10000 20000 30000 40000
50000 ∫Ldt=20.3fb-1, s=8TeV tW+jetst Z+jets QCD Single Top Dibosons
+V t t
R(lep,jet) [rad]
min Δ
0 0.5 1 1.5 2 2.5 3
Ratio
0 1 2
Figure 37: min
Jet ∆R(Leading Lepton,Jet) distribution after requiring 1 soft lepton and at least one jet with pT>20 GeV.
affects to the final limits. We will optimize the thresholds in the next section with a more sophisti-cated method.
meff : Effective massmeff is known to be sensitive to heavy particle productions since it is roughly proportional to the masses of colored particles initially produced. Figure 41 shows the correlation of the initial particle masses and the means of their meff distributions. Black points represent signal points taken from Grid-x(mχ˜0
1 is fixed at 60 GeV), which show a clear linear correlation.
However, signal points of Half-xgrids (varying mχ˜0
1), which are shown in red, distribute broader and the correlation seems week. This feature suggests that meff has a good correlation with the initial particle mass for light LSP cases. meff becomes smaller than the original particles masses for heavy LSP case, because a significant fraction of the energy is consumed to create heavy LSPs.
Since it is difficult to set an universal threshold on meff, we use meff as a final discriminating variable and perform a fit on the shape. For reference,meff distributions are shown in Fig. 42.
40
Njet
0 2 4 6 8 10 12 14 16 18 20
Events
10-3
10-2
10-1
1 10 102
103
104
105
106
107
108
109
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
30
Njet
0 2 4 6 8 10 12 14 16 18 20
Events
10-3
10-2
10-1
1 10 102
103
104
105
106
107 ∫Ldt=20.3fb-1, s=8TeV tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
Figure 38: Number of jets distributions after requiring: (left) 1 hard lepton, one jet with pT>80 GeV
and EmissT >100 GeV; (right) soft 1 lepton and EmissT >200 GeV. For signal samples, ˜q-˜q productions
with (m˜q,mχ˜±1,mχ˜0
1) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and ˜g-˜gproductions with (mg˜,mχ˜±1,mχ˜0
1) =(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line shows a degenerate point with (mg˜,mχ˜±1,mχ˜0
1)=(650,625,600).
[GeV]
mT
0 50 100 150 200 250 300
Events/5GeV
10-2
10-1
1 10 102
103
104
105
106
107
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
[GeV]
mT
0 50 100 150 200 250 300
Events/5GeV
10-3
10-2
10-1
1 10 102
103
104
105
106
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
Figure 39: mT distributions after requiring: (left) 1 hard lepton, ETmiss>150 GeV and three jets with pT>40 GeV, in which the leading jets should be harder than pT>80 GeV; (right) soft 1 lepton, EmissT >200 GeV, and three jets with pT>30 GeV. For signal samples, ˜q-˜q productions with (m˜q,mχ˜±1,mχ˜0
1) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and ˜g-˜g productions with (mg˜,mχ˜±1,mχ˜0
1) =(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line shows a degenerate point with (mg˜,mχ˜±1,mχ˜0
1)=(650,625,600).
[GeV]
miss
ET
100 200 300 400 500 600 700 800 900 1000
Events/25GeV
10-3
10-2
10-1
1 10 102
103
104
105
106
107
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
[GeV]
miss
ET
200 300 400 500 600 700 800 900 1000
Events/25GeV
10-3
10-2
10-1
1 10 102
103
104
105
106
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
Figure 40:EmissT distributions after requiring: (left) 1 hard lepton and three jets withpT>40 GeV, in which the leading jets should be harder thanpT>80 GeV; (right) soft 1 lepton and three jets withpT>30 GeV. For signal samples, ˜q-˜q productions with (m˜q,mχ˜±1,mχ˜0
1) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and ˜g-˜g productions with (mg˜,mχ˜±1,mχ˜0
1) =(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line shows a degenerate point with (mg˜,mχ˜±1,mχ˜0
1)=(650,625,600).
Initial Particle Mass [GeV]
200 400 600 800 1000 1200 1400 1600
mean [GeV]effm
500 1000 1500 2000 2500
Figure 41: Signal points in the Simplified Models with ˜g-˜g and ˜q-˜q productions are shown. x-axis represents mg˜ or m˜q and y-axis shows the mean of the meff distribution. Black points show Grid-x(mχ˜0
1=60 GeV) and red points show Half-xgrid. See Section 4.3.3 for their definitions.
[GeV]
meff
0 500 1000 1500 2000 2500
Events/200GeV
10-2
10-1
1 10 102
103
104
105
106
107
108
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
[GeV]
meff
0 500 1000 1500 2000 2500
Events/200GeV
10-2
10-1
1 10 102
103
104
105
106
107
=8TeV s
-1, Ldt=20.3fb
∫ tW+jetst
Z+jets Single Top Dibosons
+V t t
(800,560,60) q~ -q~
(800,160,60) q~ -q~
(800,560,60) g~ -g~
(800,160,60) g~ -g~
(650,625,600) g~
-g~
Figure 42: meffdistributions after requiring: (left) 1 hard lepton and three jets with 40 GeV, in which the leading jets should be harder than 80 GeV; (right) soft 1 lepton and three jets withpT>30 GeV. For signal samples, ˜q-˜q productions with (m˜q,mχ˜±1,mχ˜0
1) =(800,560,60) (dark cyan) and (800,160,60) (light cyan), and ˜g-˜gproductions with (mg˜,mχ˜±1,mχ˜0
1)=(800,560,60) (dark magenta) and (800,160,60) (light magenta) are plotted. Blue line shows a degenerate point with (mg˜,mχ˜±1,mχ˜0
1)=(650,625,600).
