and an SM quark

Fig. 9

Diagrams for LQ pair production

Fig. 10

Diagrams for direct (left) gluino, (middle) light-flavor (u, d, s, c) squark, and (right) top squark pair production, where the directly produced gluinos and squarks can decay via a long-lived ${\tilde{\mathrm{\chi }}}_1^{\pm }$. For gluinos, we assume a 1/3 decay branching fraction to each ${\tilde{\mathrm{\chi }}}_1^0$, ${\tilde{\mathrm{\chi }}}_1^{+}$, and ${\tilde{\mathrm{\chi }}}_1^{-}$, and each gluino decays to light-flavor quarks. For squarks, we assume a 1/2 branching fraction for decays to ${\tilde{\mathrm{\chi }}}_1^0$ and to the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ allowed by charge conservation. The mass of the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ is larger than the mass of the ${\tilde{\mathrm{\chi }}}_1^0$ by hundreds of $\text{Me}$. The ${\tilde{\mathrm{\chi }}}_1^{\pm }$ decays to a ${\tilde{\mathrm{\chi }}}_1^0$ via a pion, which is too soft to be detected

Fig. 11

Exclusion limits at 95% $\text{CL}$ for direct gluino pair production, where (upper) $\tilde{\text{g}}\to \text{q}\overline{\text{q}}{\tilde{\mathrm{\chi }}}_1^0$, (lower left) $\tilde{\text{g}}\to \text{q}\overline{\text{q}}{\tilde{\mathrm{\chi }}}_2^0$ and ${\tilde{\mathrm{\chi }}}_2^0\to \text{Z}{\tilde{\mathrm{\chi }}}_1^0$, or $\tilde{\text{g}}\to \text{q}{\overline{\text{q}}}^{\prime }{\tilde{\mathrm{\chi }}}_1^{\pm }$ and ${\tilde{\mathrm{\chi }}}_1^{\pm }\to {\text{W}}^{\pm }{\tilde{\mathrm{\chi }}}_1^0$, and (lower right) $\tilde{\text{g}}\to \text{q}{\overline{\text{q}}}^{\prime }{\tilde{\mathrm{\chi }}}_1^{\pm }$ and ${\tilde{\mathrm{\chi }}}_1^{\pm }\to {\text{W}}^{\pm }{\tilde{\mathrm{\chi }}}_1^0$ (with q $=$ u, d, s, or c). For the scenarios where the gluinos decay via an intermediate ${\tilde{\mathrm{\chi }}}_2^0$or ${\tilde{\mathrm{\chi }}}_1^{\pm }$, ${\tilde{\mathrm{\chi }}}_2^0$and ${\tilde{\mathrm{\chi }}}_1^{\pm }$ are assumed to be mass-degenerate, with $m_{{\tilde{\mathrm{\chi }}}_1^{\pm },{\tilde{\mathrm{\chi }}}_2^0}=0.5(m_{\tilde{\text{g}}}+m_{{\tilde{\mathrm{\chi }}}_1^0})$. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 and ±2 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming 1/3 branching fraction ($\mathcal{B}$) for each decay mode in the mixed-decay scenarios, or unity branching fraction for the indicated decay

Fig. 12

Exclusion limits at 95% $\text{CL}$ for direct gluino pair production where the gluinos decay to (left) bottom quarks and (right) top quarks. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 and ±2 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming unity branching fraction for the indicated decay

Fig. 13

Exclusion limit at 95% $\text{CL}$ for (upper left) light-flavor squark pair production, (upper right) bottom squark pair production, and (lower) top squark pair production. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 and ±2 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. The white diagonal band in the top squark pair production exclusion limit corresponds to the region $|m_{\tilde{\text{t}}}-m_{\text{t}}-m_{{\tilde{\mathrm{\chi }}}_1^0}|<25\text{Ge}$ and small $m_{{\tilde{\mathrm{\chi }}}_1^0}$. Here the efficiency of the selection is a strong function of $m_{\tilde{\text{t}}}-m_{{\tilde{\mathrm{\chi }}}_1^0}$, and as a result the precise determination of the cross section upper limit is uncertain because of the finite granularity of the available MC samples in this region of the ($m_{\tilde{\text{t}}},m_{{\tilde{\mathrm{\chi }}}_1^0}$) plane. In the same exclusion limit, the dashed black diagonal line corresponds to $m_{\tilde{\text{t}}}=m_{\text{t}}+m_{{\tilde{\mathrm{\chi }}}_1^0}$. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming unity branching fraction for the indicated decay

