Search for supersymmetry with razor variables in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$

The razor approach to search for $R$–parity conserving supersymmetric particles is described in detail. Two analyses are considered: an inclusive search for new heavy particle pairs decaying to final states with at least two jets and missing transverse energy, and a dedicated search for final states with at least one jet originating from a bottom quark. For both the inclusive study and the study requiring a bottom-quark jet, the data are examined in exclusive final states corresponding to all-hadronic, single-lepton, and dilepton events. The study is based on the data set of proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ collected with the CMS detector at the LHC in 2011, corresponding to an integrated luminosity of $4.7{\mathrm{fb}}^{-1}$. The study consists of a shape analysis performed in the plane of two kinematic variables, denoted $M_R$ and $R^2$, that correspond to the mass and transverse energy flow, respectively, of pair-produced, heavy, new-physics particles. The data are found to be compatible with the background model, defined by studying event simulations and data control samples. Exclusion limits for squark and gluino production are derived in the context of the constrained minimal supersymmetric standard model (CMSSM) and also for simplified-model spectra (SMS). Within the CMSSM parameter space considered, squark and gluino masses up to 1350 GeV are excluded at 95% confidence level, depending on the model parameters. For SMS scenarios, the direct production of pairs of top or bottom squarks is excluded for masses as high as 400 GeV.

Figure 1

Razor variables $R^2$ versus $M_R$ for simulated events: (a) QCD multijet, (b) $W(\ell \nu )+\text{jets}$ and $Z(\nu \overline{\nu })+\text{jets}$, (c) $t\overline{t}$, and (d) SUSY benchmark model LM6 [38], where the new-physics mass scale for LM6 is $M_{\mathrm{\Delta }}=831\mathrm{GeV}$. The yields are normalized to an integrated luminosity of $\sim 4.7{\mathrm{fb}}^{-1}$ except for the QCD multijet sample, where we use the luminosity of the generated sample. The bin size is 0.005 for $R^2$ and 20 GeV for $M_R$.

Figure 2

(a) The squark-antisquark production diagram for the T2 SUSY SMS reference model. The distribution of (b) $M_R$ and (c) $R^2$ for different LSP masses $m_{\tilde{\chi }}$ in the T2 scenario. (d) Distribution of T2 events in the ($M_R$, $R^2$) plane for the different LSP masses $m_{\tilde{\chi }}$. The orange bands represent contours of constant SM background. The relative suppression factors corresponding to some of the bands are indicated in the upper part of the figure.

Figure 3

(a) The $M_R$ distribution for different values of $R_{\min }^2$ for events in the HAD box of a multijet control sample, fit to an exponential function. (b) The coefficient in the exponent $S$ from fits to the $M_R$ distributions, as a function of $R_{\min }^2$.

Figure 4

(a) The $R^2$ distributions for different values of $M_R^{\min }$ for events in data selected in the HAD box of a multijet control sample, fit to an exponential function. (b) The coefficient in the exponent $S^{\prime }$ from fits to the $R^2$ distributions, as a function of $M_R^{\min }$.

Figure 5

The $M_R$ distribution for different values of $R_{\min }^2$ for events in the MU box, with the requirement of zero $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 6

Value of (a) the coefficient in the first exponent, $S_1$, and (b) the coefficient in the second exponent, $S_2$, from fits to the $M_R$ distribution, as a function of $R_{\min }^2$, for events in the MU box, with the requirement of zero $b$-tagged jets.

Figure 7

The $M_R$ distributions for different values of $R_{\min }^2$ for $W+\text{jets}$ simulated events in the MU box with the requirement of zero $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 8

Value of (a) the coefficient in the first exponent, $S_1$, and (b) the coefficient in the second exponent, $S_2$, from fits to the $M_R$ distribution, as a function of $R_{\min }^2$, for simulated $W+\text{jets}$ events in the MU box with the requirement of zero $b$-tagged jets.

Figure 9

The $R^2$ distributions for different values of $M_R^{\min }$ for events in the MU box, with the requirement of zero $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 10

Value of (a) the coefficient in the first exponent, $S_1^{\prime }$, and (b) the coefficient in the second exponent, $S_2^{\prime }$, from fits to the $R^2$ distribution, as a function of $M_R^{\min }$, for events in the MU box, with the requirement of zero $b$-tagged jets.

Figure 11

The $R^2$ distributions for different values of $M_R^{\min }$ for $W+\text{jets}$ simulated events in the MU box with the requirement of zero $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 12

Value of (a) the coefficient in the first exponent, $S_1^{\prime }$, and (b) the coefficient in the second exponent, $S_2^{\prime }$, from fits to the $R^2$ distribution, as a function of $M_R^{\min }$, for $W+\text{jets}$ simulated events in the MU box with the requirement of zero $b$-tagged jets.

