Super-razor and searches for sleptons and charginos at the LHC

Matthew R. Buckley, Joseph D. Lykken, Christopher Rogan, and Maria Spiropulu

Phys. Rev. D 89, 055020 – Published 20 March 2014

Abstract

Direct searches for electroweak pair production of new particles at the LHC are a difficult proposition, due to the large background and low signal cross sections. We demonstrate how these searches can be improved by a combination of new razor variables and shape analysis of signal and background kinematics. We assume that the pair-produced particles decay to charged leptons and missing energy, either directly or through a $W$ boson. In both cases the final state is a pair of opposite sign leptons plus missing transverse energy. We estimate exclusion reach in terms of sleptons and charginos as realized in minimal supersymmetry. We compare this super-razor approach in detail to analyses based on other kinematic variables, showing how the super-razor uses more of the relevant kinematic information while achieving higher selection efficiency on signals, including cases with compressed spectra.

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Received 11 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.055020

Authors & Affiliations

Matthew R. Buckley^1,2, Joseph D. Lykken³, Christopher Rogan^4,5, and Maria Spiropulu⁴

¹Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
²Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08954, USA
³Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
⁴Lauritsen Laboratory of Physics, California Institute of Technology, Pasadena, California 91125, USA
⁵Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Vol. 89, Iss. 5 — 1 March 2014

