Searches for electroweak production of supersymmetric particles with compressed mass spectra in $\sqrt{s}=13\mathrm{TeV}$ $pp$ collisions with the ATLAS detector

This paper presents results of searches for the electroweak production of supersymmetric particles in models with compressed mass spectra. The searches use $139{\mathrm{fb}}^{-1}$ of $\sqrt{s}=13\mathrm{TeV}$ proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider. Events with missing transverse momentum and two same-flavor, oppositely charged, low-transverse-momentum leptons are selected, and are further categorized by the presence of hadronic activity from initial-state radiation or a topology compatible with vector-boson fusion processes. The data are found to be consistent with predictions from the Standard Model. The results are interpreted using simplified models of $R$-parity-conserving supersymmetry in which the lightest supersymmetric partner is a neutralino with a mass similar to the lightest chargino, the second-to-lightest neutralino, or the slepton. Lower limits on the masses of charginos in different simplified models range from 193 to 240 GeV for moderate mass splittings, and extend down to mass splittings of 1.5 to 2.4 GeV at the LEP chargino bounds (92.4 GeV). Similar lower limits on degenerate light-flavor sleptons extend up to masses of 251 GeV and down to mass splittings of 550 MeV. Constraints on vector-boson fusion production of electroweak SUSY states are also presented.

Figure 1

Diagrams representing the two-lepton final state of (a) the production of electroweakinos ${\tilde{\chi }}_2^0{\tilde{\chi }}_1^{\pm }$ with initial-state radiation ($j$), (b) the VBF production of electroweakinos ${\tilde{\chi }}_2^0{\tilde{\chi }}_1^{\pm }$, and (c) slepton pair ($\tilde{\ell }\tilde{\ell }$) production in association with initial-state radiation ($j$). The Higgsino simplified model also considers ${\tilde{\chi }}_2^0$${\tilde{\chi }}_1^0$ and ${\tilde{\chi }}_1^{+}$${\tilde{\chi }}_1^{-}$ production.

Figure 2

Dilepton invariant mass for Higgsino and wino/bino simplified models. The end point of the distribution is determined by the difference between the masses of the ${\tilde{\chi }}_2^0$ and ${\tilde{\chi }}_1^0$. The results from simulation (histograms) are compared with analytic calculations of the expected line shape (dashed lines) presented in Ref. [60]. The product of the signed mass eigenvalues $(m({\tilde{\chi }}_2^0)\times m({\tilde{\chi }}_1^0))$ is negative for the Higgsino model and can be either negative or positive for wino/bino scenarios.

Figure 3

Signal lepton efficiencies for electrons, muons, and isolated tracks in a mix of slepton and Higgsino samples. Combined reconstruction, identification, isolation, and vertex association efficiencies are shown for leptons within detector acceptance, and with lepton $p_{\mathrm{T}}$ within a factor of 3 of $\mathrm{\Delta }m(\tilde{\ell },{\tilde{\chi }}_1^0)$ for sleptons or of $\mathrm{\Delta }m({\tilde{\chi }}_2^0,{\tilde{\chi }}_1^0)/2$ for Higgsinos. The efficiencies for isolated tracks include track reconstruction and vertex association efficiencies [112], as well as the efficiencies for track–lepton matching and track isolation, which are specific to this search. Scale factors are applied to match reconstruction efficiencies in data. The average number of interactions per crossing in the MC samples is 33.7; the number of pileup interactions match the distribution in data in spread and mean value. Uncertainty bands represent the range of efficiencies observed across all signal samples used for the given $p_{\mathrm{T}}$ bin.

Figure 4

Distributions of $R_{\mathrm{ISR}}$, the ratio of the $E_{\mathrm{T}}^{\mathrm{miss}}$ to the transverse momentum of the hadronic ISR activity, for the electroweakino (left) and slepton (right) high-$E_{\mathrm{T}}^{\mathrm{miss}}$ SRs. Distributions are shown after applying all signal selection criteria except those on $R_{\mathrm{ISR}}$. The solid red line indicates the requirement applied in the signal region; events in the region below the red line are rejected. Representative benchmark signals for the Higgsino (left) and slepton (right) simplified models are shown as circles. The gray rectangular boxes show the distribution of the total background prediction, which is primarily composed of top-like processes, diboson processes, and events with fake/nonprompt leptons. Regions at larger $m_{\ell \ell }$ and $m_{\mathrm{T}2}$ are not populated by the representative signals shown here, but are useful probes of less-compressed signal models.

