Tables 3,4,5,6 compare the event yields in the various Signal Regions with the event counts in the data. Figure 9 shows the BDT distributions after an MT cut and the MT distributions after a BDT cut for a loose and tight t ̃ → tχ ̃0 selection; Figure 10 is the same as Figure 9, but for t ̃ → bχ ̃± selections with x=0.5. Additional MT and BDT distributions can be found here

Table	Caption
	Table 3 : The result of the search for the t ̃ → tχ ̃0 BDT analysis. For each signal region the individual background contributions, total background, and observed yields are indicated. The uncertainty includes both the statistical and systematic components. The expected yields for two sample signal models are also indicated. The numbers in parentheses indicate the top squark and neutralino masses, respectively. The uncertainty is statistical.
	Table 4 : The result of the search for the t ̃ → tχ ̃0 cut-based analysis. For each signal region the individual background contributions, total background, and observed yields are indicated. The uncertainty includes both the statistical and systematic components. The expected yields for two sample signal models are also indicated. The numbers in parentheses indicate the top squark and neutralino masses, respectively. The uncertainty is statistical.
	Table 5 : The result of the search for the t ̃ → bχ ̃± BDT analysis. For each signal region the individual background contributions, total background, and observed yields are indicated. The uncertainty includes both the statistical and systematic components. The expected yields for two sample signal models are also indicated. The numbers in parentheses indicate the top squark mass, neutralino mass, and chargino mass parameter x, respectively. The uncertainty is statistical.
	Table 6 : The result of the search for the t ̃ → bχ ̃± cut-based analysis. For each signal region the individual background contributions, total background, and observed yields are indicated. The uncertainty includes both the statistical and systematic components. The expected yields for six sample signal models are also indicated. The numbers in parentheses indicate the top squark mass, neutralino mass, and chargino mass parameter x, respectively. The uncertainty is statistical.
Figure	Caption
	Figure 8a : Comparison of the MT distributions in data vs. MC for events satisfying the loosest t ̃ → tχ ̃0 BDT signal region requirements (BDT1 loose). The distribution for the t ̃ → tχ ̃0 model with m(t ̃) = 250 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding signal region requirement.
	Figure 8b : Comparison of the MT distributions in data vs. MC for events satisfying the tightest t ̃ → tχ ̃0 BDT signal region requirements (BDT4). The distribution for the t ̃ → tχ ̃0 model with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding signal region requirement. The bin to the right of the vertical line contains all events with MT > 120 GeV, and has been scaled by 1/3 to indicate the number of events per 60 GeV.
	Figure 8c : Comparison of the BDT1 output distributions in data vs. MC for t ̃ → tχ ̃0 after the MT>120 GeV requirement. The distribution for the t ̃ → tχ ̃0 model with m(t ̃) = 250 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding BDT1 loose signal region requirement.
	Figure 8d : Comparison of the BDT4 output distributions in data vs. MC for t ̃ → tχ ̃0 after the MT>120 GeV requirement is imposed. The distribution for the t ̃ → tχ ̃0 model with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding BDT4 signal region requirement.
	Figure 9a : Comparison of the MT distributions in data vs. MC for events satisfying the loosest t ̃ → bχ ̃± with x=0.5 BDT signal region requirements (BDT1). The distribution for the t ̃ → bχ ̃± model with x=0.5 and m(t ̃) = 250 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding signal region requirement.
	Figure 9b : Comparison of the MT distributions in data vs. MC for events satisfying the tightest t ̃ → bχ ̃± with x=0.5 BDT signal region requirements (BDT3). The distribution for the t ̃ → bχ ̃± model with x=0.5 and m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding signal region requirement.
	Figure 9c : Comparison of the BDT1 output distributions in data vs. MC for t ̃ → bχ ̃± with x=0.5 BDT after the MT>120 GeV. The distribution for the t ̃ → bχ ̃± model with x=0.5 and m(t ̃) = 250 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding BDT1 signal region requirement.
	Figure 9d : Comparison of the BDT3 output distributions in data vs. MC for t ̃ → bχ ̃± with x=0.5 BDT after the MT>120 GeV requirement. The distribution for the t ̃ → bχ ̃± model with x=0.5 and m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV is overlaid. The vertical dashed line indicates the corresponding BDT3 signal region requirement.

