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| CMS-PAS-FTR-18-034 | ||
| Projection of the top quark spin correlation measurement and search for top squark pair production at the HL-LHC | ||
| CMS Collaboration | ||
| June 2022 | ||
| Abstract: The CMS prospects for the high-luminosity phase of the LHC on the measurement of the top quark spin correlation is presented, using events containing two oppositely charged lepton pairs (e$\mu$) produced in proton-proton collisions at a center-of-mass energy of 14 TeV assuming an integrated luminosity of 3 ab$^{-1}$. We investigate the normalised strength of the spin correlation in the sample and hence, provide a first performance study in future spin correlation measurements at 14 TeV. As an application, these observables are used in a Deep Neural Network to search for pair production of supersymmetric (anti-)top scalar quarks decaying into (anti-)top quarks and neutralinos, which escape the detector undetected. The observables sensitive to top quark spin correlation allow to study the corridor where the mass difference between the top scalar quark and the neutralino is about equal to the top quark mass. Compared to existing Run 2 results, this work will particularly push the discovery potential to the most natural top squark mass values below 300 GeV by one order of magnitude. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Feynman diagram for the production of (anti-)top squark pairs decaying into (anti-)top quarks and neutralinos. |
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Figure 2:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles p represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 2-a:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles p represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 2-b:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles p represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 3:
Signal cross sections for top squark pair production with top squark masses between 145 and 900 GeV from [24]. All signal mass points with the same top squark mass have the same cross section. An uncertainty of 14 $%$ is associated on the cross section for each mass point. |
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Figure 4:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-a:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-b:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-c:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-d:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-e:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 4-f:
From top to bottom and left to right: diagonal terms of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ spin correlation matrix along the $r$ and $n$ axis; $\cos\varphi $ and $\cos\varphi _{\mathrm {lab}}$; $\Delta \phi $ and $\Delta \eta $ between the leptons. Lower pad shows a ratio of SUSY signal plus SM backgrounds over SM backgrounds, allowing to compare the shape of SUSY prediction versus the SM one. |
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Figure 5:
Parametric DNN output for SM background ($\mathrm{t\bar{t}}$) and SUSY signal mass points with $m_{\tilde{t}_1} = $ 185 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 10 GeV, and with $m_{\tilde{t}_1} = $ 800 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 625 GeV, respectively. |
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Figure 5-a:
Parametric DNN output for SM background ($\mathrm{t\bar{t}}$) and SUSY signal mass points with $m_{\tilde{t}_1} = $ 185 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 10 GeV, and with $m_{\tilde{t}_1} = $ 800 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 625 GeV, respectively. |
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Figure 5-b:
Parametric DNN output for SM background ($\mathrm{t\bar{t}}$) and SUSY signal mass points with $m_{\tilde{t}_1} = $ 185 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 10 GeV, and with $m_{\tilde{t}_1} = $ 800 GeV and $m_{\tilde{\chi}_{1}^{0}} = $ 625 GeV, respectively. |
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Figure 6:
Extracted values of $f_{SM}$ from laboratory-frame spin correlation variables by CMS [29] and ATLAS [30] at 13 TeV and projected values at 14 TeV. The measured and projected values with their statistical, systematic, and theoretical uncertainties are given on the right. Statistical uncertainties of the data on the projected values are smaller than 0.004 and hence, denoted with 0.00. As per Yellow Report recommendations theory uncertainties are reduced by 50% for projected values. |
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Figure 7:
DNN output on the test datasets for two different top squark masses : 225 and 550 GeV. |
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Figure 7-a:
DNN output on the test datasets for two different top squark masses : 225 and 550 GeV. |
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Figure 7-b:
DNN output on the test datasets for two different top squark masses : 225 and 550 GeV. |
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Figure 8:
Projected region of discovery potential in the top squark and neutralino mass plane. The center line corresponds to $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . |
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Figure 9:
Expected 95 $%$ CL upper limits on the SUSY cross section (in pb) as a function of the top squark and neutralino masses in the top quark corridor region (left). We highlight the limits (right) in the already excluded region in the low top squark-neutralino mass plane. In both plots we add a center line to guide the eye, which corresponds to $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . |
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Figure 9-a:
Expected 95 $%$ CL upper limits on the SUSY cross section (in pb) as a function of the top squark and neutralino masses in the top quark corridor region (left). We highlight the limits (right) in the already excluded region in the low top squark-neutralino mass plane. In both plots we add a center line to guide the eye, which corresponds to $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . |
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Figure 9-b:
Expected 95 $%$ CL upper limits on the SUSY cross section (in pb) as a function of the top squark and neutralino masses in the top quark corridor region (left). We highlight the limits (right) in the already excluded region in the low top squark-neutralino mass plane. In both plots we add a center line to guide the eye, which corresponds to $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . |
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Figure 10:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 11:
Ratio of expected 95% CL upper limits of the combined search for top squarks from Ref. [31] to the ones derived in the context of this search for the low top squark-neutralino mass plane. The center line corresponds to $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 175 GeV . |
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Figure 12:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 12-a:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 12-b:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 12-c:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 12-d:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
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Figure 12-e:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
png |
Figure 12-f:
Expected limits on signal strength calculated using asymptotic formulae. Corresponding to each top squark mass point there is a neutralino mass such that $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 145 GeV (top left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 155 GeV (top right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 165 GeV (middle left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 185 GeV (middle right), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 195 GeV (bottom left), $\Delta M(\tilde{t}_1, \tilde{\chi}_{1}^{0}) = $ 205 GeV (bottom right). The green and yellow bands represent the regions containing 68% and 95%, respectively, of the expected limits. The red dashed line indicates the approximate NLO+NLL prediction. |
| Tables | |
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Table 1:
Observables and corresponding coefficients and production spin density matrix coefficient functions. For the laboratory-frame asymmetries shown in the last three rows, there is no direct correspondence with the coefficient functions. |
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Table 2:
Event yields post cuts at 14 TeV and corresponding to 3000 fb$^{-1}$ of data. $\epsilon _{tot}$ is the fraction of events remaining after each cut relative to the original sample size, while $\epsilon _{cut}$ is the fraction of events remaining after the cut relative to the previous step. |
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Table 3:
Summary of flat systematic uncertainties. |
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Table 4:
Summary of shape-based systematic uncertainties. |
| Summary |
|
In this analysis we present a first study of the performance of the expected precision of a measurement of the strength of expected $\mathrm{t\bar{t}}$ spin correlation in 14 TeV proton-proton collisions. Unprecedented precision in measuring spin correlation variables is expected, with $D$ the most accurate variable with a 3% total uncertainty. We also presented a Deep Neural Network (DNN) based approach to searches for new physics in the low and high top quark mass corridor using top quark spin correlation. Using this method alone and extending the corridor up to masses in the 1 TeV range, we can significantly increase the ultimate reach of the LHC to discover top squarks in the degenerate mass corridor in the top squark-neutralino plane, or in the absence of a discovery exclude top squarks up to 600 GeV. In particular, in the top squark and neutralino mass corridor existing top squark pair production cross section limits can be improved by about one order of magnitude for top squark masses less than 300 GeV. Naturalness arguments still hint at the low top squark mass phase space region as a less fine-tuned implementation of SUSY, which so far might have escaped discovery given the abundance of top quarks in the same phase space folded with less favorable SUSY scenarios.\\ In principle, adding more kinematic variables to the DNN will improve the sensitivity further by an additional 5-10%. However, the purpose of this analysis is to show that $\mathrm{t\bar{t}}$ spin correlation variables will be an important asset for any type of searches for new physics involving top quark pairs. This is especially true for corners of the phase space that are difficult to access by classical searches using only kinematic variables in the low top quark mass corridor. This phase space represents less fine-tuned implementations of beyond the SM SUSY models. Given the model independent nature of this channel, other new physics signatures may be probed by this approach and make ample use of the ultimate 3 ab$^{-1}$ dataset. |
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