Figure 5

The relative systematic uncertainties in the fitted SM background as obtained from $\mathrm{CR}+\mathrm{SR}$ background-only fits for the electroweakino SRs (top), VBF SRs (middle), and slepton SRs (bottom). The uncertainty in the “SS data” includes a statistical component due to the size of the SS data sample used to estimate the background in the SR-E-$1\ell 1T$ region, and a systematic component from the SS–OS extrapolation. The “MC Statistics” uncertainty originates from the limited size of the MC samples used to model the irreducible background contributions. The “Normalization” uncertainty arises from the use of CRs to normalize the contributions of $t\overline{t}/tW$, $Z^{(*)}/{\gamma }^{*}(\to \tau \tau )+\text{jets}$ and $WW/WZ$ backgrounds, while “Background modeling” includes the different sources of theoretical modeling uncertainties in the $m_{\ell \ell }$ or $m_{\mathrm{T}2}^{100}$ line shapes for the irreducible backgrounds. All sources of uncertainty affecting the FNP background estimate are included under “Fake/nonprompt.” The uncertainties arising from the reconstruction and selection of signal leptons, jets, and $E_{\mathrm{T}}^{\mathrm{miss}}$ are included under the “Experimental” category. The individual uncertainties can be correlated and do not necessarily add up in quadrature to the total uncertainty.

Figure 6

Comparison of observed and expected event yields in the VRDF regions after a background-only fit of the CRs. The three VRDF-E regions are shown at the top, binned in $m_{\ell \ell }$ as the corresponding electroweakino SRs. The two VRDF-VBF regions are shown in the middle, also binned in $m_{\ell \ell }$. The bin $1\mathrm{GeV}<m_{\ell \ell }<2\mathrm{GeV}$ is omitted from the VRDF-VBF-high region because both the expected and observed event yields are zero. Finally, the two VRDF-S regions are shown at the bottom, binned in $m_{\mathrm{T}2}^{100}$ as the corresponding slepton SRs. Uncertainties in the background estimates include both the statistical and systematic uncertainties. The bottom panel in all three plots shows the significance of the difference between the expected and observed yields, computed following the profile likelihood method of Ref. [118] in the case where the observed yield exceeds the prediction, and using the same expression with an overall minus sign if the yield is below the prediction.

Figure 7

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the control regions CRVV-E-high (top left), CRVV-S-low (top right), CRtau-E-low (middle left), CRtau-VBF (middle right), CRtop-S-low (bottom left), and CRtop-VBF (bottom right). The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows in the distributions instead. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 8

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the validation regions VRtau-E-med (top left), VRDF-E-high (top right), VRDF-VBF, including both VRDF-VBF-high and VRDF-VBF-low (bottom left) and VRDF-S-low (bottom right). The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows in the distributions instead. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 9

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the validation regions VRSS-E-med (top), VRSS-E-high (middle), VRSS-VBF (bottom left), and VR-$1\ell 1T$ (bottom right). The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows in the distributions instead. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 10

Comparison of observed and expected event yields in the SRs after the $\mathrm{CR}+\mathrm{SR}$ background-only fits. The SRs used in searches for electroweakinos recoiling against ISR are shown at the top, and the SRs used for the VBF electroweakino search are shown in the middle, all binned in $m_{\ell \ell }$. The SRs used in searches for sleptons recoiling against ISR are shown at the bottom, binned in $m_{\mathrm{T}2}^{100}$. Uncertainties in the background estimates include both the statistical and systematic uncertainties. The bottom panel in all three plots shows the significance of the difference between the expected and observed yields, computed following the profile likelihood method of Ref. [118] in the case where the observed yield exceeds the prediction, and using the same expression with an overall minus sign if the yield is below the prediction.

Figure 11

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the signal regions sensitive to electroweakinos. The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows in the distributions instead. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 12

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the signal regions sensitive to electroweakinos produced through VBF. The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows instead in the distributions. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 13

Examples of kinematic distributions after the background-only fit of the CRs showing the data as well as the expected background in the signal regions sensitive to sleptons. The full event selection of the corresponding regions is applied, except for distributions showing blue arrows, where the requirement on the variable being plotted is removed and indicated by the arrows instead in the distributions. The first (last) bin includes underflow (overflow). The uncertainty bands plotted include all statistical and systematic uncertainties.