Figures 10 (a)-(d) show the limits in the m( t ̃) vs. m( χ ̃0) plane using the BDT method. These limits are obtained using models with unpolarized top quarks, charginos, and W-bosons in the final state. Figure 11 and Figure 23 show how the limits of Figure 10 would change under different polarization assumptions. Additional-Figure 11 gives the full BDT result for the stop --> top LSP decay mode in the case of decays into fully right handed top quarks (this more or less corresponds to the assumption in the Atlas analysis). Figure 20 (a)-(d) is the same as Figure 10 (a)-(d) but for the cut-based analysis. Figure 12 shows the limit as a function of the the t ̃ → tχ ̃0 mode.

Figure	Caption
	Figure 10a : Interpretations using the primary results from the BDT method for the t ̃ → tχ ̃0 model. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. . The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Additional Figure 11 : Interpretations using the primary results from the BDT method for the t ̃ → tχ ̃0 model for the case of right-handed decay top quarks. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 10b : Interpretations using the primary results from the BDT method for the t ̃ → bχ ̃± model with chargino mass parameter x=0.25. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 10c : Interpretations using the primary results from the BDT method for the t ̃ → bχ ̃± model with chargino mass parameter x=0.5. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 10d : Interpretations using the primary results from the BDT method for the t ̃ → bχ ̃± model with chargino mass parameter x=0.75. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 11a : Comparison of the observed excluded regions for the t ̃ → tχ ̃0 model for the case of unpolarized top quarks, right-handed top quarks, and left-handed top quarks. This information is available in electronic format here: root file (draw the contours with 'histogram->Draw("CONT3")').
	Figure 11b : Comparison of the observed excluded regions for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.5 for the nominal scenario, right-handed vs. left-handed charginos (χ ̃R and χ ̃L , respectively), and right-handed vs. left-handed Wχ ̃0χ ̃± couplings. This information is available in electronic format here: root file (draw the contours with 'histogram->Draw("CONT3")').
	Figure 23a : Comparison of the observed excluded regions for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.25 for the nominal scenario, right-handed vs. left-handed charginos (χ ̃R and χ ̃L , respectively), and right-handed vs. left-handed Wχ ̃0χ ̃± couplings. This information is available in electronic format here: root file (draw the contours with 'histogram->Draw("CONT3")').
	Figure 23b : Comparison of the observed excluded regions for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.75 for the nominal scenario, right-handed vs. left-handed charginos (χ ̃R and χ ̃L , respectively), and right-handed vs. left-handed Wχ ̃0χ ̃± couplings. This information is available in electronic format here: root file (draw the contours with 'histogram->Draw("CONT3")').
	Figure 20a : Interpretations using the results for the cut-based analysis for the t ̃ → tχ ̃0 model. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 20b : Interpretations using the results for the cut-based analysis for the t ̃ → bχ ̃± model with chargino mass parameter x=0.25. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 20c : Interpretations using the results for the cut-based analysis for the t ̃ → bχ ̃± model with chargino mass parameter x=0.5. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 20d : Interpretations using the results for the cut-based analysis for the t ̃ → bχ ̃± model with chargino mass parameter x=0.75. The color scale indicates the observed cross section upper limit. The observed, median expected, and ±1 standard deviation (σ) expected exclusion contours are indicated. The cross section limits are available in electronic format here: root file. The limits and exclusion contours can be drawn with this C file.
	Figure 12 : Observed excluded region as a function of the assumed branching fraction of the the t ̃ → tχ ̃0 mode assuming that the analysis has no acceptance to top squark pairs production when at least on of the stop quarks decay in a different mode.

Figures 2(a-i) demonstrate that the kinematical quantities are well reproduced by the Monte Carlo at the preselection level. We also include a diagram to help explain the MT2W variable (but see the MT2W paper for more information).