Fig. 14

Exclusion limit at 95% $\text{CL}$ for top squark pair production for different decay modes of the top squark. (Upper left) For the scenario where $\text{pp}\to \tilde{\text{t}}\overline{\tilde{\text{t}}}\to \text{b}\overline{\text{b}}{\tilde{\mathrm{\chi }}}_1^{\pm }{\mathrm{\chi }}_1^{\mp }$, ${\tilde{\mathrm{\chi }}}_1^{\pm }\to {\text{W}}^{\pm }{\tilde{\mathrm{\chi }}}_1^0$, the mass of the chargino is chosen to be half way in between the masses of the top squark and the neutralino. (Upper right) A mixed-decay scenario, $\text{pp}\to \tilde{\text{t}}\overline{\tilde{\text{t}}}$ with equal branching fractions for the top squark decays $\tilde{\text{t}}\to \text{t}{\tilde{\mathrm{\chi }}}_1^0$ and $\tilde{\text{t}}\to \text{b}{\tilde{\mathrm{\chi }}}_1^{+}$, ${\tilde{\mathrm{\chi }}}_1^{+}\to {\text{W}}^{\ast +}{\tilde{\mathrm{\chi }}}_1^0$, is also considered, with the chargino mass chosen such that $\Delta m\left({\tilde{\mathrm{\chi }}}_1^{\pm },{\tilde{\mathrm{\chi }}}_1^0\right)=5\text{Ge}$. (Lower) Finally, we also consider a compressed spectrum scenario where $\text{pp}\to \tilde{\text{t}}\overline{\tilde{\text{t}}}\to \text{c}\overline{\text{c}}{\tilde{\mathrm{\chi }}}_1^0{\tilde{\mathrm{\chi }}}_1^0$. In this scenario, mass ranges are considered where the $\tilde{\text{t}}\to \text{c}{\tilde{\mathrm{\chi }}}_1^0$ branching fraction can be significant. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 and ±2 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming 50% branching fraction ($\mathcal{B}$) for each decay mode in the mixed-decay scenarios, or unity branching fraction for the indicated decay

Fig. 15

Exclusion limit at 95% $\text{CL}$ for the mono-$\varphi$ model. We consider the mass range where such a model could be interesting based on a reinterpretation of previous analyses [35, 36]. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 and ±2 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. The blue star at $\left(m_{\varphi },m_{\psi }\right)=\left(1250,900\right)\text{Ge}$ indicates the best fit mass point reported in Refs. [35, 36]. Signal cross sections are calculated at LO order in ${\alpha }_S$

Fig. 16

The 95% $\text{CL}$ upper limits on the production cross sections as a function of LQ mass for LQ pair production decaying with 100% branching fraction ($\mathcal{B}$) to a neutrino and (upper left) a light quark (one of u, d, s, or c), (upper right) a bottom quark, or (lower) a top quark. The solid (dashed) black line represents the observed (median expected) exclusion. The inner green (outer yellow) band indicates the region containing 68 (95)% of the distribution of limits expected under the background-only hypothesis. The dark blue lines show the theoretical cross section for ${\mathrm{LQ}}_{\mathrm{S}}$ pair production with its uncertainty. The red (light blue) lines show the same for ${\mathrm{LQ}}_{\mathrm{V}}$ pair production assuming $\kappa =1$ (0). (Lower) Also shown in magenta is the product of the theoretical cross section and the square of the branching fraction ($\sigma {\mathcal{B}}^2$), for vector LQ pair production assuming $\kappa =1$ and a 50% branching fraction to $\text{t}{\mathrm{\nu }}_{\mathrm{\tau }}$, with the remaining 50% to $\text{b}\mathrm{\tau }$. Signal cross sections are calculated at NLO (LO) in ${\alpha }_S$ for scalar (vector) LQ pair production

