Computation of Limits with Theta

Here I compute limits for i2HDM signal with Theta package.

List of MC samples for signal (i2HDM)

The following table shows the details of MC samples for i2HDM signal, as the number of generated events and the cross section with correspondent λ₃₄₅. We consider the cases of h1h1 DM production for 8 and 13 TeV.

Benchmark	Mh1	Number of generated events (from LHE)	Cross Section (λ345) (pb)
(h1h1) DM production (8 TeV)
(h1h1) NEW DM production (13 TeV)
(h1h1) NEW DM production (8 TeV)
BM1	45	50000	0.17 (-0.010)
BM2	53	50000	0.77 (-0.024)
BM3	66	50000	0.000043 (+0.022)
BM4	82	50000	0.00012 (-0.090)
BM5	120	50000	0.000023 (-0.100)
	40	100000	0.073899 (0.01)
	41	100000	0.072681 (0.01)
	42	100000	0.071266 (0.01)
	43	100000	0.070021 (0.01)
	44	100000	0.068574 (0.01)
	45	100000	0.067103 (0.01)
	46	100000	0.065719 (0.01)
	47	100000	0.064175 (0.01)
	48	100000	0.062273 (0.01)
	49	100000	0.06049 (0.01)
	50	100000	0.058593 (0.01)
	51	100000	0.056552 (0.01)
	52	100000	0.054462 (0.01)
	53	100000	0.052094 (0.01)
	54	100000	0.049695 (0.01)
	55	100000	0.04703 (0.01)
	56	100000	0.04403 (0.01)
	57	100000	0.040899 (0.01)
	58	100000	0.037309 (0.01)
	59	100000	0.033193 (0.01)
	60	100000	0.028262 (0.01)
	61	100000	0.022176 (0.01)
	62	100000	0.012981 (0.01)
	40	100000	0.24281 (0.01)
	41	100000	0.23912 (0.01)
	42	100000	0.23478 (0.01)
	43	100000	0.23028 (0.01)
	44	100000	0.22542 (0.01)
	45	100000	0.22092 (0.01)
	46	100000	0.21604 (0.01)
	47	100000	0.21040 (0.01)
	48	100000	0.20503 (0.01)
	49	100000	0.19892 (0.01)
	50	100000	0.19255 (0.01)
	51	100000	0.18638 (0.01)
	52	100000	0.17927 (0.01)
	53	100000	0.17154 (0.01)
	54	100000	0.16370 (0.01)
	55	100000	0.15431 (0.01)
	56	100000	0.14503 (0.01)
	57	100000	0.13431 (0.01)
	58	100000	0.12249 (0.01)
	59	100000	0.10901 (0.01)
	60	100000	0.093206 (0.01)
	61	100000	0.072845 (0.01)
	62	100000	0.042620 (0.01)

Distributions

The figure below shows MET distributions (8 TeV) from CMS-EXO-12-048.

The figure below shows data and background MET distributions (8 TeV) "stolen" from CMS-EXO-12-048 compared with h1h1 from i2HDM DM signal. The DM signal comes directly from LHE level. Here we consider the following cuts on that CMS paper:

• p_T(Jet1) > 110 GeV
• |η(Jet1)| < 2.4
• MET > 500 GeV
• Additionally, for studies that take into account effects of showering // hadronization // detector response, there are additional selections on the full set of jets attending the requirements p_T(Jet1) > 30 GeV and |η(Jet1)| < 4.5:
  • If there are three or more such jets in the event: discard the event.
  • If there are exactly two of those jets (J₁, J₂n the event, AND their azimuthal distance (&Delta&phi(J₁, J₂)) is larger than 2.5: discard the event.

Computing Limits

Here we use Theta package to compute the limits.

Generator Level

The figure below shows the observed and expected limits (8 TeV) for signal in generator level, as well as the correspondent signal cross sections (for different λ₃₄₅). Here we have the peace of code used to get the limits:

Show Hide

model = build_model_from_rootfile(['EXO-12-048_data.root','background.root','i2hdm_BM4_h1h1j_8tev-single-THETA.root'])
#print model

model.set_signal_processes('i2HDMBenchmark*')
model.scale_predictions(0.06698,procname="i2HDMBenchmark1",obsname="CMS_EXO_12_048")
#model.scale_predictions(0.30338,procname="i2HDMBenchmark2",obsname="CMS_EXO_12_048")
#model.scale_predictions(0.000017,procname="i2HDMBenchmark3",obsname="CMS_EXO_12_048")
#model.scale_predictions(0.000047,procname="i2HDMBenchmark4",obsname="CMS_EXO_12_048")
#model.scale_predictions(0.000009,procname="i2HDMBenchmark5",obsname="CMS_EXO_12_048")

expected, observed = asymptotic_cls_limits(model)

print expected, observed

report.write_html('htmlout')

Since we have less data than background, the observed limits are below the expected ones. Despite the fact that data and background does not change, observed and expected limits change because signal samples have different efficiencies. The plots show limits in generator level (4-vector information from LHE files) for:

• benchmarks (left);
• and new LHE files with jet pt QCD scale (right) according cross sections from tables above.

Signal with hadronization

The plots bellow show limits for signal (using data and background from 8 TeV) after hadronization via Pythia+Delphes. These limits were computed using:

• 1 bin histogram (left); and
• and shape analysis (right).

The plots bellow compare limits for signal (using data and background from 8 TeV) after hadronization via:

• Pythia only (left); and
• Pythia+Delphes (right).

The plots bellow show the limits after relaxing the MET selection to MET > 250 GeV in case of Pythia+Delphes. We use signal with:

• jet pt scale (left); and
• DM mass scale (right).

Limits after histograms correction

Data and background distributions were corrected (bin-by-bin) in order to have the same number of events as in table 3 of CMS-EXO-12-048. These is the data and background MET distribution after correction:

The limits bellow are based on hadronization via Pythia+Delphes using

• jet pt scale (left); and
• DM mass scale (right).

The limits bellow take into account only 2 bins of the MET distribution in the following way

• 250 < MET < 300 GeV (left)
• 500 < MET < 550 GeV (middle)
• 950 < MET < 1000 GeV (right)

Bellow we have limits based on 1 bin in the MET distribution as done in fig. 4 of CMS paper CMS-EXO-12-048:

• 250 < MET < 1000 GeV (left); and
• 250 < MET < 600 GeV (to compare with fig. 4 in the CMS paper) (right).

-- assantos - 2016-03-18

Comments

Clearly BM3, BM4 and BM5 are completely out of reach. I think that the next obvious steps would be to do the limits on BM1 and BM2 in a more precise way, using PYTHIA+DELPHES for better signal modelling.

-- trtomei - 2016-04-29

I have changed the cuts that are to be applied to the analysis to take into account the showering / hadronization effects.

-- trtomei - 2016-05-17

I have included information about new i2HDM production (8 and 13 TeV) in the table.

-- assantos - 2016-05-18