Figure 13

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the HAD box in $t\overline{t}$ MC simulation. The continuous histogram is the 2D model prediction obtained from a single pseudo-experiment based on the 2D fit. The fit is performed in the ($M_R$, $R^2$) fit region and projected into the full analysis region. Only the statistical uncertainty band in the background prediction is drawn in these projections. The points show the distribution for the MC simulated events.

Figure 14

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the inclusive HAD box. The continuous histogram is the total SM prediction. The dash-dotted and dashed histograms are described in the text. The fit is performed in the ($M_R$, $R^2$) fit region (shown in Fig. 15) and projected into the full analysis region. The full uncertainty in the total background prediction is drawn in these projections, including the one due to the variation of the background shape parameters and normalization.

Figure 15

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the HAD box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$, computed from background parametrization derived in the FR. The $p$-values are also given in the table, together with the observed number of events, the median and the mode of the yield distribution, and a 68% C.L. interval.

Figure 16

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the inclusive ELE box. The fit is performed in the ($M_R$, $R^2$) fit region (shown in Fig. 17) and projected into the full analysis region. The histograms are described in the text.

Figure 17

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the ELE box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$. Further explanation is given in the Fig. 15 caption.

Figure 18

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the inclusive MU box. The fit is performed in the ($M_R$, $R^2$) fit region (shown in Fig. 19) and projected into the full analysis region. The histograms are described in the text.

Figure 19

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the MU box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$. Further explanation is given in the Fig. 15 caption.

Figure 20

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the ELE-ELE box. The continuous histogram is the total standard model prediction. The histogram is described in the text.

Figure 21

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the ELE-ELE box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$. Further explanation is given in the Fig. 15 caption.

Figure 22

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the inclusive MU-MU box. The fit is performed in the ($M_R$, $R^2$) fit region (shown in Fig. 23) and projected into the full analysis region. The histogram is described in the text.

Figure 23

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the MU-MU box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$. Further explanation is given in the Fig. 15 caption.

Figure 24

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the inclusive MU-ELE box. The fit is performed in the ($M_R$, $R^2$) fit region (shown in Fig. 25) and projected into the full analysis region. The histogram is described in the text.

Figure 25

The fit region, FR, and signal regions, $\mathrm{SR}i$, are defined in the ($M_R$, $R^2$) plane for the MU-ELE box. The color scale gives the $p$-values corresponding to the observed number of events in each $\mathrm{SR}i$. Further explanation is given in the Fig. 15 caption.

Figure 26

(Upper left panel) Observed (solid curve) and median expected (dashed orange curve) 95% C.L. limits in the ($m_0$, $m_{1/2}$) CMSSM plane (drawn according to Ref. [73]) with $\tan \beta =10$, $A_0=0$, and $\mathrm{sgn}(\mu )=+1$. The $\pm 1$ standard deviation equivalent variations due to the uncertainties are shown as a band around the median expected limit. (Upper right panel) The observed HAD-only (solid red) and leptonic-only (solid green) 95% C.L. limits are shown, compared to the combined limit (solid blue curve). The expected (dashed curve) and observed (solid curve) limits for the (lower left) HAD-only and (lower right) leptonic boxes only are also shown.

Figure 27

The diagrams corresponding to the SMS models considered in this analysis.

Figure 28

Cross section upper limits, in pb, at 95% C.L. (color scale), in the mass plane of the produced superparticles for (a) T1, (b) T2, (c) T1tttt, and (d) T2tt, for the inclusive razor analysis. The solid black line indicates the observed exclusion region, assuming the nominal $\mathrm{NLO}+\mathrm{NLL}$ SUSY production cross section. The dotted black lines show the observed exclusion taking $\pm 1$ standard deviation theoretical uncertainties around the nominal cross section. The solid green line indicates the median expected exclusion region, with dotted green lines indicating the expected exclusion with $\pm 1$ standard deviation experimental uncertainties. The solid gray region indicates model points where the selection efficiency is found to have dependence on ISR modeling in the simulation of signal events above a predefined tolerance; no interpretation is presented for these model points.

