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---+!! Computation of Limits with Theta

%TOC%

Here I compute limits for i2HDM signal with [[http://www-ekp.physik.uni-karlsruhe.de/~ott/theta/theta-auto/][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 &lambda;<sub>345</sub>. We consider the cases of *%BLUE%h1h1%ENDCOLOR%* DM production for 8 and 13 !TeV.

|  *Benchmark*  | *M<sub>h1</sub>* |  *Number of generated events (from LHE)*  |  *Cross Section (&lambda;<sub>345</sub>) (pb)*  |
|  *(h1h1) 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) |
|  *(h1h1) NEW DM production (8 TeV)*  ||||
|  |  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) |
|  *(h1h1) NEW DM production (13 TeV)*  ||||
|  |  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 [[http://cms-results.web.cern.ch/cms-results/public-results/publications/EXO-12-048/index.html][CMS-EXO-12-048]].

<img width="400" alt="" src="%ATTACHURL%/MetLep3.jpg" height="400" />

The figure below shows data and background !MET distributions (8 !TeV) "stolen" from [[http://cms-results.web.cern.ch/cms-results/public-results/publications/EXO-12-048/index.html][CMS-EXO-12-048]] compared with *%BLUE%h1h1%ENDCOLOR%* from i2HDM DM signal. The DM signal comes directly from LHE level. Here we consider the following cuts on that CMS paper:
   * p<sub>T</sub>(Jet1) &gt; 110 !GeV
   * |&eta;(Jet1)| &lt; 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<sub>T</sub>(Jet1) &gt; 30 !GeV and |&eta;(Jet1)| &lt; 4.5:
      * If there are *three or more* such jets in the event: discard the event.
      * If there are *exactly two* of those jets (J<sub>1</sub>, J<sub>2</sub>n the event, *AND* their azimuthal distance (&Delta&phi(J<sub>1</sub>, J<sub>2</sub>)) is larger than 2.5: discard the event.

<img width="400" alt="" src="%ATTACHURL%/MET_distributions.png" height="300" />

---++ Computing Limits

Here we use [[http://www-ekp.physik.uni-karlsruhe.de/~ott/theta/theta-auto/][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 &lambda;<sub>345</sub>). Here we have the peace of code used to get the limits:
%TWISTY{
mode="div"
showlink="Show "
hidelink="Hide "
class="twikiHelp"
showimgright="%ICONURLPATH{toggleopen-small}%"
hideimgright="%ICONURLPATH{toggleclose-small}%"
}%
<verbatim>
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')
</verbatim>
%ENDTWISTY%

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.

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_LHE_8TeV_shape.png" height="400" />


---+++ 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).

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_1Bin.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_shape.png" height="400" />

The plots bellow compare limits for signal (using data and background from 8 !TeV) after hadronization via:
   * Pythia only (left); and
   * Pythia+Delphes (right).
Both limits are based on shape analysis. It seems that hadronization using *Pythia only* has an improvement from 10 to 20%.

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Pythia_8TeV_shape.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_shape.png" height="400" />

The plots bellow show the limits after relaxing the MET selection to MET &gt; 250 !GeV in case of *Pythia+Delphes*. We use signal with:
   * jet pt scale (left); and
   * DM mass scale (right).
The disagreement between observed and expected limits are directly related to the excess of data in MET distribution above, which explains the selection in MET = 500 !GeV.

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET250_jetPtScale.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET250_DMmassScale.png" height="400" />


---++++ 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:

<img width="400" alt="" src="%ATTACHURL%/DataBackgMET.png" height="400" />

The limits bellow are based on hadronization via *Pythia+Delphes* using
   * jet pt scale (left); and
   * DM mass scale (right).

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET250_jetPtScale_SF.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET250_DMmassScale_SF.png" height="400" />

The limits bellow take into account only 2 bins of the MET distribution in the following way
   * 250 &lt; MET &lt; 300 !GeV (left)
   * 500 &lt; MET &lt; 550 !GeV (middle)
   * 950 &lt; MET &lt; 1000 !GeV (right)

<img width="350" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET250_300_jetPtScale.png" height="350" />
<img width="350" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET500_550_jetPtScale.png" height="350" />
<img width="350" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_MET950_1000_jetPtScale.png" height="350" />

Bellow we have limits based on 1 bin in the MET distribution as done in fig. 4 of CMS paper [[http://cms-results.web.cern.ch/cms-results/public-results/publications/EXO-12-048/index.html][CMS-EXO-12-048]]:
   * 250 &lt; MET &lt; 1000 !GeV (left); and
   * 250 &lt; MET &lt; 600 !GeV (to compare with fig. 4 in the CMS paper) (right).
In all cases, only a lower cut in MET is taken into account. The upper MET value is always 1000 !GeV. The disagreement in the range 450 &lt; MET &lt; 550 !GeV is related to the fact that our histograms contains Data much lower than background in this region (even considering the background uncertainty).