Variable Tight SR Loose SR Soft SR
Preselections
Leading leptonpT >25 GeV [10 GeV, 25 GeV] (Electron), [6 GeV, 25 GeV] (Muon) Next leading leptonpT <10 GeV <7 GeV (Electron),
<6 GeV (Muon) Signal Region specific selections
Number of jets Njet40≥5 3≤Njet40<5 Njet30≥3
Leading jet pT >120 GeV >80 GeV >100 GeV
mT >150 GeV >120 GeV >100 GeV
EmissT >350 GeV >250 GeV >300 GeV
mincl30eff Binned Binned Binned
[800,1200,1600, [450,700,950, [450,700,950,
2000,2400] 1200,1450] 1200,1450]
and>2400 GeV and>1450 GeV and>1450 GeV
Table 12: Optimized signal regions.
These lines clearly show where they have good sensitivities. ˜q-˜q production grid in Fig. 43 shows that Tight and Loose Signal Regions have similar sensitivity, cooperatively increasing the combined sensi-tivity. In the diagonal region of ˜g-˜g grid in Fig. 44, Soft Signal Region mainly drives the limit. The combined limits in the other regions are basically driven by the Tight Signal Region.
[GeV]
g~
m
400 600 800 1000 1200 1400
) 10χ∼- mg~) / (m 10χ∼- m 1±χ∼(m
0 0.2 0.4 0.6 0.8 1 1.2 1.4
=60GeV
1 χ0
,m∼ 1 χ∼0 1 χ∼0 qqqqWW
→
~g
-~g
= 8TeV s
-1, L dt = 20.3fb
∫
All limits at 95% C.L.
Obs. Limit (2011)
exp) σ
±1 Expected limit (
Tight SR Loose SR Soft SR
[GeV]
q~
m
400 600 800 1000 1200 1400
) 1
0χ∼- mq~) / (m 1
0χ∼- m 1±χ∼(m
0 0.2 0.4 0.6 0.8 1 1.2 1.4
=60GeV
1 χ0
,m∼ 1 χ∼0 1 χ∼0 qqqqWW
→ q~ -q~
= 8TeV s
-1, L dt = 20.3fb
∫
All limits at 95% C.L.
Obs. Limit (2011)
exp) σ
±1 Expected limit (
Tight SR Loose SR Soft SR
Figure 43: The expected limits are shown for Simplified Models (Grid-x) of ˜g-˜g(left) and ˜q-˜q (right) pair production. mχ˜0
1 is fixed at 60 GeV andx=(mχ˜±1 −mχ˜0
1)/(mg/˜˜ q−mχ˜0
1) is taken asy-axes. The black line shows an expected limit and the yellow band corresponds to the uncertainty of the limit. The decomposed limits obtained by three separate Signal Regions are also shown in magenta (Tight SR), blue (Loose SR) and green (Soft SR) lines.
[GeV]
g~
m
400 600 800 1000 1200 1400
[GeV] 10χ∼m
100 200 300 400 500 600 700 800 900 1000
, x=1/2 1 χ∼0 1 χ∼0 qqqqWW
→
~g
-~g
= 8TeV s
-1, L dt = 20.3fb
∫
All limits at 95% C.L.
Obs. Limit (2011)
1 0χ
∼
<m
~g
m
exp) σ
±1 Expected limit (
Tight SR Loose SR Soft SR
[GeV]
q~
m
400 600 800 1000 1200 1400
[GeV] 1 0χ∼m
100 200 300 400 500 600 700 800 900 1000
, x=1/2 1 χ∼0 1 χ∼0 qqqqWW
→ q~ -q~
= 8TeV s
-1, L dt = 20.3fb
∫
All limits at 95% C.L.
Obs. Limit (2011)
1 0χ
∼
<m
~q
m
exp) σ
±1 Expected limit (
Tight SR Loose SR Soft SR
Figure 44: The expected limits are shown for Simplified Models (Half-x) of ˜g-˜g(left) and ˜q-˜q (right) pair production. x=(mχ˜±1−mχ˜0
1)/(mg/˜˜ q−mχ˜0
1) is fixed at 1/2 andmχ˜0
1 is taken asy-axes. The black line shows an expected limit and the yellow band corresponds to the uncertainty of the limit. The decomposed limits obtained by three separate Signal Regions are also shown in magenta (Tight SR), blue (Loose SR) and green (Soft SR) lines.
6 Background estimation
6.1 Multi-jet background
QCD multi-jet events are a notorious background in the LHC due to its large cross-section. A large part of QCD multi-jet events do not accompany leptons, hence the lepton requirement greatly reduces the background. However, a small fraction of QCD multi-jet events accompany a lepton due to the following reasons:
• π0decays into two photons. Ae+e−pair is created when one of the photons hits the first layer of pixel tracker (photon conversion).
• Some fraction of heavy flavor hadrons decay into final states with leptons. Since most of such leptons are collinear to the jets, they are rejected by overlap removal (as discussed in Section 3.3.4).
The remaining leptons that are emitted far from jets contaminate our signal region.
• π±track is mis-identified as a fake electron if the track accidentally matches to a calorimeter cluster produced by charge exchangeπ0production followed by its decay,π0→γγ.
Large cross-section of QCD multi-jets obviously exceeds our computing capacity for Monte Carlo simulation. Hence, we estimate QCD multi-jets background using data itself with a method called Matrix-Method. Matrix-Method estimates the shape and yield of QCD multi-jets from the difference between fake-enriched and fake-suppressed distributions. Details of Matrix-Method are documented in Appendix C. Missing transverse momentum of QCD multi-jet events mainly originates from EmissT mis-measurement and typically quite small. Since we require at least EmissT >150 GeV for all regions, the QCD multi-jet component falls into one of the minor backgrounds.