Figure 14

Expected 95% C.L. exclusion sensitivity (blue dashed line), with $\pm 1{\sigma }_{\exp }$ (yellow band) from experimental systematic uncertainties and statistical uncertainties on the data yields, and observed limits (red solid line) with $\pm 1{\sigma }_{\text{theory}}$ (dotted red line) from signal cross-section uncertainties for simplified models of direct Higgsino (top) and wino (bottom) production. A fit of signals to the $m_{\ell \ell }$ spectrum is used to derive the limit, which is projected into the $\mathrm{\Delta }m({\tilde{\chi }}_2^0,{\tilde{\chi }}_1^0)$ vs $m({\tilde{\chi }}_2^0)$ plane. For Higgsino production, the chargino ${\tilde{\chi }}_1^{\pm }$ mass is assumed to be halfway between the ${\tilde{\chi }}_2^0$ and ${\tilde{\chi }}_1^0$ masses, while $m({\tilde{\chi }}_2^0)=m({\tilde{\chi }}_1^{\pm })$ is assumed for the wino/bino model. Following the discussion in Sec. 3, the $m_{\ell \ell }$ shape in the wino/bino model depends on the relative sign of the ${\tilde{\chi }}_1^0$ and ${\tilde{\chi }}_2^0$ mass parameters. The bottom-left plot assumes $m({\tilde{\chi }}_1^0)\times m({\tilde{\chi }}_2^0)<0$, while $m({\tilde{\chi }}_1^0)\times m({\tilde{\chi }}_2^0)>0$ is assumed on the bottom right. The gray regions denote the lower chargino mass limit from LEP [30]. The blue regions indicate the limits from ATLAS searches at 8 TeV [125, 126] and at 13 TeV with $36{\mathrm{fb}}^{-1}$ [45].

Figure 15

Expected 95% C.L. exclusion sensitivity (blue dashed line) and observed limits (red solid line) for simplified models of Higgsino (left) and wino (right) production through VBF. A fit of signals to the $m_{\ell \ell }$ spectrum in the VBF signal regions is used to derive the limit. On the left, the limit for Higgsinos is shown as a function of $m({\tilde{\chi }}_2^0)$ for a mass splitting of $\mathrm{\Delta }m({\tilde{\chi }}_2^0,{\tilde{\chi }}_1^0)=5\mathrm{GeV}$ (the chargino ${\tilde{\chi }}_1^{\pm }$ mass is assumed to be halfway between the ${\tilde{\chi }}_2^0$ and ${\tilde{\chi }}_1^0$ masses). The yellow band indicates $\pm 1{\sigma }_{\exp }$ from experimental systematic uncertainties and statistical uncertainties on the data yields. On the right, the limit for winos is projected into the $\mathrm{\Delta }m({\tilde{\chi }}_2^0,{\tilde{\chi }}_1^0)$ vs $m({\tilde{\chi }}_2^0)$ plane [$m({\tilde{\chi }}_2^0)=m({\tilde{\chi }}_1^{\pm })$ is assumed for the wino/bino model]. The red dotted line indicates the $\pm 1{\sigma }_{\text{theory}}$ from signal cross-section uncertainties, and the colored map illustrates the 95% C.L. upper limits on the cross section. The cross section corresponds to the leading-order prediction from mg5_amc@nlo for the process $pp\to {\tilde{\chi }}_2^0{\tilde{\chi }}_1^{\pm }jj$ including the parton-level requirements described in Sec. 3. The contour lines represent steps of 0.2 pb.

Figure 16

Expected 95% C.L. sensitivity (dashed lines) and observed limits (solid lines) for simplified models of direct slepton production. A fit of slepton signals to the $m_{\mathrm{T}2}^{100}$ spectrum is used to derive the limits, which are projected into the $\mathrm{\Delta }m(\tilde{\ell },{\tilde{\chi }}_1^0)$ vs $m(\tilde{\ell })$ plane. Slepton $\tilde{\ell }$ refers to the scalar partners of left- and right-handed electrons and muons. The gray region is the ${\tilde{e}}_R$ limit from LEP [30]. On the left, the sleptons are assumed to be fourfold mass degenerate with $m({\tilde{e}}_L)=m({\tilde{e}}_R)=m({\tilde{\mu }}_L)=m({\tilde{\mu }}_R)$; the expected sensitivity (blue dashed line) is shown with $\pm 1{\sigma }_{\exp }$ (yellow band) from experimental systematic uncertainties and statistical uncertainties on the data yields; the observed limit (red solid line) is shown with $\pm 1{\sigma }_{\text{theory}}$ (dotted red line) from signal cross-section uncertainties, and the blue regions are the fourfold mass-degenerate slepton limits from ATLAS Run 1 [125] and Run 2 [45]. On the right, no degeneracy is assumed for the masses of the sleptons, and the limits are presented separately for ${\tilde{e}}_L$, ${\tilde{e}}_R$, ${\tilde{\mu }}_L$, and ${\tilde{\mu }}_R$.