Figure 29

Cross section upper limits, in pb, at 95% C.L. (color scale), in the mass plane of the produced superparticles for (a) T1bbbb, (b) T2bb, (c) T1tttt, and (d) T2tt, for the $\ge 1$ $b$-tag razor analysis. The solid black line indicates the observed exclusion region, assuming the nominal $\mathrm{NLO}+\mathrm{NLL}$ SUSY production cross section. The dotted black lines show the observed exclusion taking $\pm 1$ standard deviation theoretical uncertainties around the nominal cross section. The solid green line indicates the median expected exclusion region, with the dotted green lines indicating the expected exclusion with $\pm 1$ standard deviation experimental uncertainties. The solid gray region indicates model points where the selection efficiency is found to have dependence on ISR modeling in the simulation of signal events above a predefined tolerance; no interpretation is presented for these model points.

Figure 30

Summary of the 95% C.L. excluded largest parent mass for each of the simplified models studied, for various LSP masses. The results from the $b$-jet razor analysis are shown immediately below those from the inclusive razor analysis for each of the four categories of events indicated.

Figure 31

The $M_R$ distributions for different values of $R_{\min }^2$ for $t\overline{t}$ simulated events in the HAD box with the requirement of $\ge 1$ $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 32

Value of (a) the coefficient in the first exponent, $S_1$, and (b) the coefficient in the second exponent, $S_2$, from fits to the $M_R$ distribution, as a function of $R_{\min }^2$, for $t\overline{t}$ simulated events in the HAD box with the requirement of $\ge 1$ $b$-tagged jets.

Figure 33

The $R^2$ distributions for different values of $M_R^{\min }$ for $t\overline{t}$ simulated events in the HAD box with the requirement of $\ge 1$ $b$-tagged jets. The curves show the results of fits of a sum of two exponential distributions.

Figure 34

Value of (a) the coefficient in the first exponent, $S_1^{\prime }$, and (b) the coefficient in the second exponent, $S_2^{\prime }$, from fits to the $R^2$ distribution, as a function of $M_R^{\min }$, for $t\overline{t}$ simulated events in the HAD box with the requirement of $\ge 1$ $b$-tagged jets.

Figure 35

Projection of the fit result on the (a) $M_R$ and (b) $R^2$ axis for the HAD box, obtained as explained in the text.

Figure 36

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the HAD box in the $\ge 1$ $b$-tag analysis path.

Figure 37

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag HAD box signal regions ($\mathrm{SR}i$).

Figure 38

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the ELE box in the $\ge 1$ $b$-tag analysis path.

Figure 39

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag ELE box signal regions ($\mathrm{SR}i$).

Figure 40

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the MU box in the $\ge 1$ $b$-tag analysis path.

Figure 41

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag MU box signal regions ($\mathrm{SR}i$).

Figure 42

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the ELE-ELE box in the $\ge 1$ $b$-tag analysis path.

Figure 43

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag ELE-ELE box signal regions ($\mathrm{SR}i$).

Figure 44

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the MU-MU box in the $\ge 1$ $b$-tag analysis path.

Figure 45

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag MU-MU box signal regions ($\mathrm{SR}i$).

Figure 46

Projection of the 2D fit result on (a) $M_R$ and (b) $R^2$ for the MU-ELE box in the $\ge 1$ $b$-tag analysis path.

Figure 47

The $p$-values corresponding to the observed number of events in the $\ge 1$ $b$-tag MU-ELE box signal regions ($\mathrm{SR}i$).

Figure 48

Momentum resolution for (top panel) electrons and (bottom panel) muons within the barrel region of the CMS detector (squares) and in the end caps (triangles).

Figure 49

Electron reconstruction efficiency for (top panels) tight and (bottom panels) loose electrons pointing to the ECAL (left panels) barrel and (right panels) end caps, estimated from the CMS MC simulation of $t\overline{t}$ events. The electron reconstruction is described in Ref. [45].

Figure 50

Muon reconstruction efficiency for tight muons pointing to the (top panel) barrel and (bottom panel) end caps, estimated from the CMS MC simulation of $t\overline{t}$ events. The muon reconstruction is described in Ref. [46].

Figure 51

Transverse energy resolution for jets and $E_{\mathrm{T}}^{\text{miss}}$, in the CMS MC simulation of $t\overline{t}$ events.

Figure 52

Comparison of the (left panel) $M_R$ distribution, (middle panel) $R^2$ distribution, and (right panel) the efficiency versus box obtained from the official CMS fast simulation package and the emulation procedure described in this appendix. The two distributions correspond to a T1tttt sample with 800 GeV gluino mass and 300 GeV LSP mass.

Figure 53

Bayesian upper limits, at 95% C.L., on cross sections, in pb, for simplified models, obtained by applying the razor emulation procedure described in this appendix: (left) T1tttt, to be compared with Fig. 28; (right) T2tt, to be compared with Fig. 28.