Figure	Caption
	Figure 2a : Data vs. MC simulation comparison of the MT after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2b : Data vs. MC simulation comparison of the Etmiss after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2c : Data vs. MC simulation comparison of the MT2W after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2d : Data vs. MC simulation comparison of the hadronic top χ2 after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2e : Data vs. MC simulation comparison of the HTratio after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2f : Data vs. MC simulation comparison of the minimum difference in azimuthal angle between the ETmiss and the two leading jets after event pre-selection. The distribution for the t ̃ → tχ ̃0 decay mode with m(t ̃) = 650 GeV and m(χ ̃0) = 50 GeV, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2g : Data vs. MC simulation comparison of the leading b-jet pT after event pre-selection. The distributions for the t ̃ → bχ ̃± decay mode with m(t ̃) = 650 GeV, m(χ ̃0) = 50 GeV and intermediate chargino mass parameter x=0.5, scaled by a factor of 1000, and the t ̃ → tχ ̃0 decay mode with m(t ̃) = 250 GeV and m(χ ̃0) = 100 GeV, scaled by a factor of 10, are overlaid. The last bin contains the overflow.
	Figure 2h : Data vs. MC simulation comparison of the separation in R between the lepton and the leading b-jet after event pre-selection. The distribution for the t ̃ → bχ ̃± decay mode with m(t ̃) = 650 GeV, m(χ ̃0) = 50 GeV and intermediate chargino mass parameter x=0.5, scaled by a factor of 1000, are overlaid. The last bin contains the overflow.
	Figure 2i : Data vs. MC simulation comparison of the lepton transverse momentum after event pre-selection. The distribution for the t ̃ → bχ ̃± decay mode with m(t ̃) = 250 GeV, m(χ ̃0) = 150 GeV and intermediate chargino mass parameter x=0.5, scaled by a factor of 10, are overlaid. The last bin contains the overflow.
	Additional figure : Schematic of MT2W for a dilepton tt event. Here p2 is the four-momentum of the entire missing on-shell W and p1 is the four-momentum of the neutrino that gets paired with the visible lepton to form the other on-shell W. The dashed lines represent unseen particles, the solid lines indicate reconstructed particles, and the dotted line surround the lepton-neutrino pairs that are constrained to have a mass equal to that of the W boson.

Table 1 summarizes the requirements that define the cut-and-count signal regions. A number of BDTs were optimized to target different scenarios of SUSY particle masses and top squark decay modes. Figure 3(a)-(d) show the regions in the plane of top squark mass vs. LSP mass (for different decay modes) corresponding to each BDT.

Table	Caption
	Table 1 : Summary of the variables used as inputs for the BDTs and of the kinematic requirements in the cut-based analysis. All signal regions are defined with MT > 120 GeV. For the t ̃ → tχ ̃0 BDT trained in region 5 where the top quark is off-shell, the hadronic top χ2 is not included and the leading b-jet pT is included.
Figure	Caption
	Figure 3a : The regions used to train the BDTs, in the m(χ ̃0) vs. m(t ̃) parameter space for the t ̃ → tχ ̃0 decay mode.
	Figure 3b : The regions used to train the BDTs, in the m(χ ̃0) vs. m(t ̃) parameter space for the t ̃ → bχ ̃± decay mode with x=0.25.
	Figure 3c : The regions used to train the BDTs, in the m(χ ̃0) vs. m(t ̃) parameter space for the t ̃ → bχ ̃± decay mode with x=0.5.
	Figure 3d : The regions used to train the BDTs, in the m(χ ̃0) vs. m(t ̃) parameter space for the t ̃ → bχ ̃± decay mode with x=0.75.

Figure 5 demonstrates that the jet multiplicity in ttbar dilepton events is well understood. Figure 6(a)-(f) shows sample MT and BDT distributions for the dilepton control sample (CR-2l), the lepton+track control sample (CR-lt), and the Wjets control sample (CR-0b). The MT distributions are shown after the after applying the signal-like requirement on the BDT (indicated by the dashed line in the BDT distribution for the corresponding control sample). Figure 7 shows the transverse mass distribution for a sample enriched in Wjets events.