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Figure 1
Sketch of the three sets of frames relevant to the razor reconstruction: the lab frame, the pair production frame for $S_{1}$ and $S_{2}$ , and the two decay frames of the particles $S_{i}$ . The approximate razor frame identified with each physically relevant frame is also shown, along with the actual and approximate boosts from one frame to the next. By convention, we label each boost by the destination frame (i.e. boost ${\vec{β}}^{CM}$ takes you from the lab to the pair production center of mass frame).
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Figure 2
Distributions of razor variable $M_{R}$ normalized to $\sqrt{\hat{s}}$ (left) and ${\sqrt{\hat{s}}}_{R}$ normalized to $\sqrt{\hat{s}} / 2$ (right) vs CM $p_{T}$ compared for 150 GeV slepton pair production followed by decay to leptons and massless neutralinos. See Sec. 3 for details of the simulation.
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Figure 3
Top row: Distributions of $β_{R}$ for 150 GeV selectrons (left) or charginos (right) decaying into neutralinos and electrons, for a range of neutralino masses. Also shown is the distribution of the $W^{-} W^{+}$ background. Bottom row: Distributions of normalized $β_{R} / β_{T}^{CM}$ (right) for 150 GeV selectrons (left) or charginos (right) decaying into neutralinos, again for a range of neutralino masses.
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Figure 4
Top row: Distributions of $β_{R + 1}$ for 150 GeV selectrons (left) or charginos (right) decaying into neutralinos and electrons, for a range of neutralino masses. Also shown is the distribution of the $W^{-} W^{+}$ background. Bottom row: Distributions of normalized $β_{R + 1} / β^{decay}$ (right) for 150 GeV selectrons (left) or charginos (right) decaying into neutralinos, again for a range of neutralino masses.
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Figure 5
Top row: Distributions of ${\sqrt{\hat{s}}}_{R}$ for a 150 GeV slepton (left) or chargino (right) and a range of neutralino masses. Also shown is the distribution of the $W^{-} W^{+}$ background. Bottom row: Distributions of ${\sqrt{\hat{s}}}_{R}$ normalized to $2 γ^{decay} M_{Δ}$ for selectrons (left) and charginos (right), again for a range of neutralino masses.
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Figure 6
Top row: Distributions of $M_{Δ}^{R}$ for a 150 GeV slepton (left) or chargino (right) and a range of neutralino masses. Also shown is the distribution of the $W^{-} W^{+}$ background. For the $W$ background, $M_{Δ} = m_{W}$ . Bottom row: Distributions of $M_{Δ}^{R}$ normalized to $M_{Δ}$ for selectrons (left) and charginos (right), again for a range of neutralino masses.
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Figure 7
Top row: Distributions of ${\sqrt{\hat{s}}}_{R} / \sqrt{\hat{s}}$ vs $M_{Δ}^{R} / M_{Δ}$ for 150 GeV sleptons and a range of $m_{\tilde{χ}}$ masses. Bottom row: Distributions of ${\sqrt{\hat{s}}}_{R} / 2 γ^{decay} M_{Δ}$ vs $M_{Δ}^{R} / M_{Δ}$ for 150 GeV sleptons and a range of $m_{\tilde{χ}}$ ) masses.
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Figure 8
Schematic example of the definition of the azimuthal angle $Δ ϕ_{R}^{β}$ . The lab frame (seen here down the beam line) contains two visible objects, $q_{1}$ and $q_{2}$ . The direction of the boost ${\vec{β}}_{R}$ [defined in Eq. (10)], in the lab frame is also shown. In the frame $R$ , arrived at by performing the boost ${\vec{β}}_{R}$ , the visible momenta $q_{1}$ and $q_{2}$ are shown, along with their sum. The azimuthal angle between their sum $q_{1} + q_{2}$ and the boost direction ${\vec{β}}_{R}$ in frame $R$ defines $Δ ϕ_{R}^{β}$ .
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Figure 9
Distributions of $Δ ϕ_{R}^{β}$ for a 150 GeV slepton (left) or chargino (right) and a range of neutralino masses. Also shown are the distributions of the $W^{-} W^{+}$ and Drell-Yan $Z$ backgrounds.
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Figure 10
Distribution of $| \cos θ_{R + 1} |$ for 150 GeV selectron (left) and chargino (right) pair production, decaying into a range of neutralino masses. Also shown are the $W^{-} W^{+}$ and Drell-Yan $Z$ background distributions.
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Figure 11
Upper row: Distribution of $| \cos θ_{R + 1} |$ vs $M_{Δ}^{R}$ for 150 GeV selectron (left) or chargino (right) pair production, decaying into 50 GeV neutralinos. Lower row: $| \cos θ_{R + 1} |$ vs $M_{Δ}^{R}$ for $W^{-} W^{+}$ pair production (left) or Drell-Yan $Z$ (right) backgrounds decaying into leptons.
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Figure 12
