JohnBackusMayesSandbox < Sandbox

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%CERTIFY%
---+!!<nop>Jets with pileup in 2011
%TOC%     <!--optional-->
%STARTINCLUDE%

<table width="97%" border="0"> <tbody> <tr> <td width="60%" valign="top">

---+ Introduction

Due to decreased bunch spacing, varying bunch configuration and increased per-bunch luminosity, the effect of pile-up on jets is significantly different in 2011 as compared to 2010. Consequently, we have this dedicated TWiki page to summarize the impact of pile-up on jets for the new data.

<!--This page is split into 5 sections based on the method used to study as well as correct for the pile-up: Jet constituent (towers, clusters), tracks, jet vertex fraction, jet area, and of course, jets.-->

%BLUE% *Goal*: __Summarize the current understanding of the effects of pile-up on jets in ATLAS and the methods and techniques available to mitigate these effects on physics analysis.__ %ENDCOLOR%

Some related TWiki pages are:
   * JetsWithPileup
   * JetCalibTools
   * TrackJetsInAthena
   * JetVertexFraction
   * OffsetCorrection
 
</td> <td width="5%" valign="top"> </td> <td width="35%" valign="top">

%IMAGE{"JiveXML_177531_183764-YX-RZ-EventInfo-RZ-2011-03-13-22-38-43.png"
  type="frame" 
  align="center"
  size="300"
  caption="A collision event from the first 2011 fill with stable beams, which were declared at 18:04 on Sunday 13 March."
}%

</td></tr></tbody></table>

---++ In-time pile-up

The result of additional interactions in the current bunch crossing. The amount of in-time pile-up is described (on average) by the number of reconstructed primary vertices in an event, N<sub>PV</sub>. However, other variables may provide a more ideal parametrization of in-time pile-up.  For example, the number of tracks not associated with the hard scatter primary vertex, N<sub>trk</sub><sup>out</sup>, may be a more precise measure of pile-up activity, and it is less sensitive to vertex reconstruction efficiencies.

---++ Out-of-time pile-up

Because the integration times in the calorimeter span many successive bunch crossings, minimum bias interactions from several preceding and some following bunch crossings may affect the response of the calorimeter to in-time signals. The effect of out-of-time pile-up depends on several factors that are specific to each event.  Signal shaping in the calorimeter is designed such that out-of-time pileup should have an overall negative effect that cancels the positive effect from in-time pile-up on average. However, this only works if the bunch intensity is constant over the integration time of the calorimeter.  For example, at the beginning of a bunch train there is insufficient out-of-time pile-up to cancel the in-time pile-up, so the calorimeter response is systematically higher for these events.

Currently, we do not have a way to directly measure the number of interactions in preceding and following bunch crossings, so we use the instantaneous luminosity to roughly estimate the amount of out-of-time pile-up.  The variable &mu; is the mean number of inelastic interactions per bunch crossing, calculated directly from the instantaneous luminosity, inelastic cross-section, and beam parameters for the luminosity block that contains the event of interest. Work is ongoing to provide a more precise estimate of the out-of-time pile-up, for example using the BCID-specific luminosity to take into account variations in bunch intensity.

---++ Effect on the jet energy scale

Perhaps the largest effect that pile-up has on reconstructed jets is to shift the jet energy scale.  We are primarily interested in measuring and correcting for this shift, though studies of other pile-up effects on jets are also ongoing.

Pile-up interactions result in both diffuse, low-p<sub>T</sub> and point-like, high-p<sub>T</sub> energy deposits in the calorimeter. The average shift in the JES is due to the low-p<sub>T</sub> component of pile-up. Diffuse in-time pile-up contributes a fixed amount of energy (dependent on jet &eta;) to each jet for every additional minimum bias interaction. On the other hand, out-of-time pileup can either add or subtract energy from the jet, depending on the distribution in time of contributions from surrounding bunch crossings.