<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_oneBin_250_1000_jetPtScale.png" height="400" />
<img width="400" alt="" src="%ATTACHURL%/i2HDM_limits_Delphes_8TeV_oneBin_250_600_jetPtScale.png" height="400" />


-- %USERSIG{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.

-- %BUBBLESIG{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.

-- %BUBBLESIG{trtomei - 2016-05-17}%


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

-- %BUBBLESIG{assantos - 2016-05-18}%
%COMMENT%

Attachments

Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
png	DataBackgMET.png	r1	manage	19.6 K	2016-06-23 - 15:25	UnknownUser	Data / Backg after correction
png	MET_distributions.png	r1	manage	19.2 K	2016-03-18 - 13:28	UnknownUser	MET distribution with h1h1 from i2HDM DM signal
jpg	MetLep3.jpg	r1	manage	96.7 K	2016-03-18 - 13:24	UnknownUser	MET distribution from CMS-EXO-12-048
png	i2HDM_limits.png	r1	manage	19.9 K	2016-03-18 - 13:47	UnknownUser	Limits for i2HDM DM signal in 8 TeV
png	i2HDM_limits_Delphes_8TeV.png	r1	manage	16.3 K	2016-05-19 - 14:55	UnknownUser	Limits for Delphes 8 TeV
png	i2HDM_limits_Delphes_8TeV_1Bin.png	r1	manage	15.9 K	2016-06-02 - 14:48	UnknownUser	Limits for Pythia+Delphes 8 TeV (1 bin)
png	i2HDM_limits_Delphes_8TeV_MET250_300_jetPtScale.png	r1	manage	16.0 K	2016-06-23 - 15:34	UnknownUser	Limits for Pythia+Delphes 8 TeV (250 < MET < 300)
png	i2HDM_limits_Delphes_8TeV_MET250_DMmassScale.png	r1	manage	15.9 K	2016-06-09 - 14:49	UnknownUser	Limits for Pythia+Delphes 8 TeV (MET > 250)
png	i2HDM_limits_Delphes_8TeV_MET250_DMmassScale_SF.png	r1	manage	15.8 K	2016-06-23 - 15:29	UnknownUser	Limits for Pythia+Delphes 8 TeV (MET > 250) after histo correction
png	i2HDM_limits_Delphes_8TeV_MET250_jetPtScale.png	r1	manage	16.3 K	2016-06-09 - 14:48	UnknownUser	Limits for Pythia+Delphes 8 TeV (MET > 250)
png	i2HDM_limits_Delphes_8TeV_MET250_jetPtScale_SF.png	r1	manage	16.3 K	2016-06-23 - 15:29	UnknownUser	Limits for Pythia+Delphes 8 TeV (MET > 250) after histo correction
png	i2HDM_limits_Delphes_8TeV_MET500_550_jetPtScale.png	r1	manage	16.9 K	2016-06-23 - 15:35	UnknownUser	Limits for Pythia+Delphes 8 TeV (500 < MET < 550)
png	i2HDM_limits_Delphes_8TeV_MET950_1000_jetPtScale.png	r1	manage	19.7 K	2016-06-23 - 15:36	UnknownUser	Limits for Pythia+Delphes 8 TeV (950 < MET < 1000)
png	i2HDM_limits_Delphes_8TeV_noNorm.png	r1	manage	16.0 K	2016-05-30 - 12:10	UnknownUser	Limits for Pythia+Delphes 8 TeV
png	i2HDM_limits_Delphes_8TeV_oneBin_250_1000_jetPtScale.png	r1	manage	18.5 K	2016-06-30 - 13:09	UnknownUser	Limits for Pythia+Delphes 8 TeV (1 bin) MET[250 - 1000]
png	i2HDM_limits_Delphes_8TeV_oneBin_250_600_jetPtScale.png	r1	manage	17.1 K	2016-06-30 - 13:10	UnknownUser	Limits for Pythia+Delphes 8 TeV (1 bin) MET[250 - 600]
png	i2HDM_limits_Delphes_8TeV_shape.png	r1	manage	16.1 K	2016-06-02 - 15:09	UnknownUser	Limits for Pythia+Delphes 8 TeV (shape analysis)
png	i2HDM_limits_LHE_8TeV_shape.png	r1	manage	17.8 K	2016-06-03 - 17:50	UnknownUser	Limits for LHE 8 TeV
png	i2HDM_limits_Pythia_8TeV.png	r1	manage	16.0 K	2016-05-18 - 20:07	UnknownUser	Limits for Pythia 8 TeV
png	i2HDM_limits_Pythia_8TeV_shape.png	r1	manage	16.1 K	2016-06-06 - 16:24	UnknownUser	Limits for Pythia 8 TeV

Topic revision: r2 - 2022-08-22 - trtomei

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