Representative distribution of $Δ ϕ_{R}^{β}$ vs $M_{Δ}^{R}$ (top row) and $Δ ϕ_{R}^{β}$ vs $| \cos θ_{R + 1} |$ (bottom row) for 150 GeV selectrons decaying to 50 GeV neutralinos (left) and $W^{-} W^{+}$ background (right).
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Figure 13
Left: First or second generation left-handed (blue) and right-handed (green) slepton pair production cross sections. Right: Chargino pair production cross section. Cross sections calculated using Prospino [54] at NLO for the LHC with $\sqrt{s} = 8 TeV$ . Theoretical errors indicated by width of lines.
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Figure 14
Distributions of $M_{Δ}$ estimating variables for sleptons (top row) and charginos (bottom row) with mass 150 GeV decaying into neutralinos and leptons, for a range of neutralino masses. Variables include $M_{Δ}^{R}$ (left), $M_{C T ⊥}$ (center) and $M_{T 2}$ (right), all normalized to the true value of $M_{Δ}$ for each sample.
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Figure 15
Distributions of $M_{Δ}$ estimating variables for charginos with mass 150 GeV decaying into 50 GeV neutralinos and leptonically decaying $W$ bosons, as a function of reconstructed jet multiplicity. Variables include $M_{Δ}^{R}$ (left), $M_{C T ⊥}$ (center) and $M_{T 2}$ (right), all normalized to the true value of $M_{Δ}$ for each sample.
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Figure 16
Efficiency of the CMS (left) and ATLAS (right) selections for the slepton (top) and chargino (bottom) signal models. Selection efficiencies are calculated as a function of parent sparticle and neutralino mass and include all final state categories.
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Figure 17
Efficiency times cross section for slepton signal samples, as a function of neutralino mass, for the CMS (top) and ATLAS (bottom) selections with additional requirement that the mass sensitive variable ( $M_{Δ}$ , left; $M_{C T ⊥}$ , top right; $M_{T 2}$ , bottom right) is in excess of 100 GeV.
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Figure 18
Efficiency times cross section for chargino signal samples, as a function of neutralino mass, for the CMS (top) and ATLAS (bottom) selections with the additional requirement that the mass sensitive variable ( $M_{Δ}$ , left; $M_{C T ⊥}$ , top right; $M_{T 2}$ , bottom right) is in excess of 100 GeV.
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Figure 19
Distributions of $M_{Δ}^{R}$ vs $1 / γ_{R + 1}$ for simulated event samples with baseline selection applied. Top left: $W W$ . Top right: $Z / γ * + jets$ . Bottom left: Dislepton production with $m_{\tilde{ℓ}} = 150 GeV$ and $m_{{\tilde{χ}}_{1}^{0}} = 50 GeV$ . Bottom right: Dichargino production with $m_{{\tilde{χ}}_{1}^{\pm}} = 150 GeV$ and $m_{{\tilde{χ}}_{1}^{0}} = 50 GeV$ .
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Figure 20
Distributions of $| Δ ϕ ({\vec{p}}_{ℓ ℓ}^{lab}, {\vec{E}}_{T}^{miss}) |$ vs $Δ ϕ_{R}^{β}$ for simulated events samples. Top row: Inclusive baseline event selection. Bottom row: Additional $γ_{R + 1} < 4$ requirement. Samples correspond to dislepton production (left), dileptonic $t \bar{t}$ (center), and $Z / γ^{*} + jets$ . The choice of $γ_{R + 1} < 4$ is to make the effect clearly visible; in actual application, we relax the cut to $γ_{R + 1} < 10$ .
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Figure 21
Selection efficiencies (left) and efficiency times cross section (right) for left-handed selectrons (upper row) and chargino (lower row) signal samples, as a function of neutralino mass for the razor selection criteria, described in the text.
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Figure 22
Expected background yields in the $e e$ final state passing the CMS selection, normalized to $20 {fb}^{- 1}$ of data, for different jet multiplicities. Sample left-handed diselectron signals are included with ( $m_{{\tilde{ℓ}}_{L}} = 350$ , $m_{{\tilde{χ}}_{1}^{0}} = 100$ ) and ( $m_{{\tilde{ℓ}}_{L}} = 250$ , $m_{{\tilde{χ}}_{1}^{0}} = 100$ ) GeV. Top: $M_{Δ}^{R}$ distribution. Bottom: $M_{C T ⊥}$ distribution. Left: $N_{jet} = 0$ . Center: $N_{jet} = 1$ . Right: $N_{jet} \geq 2$ .
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Figure 23
Expected background yields in the $e μ$ , $N_{jet} = 0$ final state passing the CMS or ATLAS selections, normalized to $20 {fb}^{- 1}$ of data. Top left: $M_{Δ}^{R}$ with the ATLAS selection applied. Sample dichargino signals are included with ( $m_{{\tilde{χ}}_{1}^{\pm}} = 200$ , $m_{{\tilde{χ}}_{1}^{0}} = 50$ ) and ( $m_{{\tilde{χ}}_{1}^{\pm}} = 150$ , $m_{{\tilde{χ}}_{1}^{0}} = 50$ ) GeV. Top right: $M_{T 2}$ with ATLAS selection. Bottom left: $M_{Δ}^{R}$ with CMS selection. Bottom right: $M_{C T ⊥}$ with CMS selection.
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Figure 24