The effect of diffuse in-time and out-of-time pile-up is to induce an additive offset in the jet energy scale, independent of the jet p<sub>T</sub>. We expect this offset to depend linearly on the numbers of additional in-time and out-of-time interactions. Therefore, we propose the following form for an offset correction:

%MATHMODE{{\rm Offset} = A \times (\mu - \mu^{\rm ref}) + B \times (N_{\rm PV} - N_{\rm PV}^{\rm ref})}%

Both _A_ and _B_ must depend on jet &eta;, and they must be determined separately for each type of jet (algorithm, radius, EM vs. LC).  The quantities &mu;<sup>ref</sup> and N<sub>PV</sub><sup>ref</sup> are used to control the output energy scale of the correction, which should match the assumed input energy scale of any subsequent jet calibration.

To take into account the incomplete cancellation of in-time and out-of-time pile-up near the beginning of each bunch train, the coefficient _A_ may be binned according to the time elapsed since the last empty bunch crossing. Coarse binning in the size of the gap preceding the current bunch train may also be necessary.

To begin, we have determined a jet p<sub>T</sub> offset of this form by matching reconstructed jets to truth jets in simulated QCD dijet events; the next section is a description of the resulting correction.


---+ MC-based offset correction

The correction uses two variables to parametrize pile-up: the number of primary vertices in an event (N<sub>PV</sub>) and the number of average interactions in a lumi block (&mu;). *Note that for the purposes of this correction, we define N<sub>PV</sub> as the number of reconstructed primary vertices with at least two associated tracks.*

The correction is p<sub>T</sub> independent, and it is given in seven |&eta;| bins: 0.0-0.3, 0.3-0.8, 0.8-1.2, 1.2-2.1, 2.1-2.9, 2.9-3.5, 3.5-5.0. Also, the correction depends on two other parameters that serve to connect the correction with the subsequent JES calibration: the reference values of N<sub>PV</sub> and &mu;. These should be taken from the MC sample from which the JES was derived, and should be equal to the mean values of N<sub>PV</sub> and &mu; in that sample. The correction should be applied before the JES, taking into account the reference values of N<sub>PV</sub> and &mu;.

Note that this correction, as a first pass, does not take into account the incomplete cancellation of in-time and out-of-time pile-up near the beginning of a bunch train. It is derived from events that are at least 600 ns from the beginning of a train. However, any mismodeling of the average effect from incomplete cancellation is taken into account in the determination of associated systematic uncertainties.

---++ Correction for Release 16 (MC10b)

The latest version of this correction was presented at the 2011 ATLAS hadronic calibration workshop at SLAC ([[https://indico.cern.ch/getFile.py/access?contribId=29&sessionId=0&resId=0&materialId=slides&confId=132005][contribution by Carlos Sandoval]]), and all the plots supporting it can be found here:
   * *AntiKt6 EM jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6Topo_correctionpT.html
   * *AntiKt6 LC jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6LCTopo_correctionpT.html
   * *AntiKt4 EM jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4Topo_correctionpT.html
   * *AntiKt4 LC jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4LCTopo_correctionpT.html

---++ Correction for Release 17 (MC11a)

The latest version of this correction was presented at the Jet/Etmiss Phone Conference of 9 November 2011 ([[http://indico.cern.ch/getFile.py/access?contribId=8&resId=0&materialId=slides&confId=161038][presentation by Carlos Sandoval]]), and all the plots supporting it can be found here:
   * *AntiKt6 EM jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6Topo_correctionMC11.html
   * *AntiKt6 LC jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6LCTopo_correctionMC11.html
   * *AntiKt4 EM jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4Topo_correctionMC11.html
   * *AntiKt4 LC jets* http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4LCTopo_correctionMC11.html

---++ Code

Please note that this code is not optimized for performance; it is presented here primarily to serve as reference. Please see [[https://svnweb.cern.ch/trac/atlasoff/browser/Reconstruction/Jet/JetCalibTools/tags/JetCalibTools-00-01-17/CalibConstants/TruthOffsetConstants.py][the official code in JetCalibTools]] for a more optimal implementation of the MC-based correction.