Figure	Caption
	Figure 5 : Comparison of the jet multiplicity distributions in data and MC simulation for the sample dominated by dilepton tt events.
	Figure 6a : Data vs. MC simulation comparison in the control region CR-2l of the BDT output distribution for the t ̃ → tχ ̃0 model in training region 1. The last bin contains the overflow.
	Figure 6b : Data vs. MC simulation comparison in the control region CR-2l of the MT distribution after the signal-like requirement on the BDT output (indicated by the dashed line in Fig. 6a) for the t ̃ → tχ ̃0 model in training region 1. The last bin contains the overflow.
	Figure 6c : Data vs. MC simulation comparison in the control region CR-lt of the BDT output distribution for the t ̃ → tχ ̃0 model in training region 1. The last bin contains the overflow.
	Figure 6d : Data vs. MC simulation comparison in the control region CR-lt of the MT distribution after the signal-like requirement on the BDT output (indicated by the dashed line in Fig. 6c) for the t ̃ → tχ ̃0 model in training region 1. The last bin contains the overflow.
	Figure 6e : Data vs. MC simulation comparison in the control region CR-0b of the BDT output distribution for the t ̃ → tχ ̃0 model in training region 1. The last bin contains the overflow.
	Figure 6f : Data vs. MC simulation comparison in the control region CR-0b of the MT distribution after the signal-like requirement on the BDT output (indicated by the dashed line in Fig. 6e) for the t ̃ → tχ ̃0 model in training region 1. The scale factor on the W+jets component is applied to the MC in the MT tail. The last bin contains the overflow.
	Figure 7 : MT distributions for CR-0b events after the pre-selection requirements only. The MT tail in the MC needs to be rescaled by a factor of ~ 1.2 to agree with the data.

Table 2,7,8, and 9 show the breakdown of the systematic uncertainties for the BDT (Tables 2 and 8) and cut-and-count (Tables 7 and 9) background predictions.

Table	Caption
	Table 2 : Breakdown of the sources of uncertainty as well as the total relative uncertainty (in percent), shown on the bottom row, on the total background predictions for the t ̃ → tχ ̃0 BDT signal regions.
	Table 7 : Breakdown of the sources of uncertainty as well as the total relative uncertainty (in percent), shown on the bottom row, on the total background predictions for the t ̃ → tχ ̃0 cut-based signal regions.
	Table 8 : Breakdown of the sources of uncertainty as well as the total relative uncertainty (in percent), shown on the bottom row, on the total background predictions for the t ̃ → bχ ̃± BDT signal regions.
	Table 9 : Breakdown of the sources of uncertainty as well as the total relative uncertainty (in percent), shown on the bottom row, on the total background predictions for the t ̃ → bχ ̃± cut-based signal regions.

Here we show the full set of MT and BDT distributions to complete those that were shown in the "Results" section above.

Figure	Caption
	Figure 13a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT1 tight t ̃ → tχ ̃0 signal region requirements. The vertical dashed line indicates the MT corresponding signal region requirement.
	Figure 13b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT2 t ̃ → tχ ̃0 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 13c : Comparison of the BDT1 output distributions in data vs. MC simulation for t ̃ → tχ ̃0 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT1 tight signal region requirement.
	Figure 13d : Comparison of the BDT2 output distributions in data vs. MC simulation for t ̃ → tχ ̃0 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT2 signal region requirement.
	Figure 14a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT3 t ̃ → tχ ̃0 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 14b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT5 t ̃ → tχ ̃0 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 14c : Comparison of the BDT3 output distributions in data vs. MC simulation for t ̃ → tχ ̃0 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT3 signal region requirement.
	Figure 14d : Comparison of the BDT5 output distributions in data vs. MC simulation for t ̃ → tχ ̃0 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT5 signal region requirement.
	Figure 15a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT1 t ̃ → bχ ̃± x=0.25 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 15b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT2 t ̃ → bχ ̃± x=0.25 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 15c : Comparison of the BDT1 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.25 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT1 signal region requirement.
	Figure 15d : Comparison of the BDT2 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.25 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT2 signal region requirement.
	Figure 16a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT3 loose t ̃ → bχ ̃± x=0.25 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 16b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT2 loose t ̃ → bχ ̃± x=0.5 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 16c : Comparison of the BDT3 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.25 after the MT > 120 GeV requirement is imposed. The vertical dashed line indicates the corresponding BDT3 signal region requirement.
	Figure 16d : Comparison of the BDT2 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.5 after the MT > 120 GeV requirement is imposed. The vertical dashed line indicates the corresponding BDT2 loose signal region requirement.
	Figure 17a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT2 tight t ̃ → bχ ̃± x=0.5 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 17b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT4 t ̃ → bχ ̃± x=0.5 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 17c : Comparison of the BDT2 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.5 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT2 tight signal region requirement.
	Figure 17d : Comparison of the BDT4 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.5 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT4 signal region requirement.
	Figure 18a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT1 t ̃ → bχ ̃± x=0.75 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 18b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT2 t ̃ → bχ ̃± x=0.75 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 18c : Comparison of the BDT1 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.75 BDT after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT1 signal region requirement.
	Figure 18d : Comparison of the BDT2 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.75 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT2 signal region requirement.
	Figure 19a : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT3 t ̃ → bχ ̃± x=0.75 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 19b : Comparison of the MT distributions in data vs. MC simulation for events satisfying the BDT4 t ̃ → bχ ̃± x=0.75 signal region requirements. The vertical dashed line indicates the corresponding MT signal region requirement.
	Figure 19c : Comparison of the BDT3 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.75 after the MT > 120 GeV requirement. The vertical dashed line indicates the corresponding BDT3 signal region requirement.
	Figure 19d : Comparison of the BDT4 output distributions in data vs. MC simulation for t ̃ → bχ ̃± x=0.75 after the MT > 120 GeV requirement is imposed. The vertical dashed line indicates the corresponding BDT4 signal region requirement.