Expected background yields in the $N_{jet} = 0$ final state passing the razor selection for $Δ ϕ_{R}^{β}$ , normalized to $20 {fb}^{- 1}$ of data. Left: $e e$ final state including sample left-handed diselectron signals with $m_{\tilde{ℓ}} = 300 GeV$ and varying neutralino masses. Right: $e μ$ final state including sample dichargino signals with $m_{{\tilde{χ}}^{\pm}} = 200 GeV$ and varying neutralino masses.
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Figure 25
Expected background yields in the $M_{Δ}^{R} \times | \cos θ_{R + 1} |$ plane, normalized to $20 {fb}^{- 1}$ of data. Top: Expected event yields for the $e e$ final state with $N_{jet} = 0$ and the razor selection applied. Bottom: Analogous figures for the $e μ$ final state. Left: Kinematic distributions for sample signal models including diselectron production with ( $m_{{\tilde{ℓ}}_{L}} = 250$ , $m_{{\tilde{χ}}_{1}^{0}} = 100$ ) GeV (top left) and dichargino production with ( $m_{{\tilde{χ}}_{1}^{\pm}} = 250$ , $m_{{\tilde{χ}}_{1}^{0}} = 50$ ) GeV (bottom left). Right: Total of expected SM background yields.
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Figure 26
Distributions of $λ$ , assuming both signal and background-only scenarios. Left: Test-statistic distributions for the one-dimensional $M_{C T ⊥}$ analysis searching for diselectron production with ( $m_{{\tilde{ℓ}}_{L}} = 250 GeV$ , $m_{{\tilde{χ}}_{1}^{0}} = 150 GeV$ ). Right: $λ$ distributions for the one-dimensional $M_{Δ}^{R}$ analysis, using the same mass point.
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Figure 27
Expected exclusion limits (in units of $σ$ ) for left-handed selectrons decaying to leptons and neutralinos using $20 {fb}^{- 1}$ of 8 TeV data, as a function of both selectron and neutralino masses. Expected limits are shown for our 1D $M_{Δ}^{R}$ analysis using CMS (upper left) and ATLAS (lower left) selection cuts, and directly compared to our expected exclusions using our simulated CMS $M_{C T ⊥}$ (upper right) and ATLAS $M_{T 2}$ (lower right) analyses.
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Figure 28
Expected exclusion limits (in units of $σ$ ) for charginos decaying to neutralinos and leptonic $W$ bosons using $20 {fb}^{- 1}$ of 8 TeV data, as a function of both selectron and neutralino masses. Expected limits are shown for our 1D $M_{Δ}^{R}$ analysis using CMS (upper left) and ATLAS (lower left) selection cuts, and directly compared to our expected exclusions using our simulated CMS $M_{C T ⊥}$ (upper right) and ATLAS $M_{T 2}$ (lower right) analyses.
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Figure 29
Expected exclusion limits (in units of $σ$ ) for left-handed selectrons decaying to leptons and neutralinos using $20 {fb}^{- 1}$ of 8 TeV data, as a function of neutralino mass with 300 GeV selectrons (left) or as a function of selectron mass with 100 GeV neutralinos (right). Expected limits are shown for our 1D $M_{Δ}^{R}$ analysis using CMS (blue) and ATLAS (green) selection cuts, and directly compared to our expected exclusions using our simulated CMS $M_{C T ⊥}$ (red) and ATLAS $M_{T 2}$ (orange) analyses.
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Figure 30
Expected exclusion limits (in units of $σ$ ) for left-handed selectrons (upper left), right-handed selectrons (upper right), and charginos decaying to neutralinos and leptonic $W$ bosons (bottom center) using $20 {fb}^{- 1}$ of 8 TeV data, as a function of both selectron/chargino and neutralino masses. Expected limits are derived using our multidimensional $M_{Δ}^{R}$ , $Δ ϕ_{R}^{β}$ and $| \cos θ_{R + 1} |$ analysis super-razor analyses with the razor selection cuts described in the previous section.
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Figure 31
Expected exclusion limits (in units of $σ$ ) for left-handed selectrons decaying to leptons and neutralinos using $20 {fb}^{- 1}$ of 8 TeV data, as a function of neutralino mass with 350 GeV selectrons (upper and lower left) or as a function of selectron mass with 150 GeV neutralinos (upper and lower right). Expected limits are shown for our multidimensional razor analysis (red), and compared to either ATLAS (upper plots) or CMS (lower plots) mass variables and selection criteria.
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Figure 32
Expected exclusion limits (in units of $σ$ ) for charginos decaying to neutralinos and leptonic $W$ bosons using $20 {fb}^{- 1}$ of 8 TeV data, as a function of neutralino mass with 250 GeV charginos (upper and lower left) or as a function of selectron mass with 100 GeV neutralinos (upper and lower right). Expected limits are shown for our multidimensional razor analysis (red), and compared to either ATLAS (upper plots) or CMS (lower plots) mass variables and selection criteria.
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