%TWISTY{
 mode="div"
 showlink="Show MC-based offset correction code"
 hidelink="Hide MC-based offset correction code"
 showimgleft="%ICONURLPATH{toggleopen-small}%"
 hideimgleft="%ICONURLPATH{toggleclose-small}%"
 start="hide"
 class="none"
}%
|<verbatim>
///=========================================                                                                                                                                       
/// GetOffsetCorrection NPV                                                                                                                                                        
///=========================================                                                                                                                                       
float AnalysisBase::GetOffsetNPV(float jetEta, float mu, float NPV, TString tag, float NPVref, float MUref, bool m_fDebug) {


  // Offset correction table                                                                                                                                                       

  //slope and intercept                                                                                                                                                            
  const static float slope_MC10b_AKt6_topoEM[7] = {
    0.554206,0.560879,0.615631,0.604061,0.643603,0.627901,0.645477};
  const static float intercept_MC10b_AKt6_topoEM[7] = {
    0.113253,0.0988858,0.0229146,0.0216436,-0.117142,-0.251135,-0.330684};
  const static float slope_MC10b_AKt6_lct[7] = {
    0.841648,0.856677,0.919961,0.92832,0.909487,0.913625,0.754934};
  const static float intercept_MC10b_AKt6_lct[7] = {
    0.157548,0.130792,0.0549006,0.0753573,-0.131852,-0.373156,-0.412353};

  const static float slope_MC10b_AKt4_topoEM[7] = {
    0.297376,0.2657,0.287447,0.316899,0.340274,0.362528,0.363839};
  const static float intercept_MC10b_AKt4_topoEM[7] = {
    0.0262287,0.0143564,-0.0311566,-0.0125061,-0.124887,-0.185109,-0.238533};
  const static float slope_MC10b_AKt4_lct[7] = {
    0.406266,0.375533,0.4012,0.449796,0.451956,0.508713,0.400553};
  const static float intercept_MC10b_AKt4_lct[7] = {
    0.0241725,0.0339716,-0.0238977,-0.0173475,-0.16973,-0.300495,-0.30317};

  const static float slope_MC11_AKt6_topoEM[7] = {
    0.55317,0.566214,0.592801,0.595636,0.642784,0.570846,0.611743};
  const static float intercept_MC11_AKt6_topoEM[7] = {
    0.077248,0.0651614,0.05082,0.0694886,-0.104221,-0.368601,-0.365378};
  const static float slope_MC11_AKt6_lct[7] = {
    0.87382,0.937068,0.931847,1.04197,1.04428,0.880914,0.756087};
  const static float intercept_MC11_AKt6_lct[7] = {
    0.0583321,0.148085,0.191317,0.157699,-0.129749,-0.528437,-0.412108};

  const static float slope_MC11_AKt4_topoEM[7] = {
    0.252522,0.285027,0.303536,0.305193,0.356775,0.338547,0.362128};
  const static float intercept_MC11_AKt4_topoEM[7] = {
    0.153442,-0.0160134,-0.0193743,-0.0919976,-0.168367,-0.250434,-0.211702};
  const static float slope_MC11_AKt4_lct[7] = {
    0.387692,0.439022,0.453936,0.476658,0.512217,0.500963,0.404941};
  const static float intercept_MC11_AKt4_lct[7] = {
    0.191242,-0.0123295,-0.0152481,-0.0551463,-0.23288,-0.394158,-0.255641};


  if (m_fDebug) cout << "In GetOffsetNPV()" << endl;

  float jet_NPV_offset = 0.0;


  int eta_index = -1;

  if(fabs(jetEta) <= 0.3)                       eta_index = 0;
  if(fabs(jetEta) > 0.3 && fabs(jetEta) <= 0.8) eta_index = 1;
  if(fabs(jetEta) > 0.8 && fabs(jetEta) <= 1.2) eta_index = 2;
  if(fabs(jetEta) > 1.2 && fabs(jetEta) <= 2.1) eta_index = 3;
  if(fabs(jetEta) > 2.1 && fabs(jetEta) <= 2.9) eta_index = 4;
  if(fabs(jetEta) > 2.9 && fabs(jetEta) <= 3.5) eta_index = 5;
  if(fabs(jetEta) > 3.5 && fabs(jetEta) <= 5.0) eta_index = 6;