The modeling of initial state radiation is important for the understanding of the signal acceptance when the LSP is produced in a SUSY decay with small Q-value. Figure 24 and 25 show how well initial state radiation is modeled in the CMS Monte Carlo.

Figure	Caption
	Figure 24a : Comparison of data to MC predictions for the dilepton pT in dilepton Z+jets events. The MC prediction is normalized to the total data yield to compare the shapes of the distributions. The ratio of data/MC is shown at the top of the figure, and the light blue band shows the weights derived for simulation and the variation to assess systematic uncertainties.
	Figure 24b : Comparison of data to MC predictions for the jet recoil system pT in dilepton Z+jets events, where the "jet recoil system" is taken as the vector sum of all jets in the event. The MC prediction is normalized to the total data yield to compare the shapes of the distributions. The ratio of data/MC is shown at the top of the figure, and the light blue band shows the weights derived for simulation and the variation to assess systematic uncertainties.
	Figure 25 : Comparison of data to MC prediction for the jet recoil system pT in dilepton ttbar events, where the "jet recoil system" is taken as the vector sum of all jets in the event which are not b-tagged. The MC prediction is normalized to the total data yield to compare the shapes of the distributions. The ratio of data/MC is shown at the top of the figure, and the light blue band shows the weights derived for MC and the variation to assess systematic uncertainties.

Here we show maps of "best a-priori signal region" as a function of decay model and SUSY parameters for both the BDT and cut-and-count searches. At any point in SUSY parameter space the cross-section limits are extracted using the results from the "best a-priori signal region", ie, the signal region with the most stringent expected cross-section limit.

	Figure 21a : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the BDT t ̃ → tχ ̃0 analysis. The number indicates the BDT training region.
	Figure 21b : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the BDT t ̃ → bχ ̃± analysis with chargino mass parameter x=0.25. The number indicates the BDT training region.
	Figure 21c : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the BDT t ̃ → bχ ̃± analysis with chargino mass parameter x=0.5. The number indicates the BDT training region.
	Figure 21d : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the BDT t ̃ → bχ ̃± analysis with chargino mass parameter x=0.75. The number indicates the BDT training region.
	Figure 22a : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the cut-based t ̃ → tχ ̃0 analysis. LM and HM refer to low ∆M and high ∆M, respectively, and the number indicates the ETmiss requirement.
	Figure 22b : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the cut-based t ̃ → bχ ̃± analysis with chargino mass parameter x=0.25. LM and HM refer to low ∆M and high ∆M, respectively, and the number indicates the ETmiss requirement.
	Figure 22c : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the cut-based t ̃ → bχ ̃± analysis with chargino mass parameter x=0.5. LM and HM refer to low ∆M and high ∆M, respectively, and the number indicates the ETmiss requirement.
	Figure 22d : The most sensitive signal region in the m(χ ̃0) vs. m(t ̃) parameter space in the cut-based t ̃ → bχ ̃± analysis with chargino mass parameter x=0.75. LM and HM refer to low ∆M and high ∆M, respectively, and the number indicates the ETmiss requirement.

Additional Figures 1->4 further demonstrate the level of understanding of initial state radiation. Additional Figure 5 show how the acceptance to the MT cut evolves in the compressed region of the SUSY spectrum. Additional Figure 6 can be used to help understand what is going on in Additional Figure 5. The improvement in sensitivity in the BDT analysis with respect to the cut-and-count analysis can be seen in Additional Figures 7->10. The remaining Additional Figures (12 -> 17) illustrate the signal vs. background separation of the kinematical variables used in the BDT.