Fig. 17

Exclusion limits at 95% $\text{CL}$ for direct gluino pair production where the gluinos decay to light-flavor (u, d, s, c) quarks, with $c{\tau }_0({\tilde{\mathrm{\chi }}}_1^{\pm })=$ (upper left) 10$\text{cm}$, (upper right) 50$\text{cm}$, and (lower) 200$\text{cm}$. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. The white band for masses of the ${\tilde{\mathrm{\chi }}}_1^0$ below 91.9$\text{Ge}$ represents the region of the mass plane excluded at the CERN LEP [151]. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 18

Exclusion limits at 95% $\text{CL}$ for light squark pair production with $c{\tau }_0({\tilde{\mathrm{\chi }}}_1^{\pm })=$ (upper left) 10$\text{cm}$, (upper right) 50$\text{cm}$, and (lower) 200$\text{cm}$. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. The white band for masses of the ${\tilde{\mathrm{\chi }}}_1^0$ below 91.9$\text{Ge}$ represents the region of the mass plane excluded at the CERN LEP [151]. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 19

Exclusion limits at 95% $\text{CL}$ for top squark pair production with $c{\tau }_0({\tilde{\mathrm{\chi }}}_1^{\pm })=$ (upper left) 10$\text{cm}$, (upper right) 50$\text{cm}$, and (lower) 200$\text{cm}$. The area enclosed by the thick black curve represents the observed exclusion region, while the dashed red lines indicate the expected limits and their ±1 standard deviation (s.d.) ranges. The thin black lines show the effect of the theoretical uncertainties in the signal cross section. The white band for masses of the ${\tilde{\mathrm{\chi }}}_1^0$ below 91.9$\text{Ge}$ represents the region of the mass plane excluded at the CERN LEP [151]. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 20

Exclusion limits at 95% $\text{CL}$ on the ${\tilde{\mathrm{\chi }}}_1^0$ mass, with $m_{{\tilde{\mathrm{\chi }}}_1^{\pm }}=m_{{\tilde{\mathrm{\chi }}}_1^0}+\mathcal{O}(100\text{Me})$, as a function of the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ proper decay length, for (upper) direct gluino and (lower) direct light-flavor (u, d, s, c) squark pair production, as obtained for representative gluino and squark masses. The gluinos decay to light-flavor quarks. For direct squark pair production, we assume either (lower left) one–fold or (lower right) eight–fold squark degeneracy. The area enclosed by the solid (dashed) black curve represents the observed (median expected) exclusion region, while the inner green (outer yellow) band indicates the region containing 68 (95)% of the distribution of limits expected under the background-only hypothesis. At short decay lengths, horizontal exclusion lines are obtained from the inclusive $M_{\mathrm{T}2}$ search, as this is not affected by track reconstruction inefficiencies, which may arise when the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ decays before the CMS tracker, and therefore shows better sensitivity to scenarios with very small $c{\tau }_0({\tilde{\mathrm{\chi }}}_1^{\pm })$ compared to the disappearing track search, based on median expected limits. The horizontal dashed lines at (upper) $m_{\tilde{\text{g}}}=m_{{\tilde{\mathrm{\chi }}}_1^0}$ and (lower) $m_{\tilde{\text{q}}}=m_{{\tilde{\mathrm{\chi }}}_1^0}$ bound the mass range in which the decays are kinematically allowed. If all kinematically allowed ${\tilde{\mathrm{\chi }}}_1^0$ masses ($m_{{\tilde{\mathrm{\chi }}}_1^0}\le m_{\tilde{\text{g}}}$, or $m_{{\tilde{\mathrm{\chi }}}_1^0}\le m_{\tilde{\text{q}}}$) are excluded, the curves, including 68 and 95% expected, tend to overlap. The band at masses of the ${\tilde{\mathrm{\chi }}}_1^0$ below 91.9$\text{Ge}$ represents the region of the mass plane excluded at the CERN LEP [151]. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 21