  if(tag.Contains("AKt6_TopoEM_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt6_topoEM[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt6_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt6_LCTopo_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt6_lct[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt6_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt4_TopoEM_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt4_topoEM[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt4_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt4_LCTopo_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt4_lct[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt4_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt6_TopoEM_MC11")) {
   jet_NPV_offset = slope_MC11_AKt6_topoEM[eta_index] * (NPV-NPVref) + intercept_MC11_AKt6_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt6_LCTopo_MC11")) {
    jet_NPV_offset = slope_MC11_AKt6_lct[eta_index] * (NPV-NPVref) + intercept_MC11_AKt6_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt4_TopoEM_MC11")) {
    jet_NPV_offset = slope_MC11_AKt4_topoEM[eta_index] * (NPV-NPVref) + intercept_MC11_AKt4_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt4_LCTopo_MC11")) {
    jet_NPV_offset = slope_MC11_AKt4_lct[eta_index] * (NPV-NPVref) + intercept_MC11_AKt4_lct[eta_index] * (mu-MUref);
  }


  else cout << "WARNING: cannot find offset correction for tag = " << tag << "; Please use a supported tag." << endl;


  // Some debugging                                                                                                                                                                
  if (m_fDebug)     cout << "Eta = " << jetEta
                         << " ; eta bin in graph = " << eta_index
                         << " ; mu = " << mu
                         << " ; NPV = " << NPV
                         << " ; Jet NPV offset = " <<  jet_NPV_offset
                         << " ; Tag = " <<  tag
                         << endl;


  // Done                                                                                                                                                                          
  return jet_NPV_offset;
}
</verbatim>|
%ENDTWISTY%

---++ Instructions

The correction returns a number that should be subtracted from the p<sub>T</sub> of the jet (uncalibrated, i.e. no JES) in GeV. It should be applied as follows:  

%MATHMODE{p_T^{\rm EM+JES} = (p_T^{\rm EM} - {\rm Offset}) / R^{\rm JES}}%

where "Offset" is obtained from the =GetOffsetNPV()= function defined in the code above. It has 6 input parameters: N<sub>PV</sub>, &mu;, jet &eta;, N<sub>PV</sub><sup>ref</sup>, &mu;<sup>ref</sup>, and a tag. The tag tells the correction which jet collection you are interested in, as well as which MC version you are using. This is the list of tags that should be used:

   *  "AKt6_TopoEM_MC10b"          
   *  "AKt6_LCTopo_MC10b"                     
   *  "AKt4_TopoEM_MC10b"
   *  "AKt4_LCTopo_MC10b"
   *  "AKt6_TopoEM_MC11"          
   *  "AKt6_LCTopo_MC11"                     
   *  "AKt4_TopoEM_MC11"
   *  "AKt4_LCTopo_MC11"

The following table gives the values of NPVref and MUref that correspond to the default JES corrections in MC10b and MC11a:

| ** |  *N<sub>PV</sub><sup>ref</sup>*  |  *&mu;<sup>ref</sup>*  | *Comments*  |
| MC10b |  6.1  |  8.3  | Default JES was derived from MC10a.  |
| MC11a |  4.9  |  5.4  | Default JES was derived from mc11_valid.  |

For example, if you plan to use the default JES in MC10b, then NPVref=6.1 and  MUref=8.3, and you should be sure to specify a tag with "MC10b". To obtain the correction for an AntiKt6 LC jet, you would call =GetOffsetNPV(jetEta, mu, NPV, "AKt6_LCTopo_MC10b", 6.1, 8.3, false)=.


---+ In-situ validation techniques

The MC-based jet p<sub>T</sub> offset is validated by comparison to offsets obtained from two in-situ techniques: matching calorimeter jets to track jets, and exploiting momentum conservation in events with a photon back-to-back with a jet.

---++ Track-jet validation

We construct track jets from tracks that are matched to the chosen primary vertex. By matching these jets to calorimeter jets, we obtain an estimate of the jet p<sub>T</sub> that is insensitive to pile-up. For a given track-jet p<sub>T</sub>, the median value of the matched calorimeter p<sub>T</sub> is shifted by in-time and out-of-time pile-up in the same way as the MC-based jet p<sub>T</sub> offset.