Figure	Caption
	Additional Figure 1 : Comparison of data to MC predictions for the number of jets in dilepton Z+jets events. The MC prediction is normalized to the total data yield to compare the shapes of the distributions.
	Additional Figure 2 : Comparison of data to MC predictions for the number of jets in addition to the two b-tagged jets from the top quark decay in dilepton ttbar events. The MC prediction is normalized to the total data yield to compare the shapes of the distributions.
	Additional Figure 3 : Comparison of data to MC predictions for the jet recoil system pT in trilepton WZ+jets events, where the "jet recoil system" is taken as the vector sum of all jets in the event. The MC prediction is normalized to the total data yield to compare the shapes of the distributions. The ratio of data/MC is shown at the top of the figure, and the light blue band shows the weights derived for simulation and the variation to assess systematic uncertainties.
	Additional Figure 4 : Comparison of data to MC predictions for the number of jets in trilepton WZ+jets events. The MC prediction is normalized to the total data yield to compare the shapes of the distributions.
	Additional Figure 5 : Comparison of the MT distributions for the SM background and the 3 signal points with the same top squark mass 250 GeV and different neutralino mass, 50, 75 and 100 GeV.
	Additional Figure 6 : Comparison of the generator-level momentum of the χ ̃0 in the decay t ̃ → tχ ̃0, in the top squark rest frame, for 3 signal points with the same top squark mass 250 GeV and different neutralino mass, 50, 75 and 100 GeV.
	Additional Figure 7 : Comparison of the expected limits from the BDT and cut-based analyses for the t ̃ → tχ ̃0 model. The colors and numbers represent the ratio of the expected cross section limits, BDT divided by cut-based. The expected exclusion contours from the two approaches are also indicated.
	Additional Figure 8 : Comparison of the expected limits from the BDT and cut-based analyses for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.75. The colors and numbers represent the ratio of the expected cross section limits, BDT divided by cut-based. The expected exclusion contours from the two approaches are also indicated.
	Additional Figure 9 : Comparison of the expected limits from the BDT and cut-based analyses for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.5. The colors and numbers represent the ratio of the expected cross section limits, BDT divided by cut-based. The expected exclusion contours from the two approaches are also indicated.
	Additional Figure 10 : Comparison of the expected limits from the BDT and cut-based analyses for the t ̃ → bχ ̃± model with chargino mass parameter x = 0.25. The colors and numbers represent the ratio of the expected cross section limits, BDT divided by cut-based. The expected exclusion contours from the two approaches are also indicated.
	Additional Figure 12 : Comparison of the signal vs. background distributions of the MT2W quantity. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 13 : Comparison of the signal vs. background distributions of the leading b-tagged jet pT. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 14 : Comparison of the signal vs. background distributions of the hadronic top chi^2. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 15 : Comparison of the signal vs. background distributions of the opening angle between the lepton and leading b-tagged jet. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 16 : Comparison of the signal vs. background distributions of the HTratio, the fraction of the event HT in the same hemisphere as the ETmiss. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 17 : Comparison of the signal vs. background distributions of the minimum delta(phi) between either of the 2 leading jets and ETmiss. The event pre-selection requirements and the MT > 120 GeV requirement are applied.
	Additional Figure 18a : Comparison of the lepton transverse momentum for unpolarized top quarks (black), left-handed top quarks (red), and right-handed top quarks (blue), for the t ̃(450) → tχ ̃0(25) signal model.
	Additional Figure 18b : Comparison of the transverse mass for unpolarized top quarks (black), left-handed top quarks (red), and right-handed top quarks (blue), for the t ̃(450) → tχ ̃0(25) signal model.
	Additional Figure : Event display for a signal candidate event in data.
	Additional Figure : Event display for a signal candidate event in data.

Here is code to calculate the hadronic top chisquared and the MT2W variable used in the analysis. This code is also included in a bigger tarfile described below under "Electronic Material".

The attached tgz file contain the observed cross section limits and the observed and expected exclusion contours as root histograms. For each root file there is a corresponding C file which can be used to draw the limits and contours. It also contains the code for calculating the hadronic top chisquared and MT2W variables, as well as rrot files with the acceptance maps for the cut-based analysis.