Exclusion limits at 95% $\text{CL}$ on the ${\tilde{\mathrm{\chi }}}_1^0$ mass, with $m_{{\tilde{\mathrm{\chi }}}_1^{\pm }}=m_{{\tilde{\mathrm{\chi }}}_1^0}+\mathcal{O}(100\text{Me})$, as a function of the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ proper decay length, for direct top squark pair production, as obtained for a representative top squark mass. The area enclosed by the solid (dashed) black curve represents the observed (median expected) exclusion region, while the inner green (outer yellow) band indicates the region containing 68 (95)% of the distribution of limits expected under the background-only hypothesis. At short decay lengths, horizontal exclusion lines are obtained from the inclusive $M_{\mathrm{T}2}$ search, as this is not affected by track reconstruction inefficiencies, which may arise when the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ decays before the CMS tracker, and therefore shows better sensitivity to scenarios with very small $c{\tau }_0({\tilde{\mathrm{\chi }}}_1^{\pm })$ compared to the disappearing track search, based on median expected limits. The horizontal dashed line at $m_{\tilde{\text{t}}}=m_{{\tilde{\mathrm{\chi }}}_1^0}+100\text{Ge}$ indicates the minimum simulated mass difference between top squark and ${\tilde{\mathrm{\chi }}}_1^0$, chosen such that the decay of top quarks to on-shell $\text{W}$ bosons is allowed. If all kinematically allowed ${\tilde{\mathrm{\chi }}}_1^0$ masses ($m_{{\tilde{\mathrm{\chi }}}_1^0}\le m_{\tilde{\text{t}}}-100\text{Ge}$) are excluded, the curves, including 68 and 95% expected, tend to overlap. The band at masses of the ${\tilde{\mathrm{\chi }}}_1^0$ below 91.9$\text{Ge}$ represents the region of the mass plane excluded at the CERN LEP [151]. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 22

Exclusion limits at 95% $\text{CL}$ on $\sigma /{\sigma }_{\mathrm{theory}}$ as a function of the ${\tilde{\mathrm{\chi }}}_1^{\pm }$ decay length, for a choice of signal models of (upper) direct gluino pair production where the gluinos decay to light-flavor (u, d, s, c) quarks, (lower left) direct light-flavor squark pair production, and (lower right) direct top squark pair production, as obtained from the search for disappearing tracks. The area enclosed by the solid (dashed) black curve below the horizontal dashed line at $\sigma /{\sigma }_{\mathrm{theory}}=1$ represents the observed (median expected) exclusion region, while the inner green (outer yellow) band indicates the region containing 68 (95)% of the distribution of limits expected under the background-only hypothesis. Signal cross sections are calculated at approximately NNLO+NNLL order in ${\alpha }_S$ [–147], assuming decay branching fractions ($\mathcal{B}$) as indicated in the figure

Fig. 23

(Upper) Comparison of the estimated background and observed data events in each signal bin in the very-low-$H_{\mathrm{T}}$ region. The hatched bands represent the full uncertainty in the background estimate. The notations j, b indicate $N_{\mathrm{j}}$, $N_{\text{b}}$ labeling. (Lower) Same for the low-$H_{\mathrm{T}}$ region. On the x axis, the $M_{\mathrm{T}2}$ binning is shown in units of GeV

Fig. 24

(Upper) Comparison of the estimated background and observed data events in each signal bin in the high-$H_{\mathrm{T}}$ region. The hatched bands represent the full uncertainty in the background estimate. The notations j, b indicate $N_{\mathrm{j}}$, $N_{\text{b}}$ labeling. (Lower) Same for the extreme-$H_{\mathrm{T}}$ region. On the x axis, the $M_{\mathrm{T}2}$ binning is shown in units of GeV