Some recent results from Giovanni Zevi Della Porta on track-jet validation of the MC-based offset correction:

   * [[https://indico.cern.ch/getFile.py/access?contribId=5&resId=0&materialId=slides&confId=159209][Investigation of the p<sub>T</sub> dependence of track-jet validation, and results from mc11_valid samples.]]
   * [[http://indico.cern.ch/getFile.py/access?contribId=12&resId=2&materialId=slides&confId=157555][Track-jet validation results from 2/fb of 2011 data.]]
   * [[http://indico.cern.ch/getFile.py/access?contribId=77&sessionId=0&resId=0&materialId=slides&confId=132005][Contribution to ATLAS Hadronic Calibration Workshop at SLAC: Track-jet validation of the MC10b-based offset correction using 1/fb of 2011 data.]]

---++ &gamma;-jet p<sub>T</sub> balance

To a good approximation, the reconstructed energy of photons is insensitive to pile-up, and its resolution is much better than the jet energy resolution.  Consequently, in events where a jet is balanced against a photon, momentum conservation allows us to use the photon p<sub>T</sub> as a very good estimate of the true jet p<sub>T</sub>.  The difference between the jet p<sub>T</sub> and photon p<sub>T</sub> is shifted by in-time and out-of-time pile-up in the same way as the MC-based jet p<sub>T</sub> offset.

A [[http://indico.cern.ch/getFile.py/access?contribId=14&resId=0&materialId=slides&confId=157555][recent presentation]] by Andres Tanasijczuk summarizes the results from &gamma;-jet p<sub>T</sub> balance validating the MC10b-based offset correction.


---+ Systematic uncertainties

By comparing the MC-based offset with other offsets derived from the validation techniques described above, we can derive the systematic error in the modeling of the jet p<sub>T</sub> offset from pile-up.  *Note that the application of a MC-based offset correction does not reduce the systematic error, as any difference between data and simulation would persist both before and after applying the correction.*

Comparing MC10b with 2/fb of 2011 data, the derivation of the systematic uncertainty in the effect of pileup on the jet p<sub>T</sub> is described in [[https://indico.cern.ch/getFile.py/access?contribId=8&resId=2&materialId=slides&confId=161038][this presentation]] from John Backus Mayes at the Jet/Etmiss Phone Conference of 9 November 2011.

Caterina Doglioni implemented these uncertainties for release 16 top analyses in JetUncertainties-00-03-04-01, and she updated a few relevant TWiki pages as well:

   * https://twiki.cern.ch/twiki/bin/view/AtlasProtected/TopJetLiaison#JES_uncertainty_for_multi_je_AN1
   * https://twiki.cern.ch/twiki/bin/view/AtlasProtected/MultijetJESUncertaintyProviderTop#UncertaintyCompsPileup
   
This updated uncertainty represents an improvement over the recommendation that was delivered for EPS 2011, as it is generally 1-2% smaller than the previous uncertainty and has a finer pT/eta binning that is more suitable for profiling studies. Please note that this uncertainty does not account for any mismodeling of the effect of pile-up on the jet mass, and thus does not cover the observed non-closure of the JES at low jet p<sub>T</sub>.

Work is ongoing to obtain new uncertainties by comparing MC11a with at least 4/fb of 2011 data in release 17. These should be ready before December 2011.


---+ Deprecated material

%TWISTY{
 mode="div"
 showlink="Show old tower studies"
 hidelink="Hide old tower studies"
 showimgleft="%ICONURLPATH{toggleopen-small}%"
 hideimgleft="%ICONURLPATH{toggleclose-small}%"
 start="hide"
 class="none"
}%
---+!! Effect of pileup on EM Scale jet constituents (Calo,TopoTowers) 

The effect of pileup on 2011 ZeroBias data for periods D-H was studied using un-calibrated, EM scale calorimeter towers. The goal of the study was to first understand the in-time and out-of-time effects of pileup on the towers and then use this information to calculate an offset correction, similar to the pileup offset correction used on 2010 data. 
 
<table width="95%" border="0"><tr><td width="30%" valign="top">
%IMAGE{"h_CaloTower_ET_vs_Eta_formatted.gif"
  type="frame" 
  align="center"
  size="275"
  caption="Average EM Scale calorimeter tower transverse energy as a function of the pseudo-rapidity, binned in NPV "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_CaloTowerET_vs_NPV_gt1000_eta0_0p3_formatted.gif"
  type="frame" 
  align="center"
  size="275"
  caption="Average EM Scale calorimeter tower transverse energy as a function of the number of primary vertices, binned in mu "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_CaloTowerET_vs_DFE_central_formatted.gif"
  type="frame" 
  align="center"
  size="275"
  caption="Average EM Scale calorimeter tower transverse energy as a function of the event's distance from the last empty bunch, binned in mu "
}%
</td></tr></table>

The above plots represent the average effects of pileup on calorimeter towers. For events with lower than average measured interactions, quantized by the number of primary vertices, the average transverse energy is less than zero due to the negative portion of the LAr shaping pulse from the previous bunch crossings (see David Miller's [[JetsWithPileup#Bunch_spacing_and_pile_up_toy_mo][Toy MC]]). As the number of interactions increase, the average transverse energy increases linearly, as shown in the middle figure. The data for the figure in the middle is required to to have been from events sufficiently far away in time from the beginning of the bunch train. This is done to separate the large out-of-time LAr effect seen at the beginning of the train, shown in the figure on the right. When binned in <&mu;>, events at the beginning of the train tend to have increasing transverse energy with increasing <&mu;>, while events lying in the "plateau" region (%$D_{FE}$%&gt;1ns) tend to show decreasing transverse energy with increasing <&mu;>. 

---++!! Tower based correction
The tower based correction is derived from the average change in transverse energy at the tower level with respect to various pileup parameters. The tower level correction is translated to the jet level correction by scaling it by some tower area of the jet. Two possibilities for the tower area are:
   * NumTowers - the moment associated with the jet describing the number of towers that would be associated to a jet.
   * %$\pi R^2 / (0.1)^2 $%- For large R, the number of towers that fit in a cone or circle of radius R (0.4, 0.6). 
 
Currently, closure has only been shown for the %$N_{PV}$% based correction using the latter area above, but results for both (%$N_{PV}$% and%$D_{FE}$%) are shown in the links below. 
   * Presentations outlining the correction
      * DOE site visit at the Santa Cruz Institute for Particle Physics [[%ATTACHURLPATH%/Pileup_Manning_08_07_11.pdf][here]]
      * July Performance week [[%ATTACHURLPATH%/Pileup_Manning_07_12_11.pdf][Initial]] [[%ATTACHURLPATH%/Pileup_Manning_07_26_11.pdf][Update]] [[https://indico.cern.ch/conferenceDisplay.py?confId=146007][Indico]]
   * Validation/Closure Plots for Anti-kt R=0.6,0.6 Topo and Tower jets, comparing the use of NumTowers and absolute tower area (&pi;R*R/
      * [[https://pmanning.web.cern.ch/pmanning/DFEOffset/DFEOffsetCorrection.htm][%$D_{FE}$% Based Correction]]
      * [[https://pmanning.web.cern.ch/pmanning/NPVOffset/NPVOffsetCorrection.htm][%$N_{PV}$% Based Correction]]

   * Implementation in the JetCalibTools package
      * [[https://indico.cern.ch/getFile.py/access?contribId=0&resId=0&materialId=slides&confId=147034][General presentation about software for pileup corrections (Pierre-Antoine Delsart)]]
      * Tested with 17.0.X.Y, but not yet validated. To test, check out the trunk of Reconstruction/Jet/JetCalibTools, https://svnweb.cern.ch/trac/atlasoff/browser/Reconstruction/Jet/JetCalibTools/trunk .
         * For data, edit JetCalibTools/python/SetupJetCalibrator.py <verbatim>
def doEMOffset(finder, mainParam, input, **options):
   ...
   isMC=False
</verbatim>
         * For MC10b, edit JetCalibTools/python/SetupJetCalibrator.py  <verbatim>
def doEMOffset(finder, mainParam, input, **options):
   ...
   isMC=True
</verbatim>
         * Schedule jet reconstruction as usual, requiring calibType to include OFFSET, for example <verbatim>
from JetRec.JetGetters import make_StandardJetGetter
make_StandardJetGetter('AntiKt',0.4, 'Topo', calibName ='EM:ORIGIN_OFFSET',outputCollectionName='AntiKt4TopoEMOFFSETJets')
</verbatim>
%ENDTWISTY%

%TWISTY{
 mode="div"
 showlink="Show Pileup in MC10b - old"
 hidelink="Hide Pileup in MC10b - old"
 showimgleft="%ICONURLPATH{toggleopen-small}%"
 hideimgleft="%ICONURLPATH{toggleclose-small}%"
 start="hide"
 class="none"
}%
---+!!Pileup in MC10b - not-reweighted
The digitization and reconstruction of MC10b is done with the configuration of the bunch train pileup with three trains with 9BC=225ns separation , within trains are 36 filled bunches with 50ns bunch separation and variable pileup rate configuration , where MB means Pythia6 ND+SD+DD mixed minbias channels. For more information, see AtlasProductionGroupMC10b. 
<table width="95%" border="0"><tr><td width="30%" valign="top">
%IMAGE{"h_NVertices_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of primary vertices in ~400K minbias MC10b events. "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_n_trk_out_Ecut_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of tracks outside the leading primary vertex for ~400K minbias MC10b events. "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_NVtx_nTrkOut_Ecut_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of tracks outside the leading PV as a function of the number of PVs for ~400K minbias MC10b events. "
}%
</td></tr></table>

<table width="95%" border="0"><tr><td width="30%" valign="top">
%IMAGE{"mu_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="&lt;mu&gt; - Average number of interactions per bunch crossing. "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_npv_vs_mu_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of primary vertices as a function of &lt;mu&gt;. "
}%
</td><td width="30%" valign="top">
%IMAGE{"h_ntrkout_vs_mu_mc10b_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of tracks outside of the leading PV as a function of &lt;mu&gt;."
}%
</td></tr></table>
%ENDTWISTY%

%TWISTY{
 mode="div"
 showlink="Show Pileup in Data - old"
 hidelink="Hide Pileup in Data - old"
 showimgleft="%ICONURLPATH{toggleopen-small}%"
 hideimgleft="%ICONURLPATH{toggleclose-small}%"
 start="hide"
 class="none"
}%
---+!!Pileup in Data
---+!!Effect of bunch spacing on raw calorimeter energy density
---++!! Comparison between 2010 PeriodI , 2011 run178109 (75ns bs) and run 179153 (50ns bs)
As an initial study, we looked at the differences between the average calorimeter tower energy vs. the number of primary vertices for late 2010 data, early 2011 75ns data and recent 2011 50ns data. While these plots show that there are significant differences between the data periods, it does not illustrate why. It was not clear if the bunch spacing alone was the cause of the differences. The next set of plots shows the differences between several 50ns runs, indicating that the bunch spacing alone is not the cause of the varying average tower energy. 
<table width="95%" border="0"><tr><td width="45%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_0_08.150ns.75ns.50ns.comp.png"
  type="frame" 
  align="center"
  size="300"
  caption=""
}%
</td>
<td width="45%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_32_5.150ns.75ns.50ns.comp.png"
  type="frame" 
  align="center"
  size="300"
  caption=""
}%
</td></tr></table>

---++!! Comparison between several runs with 50ns bunch spacings
As mentioned above, bunch spacing alone does not explain why there is a run-by-run difference in the average calorimeter tower energy, as shown below. 
<table width="95%" border="0"><tr><td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_0_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_1_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_2_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_3_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td></tr>
<tr><td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_4_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_5_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_6_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td>
<td width="25%" valign="top">
%IMAGE{"h_tower_E_NV_Eta_7_50ns_runcomp.png"
  type="frame" 
  align="center"
  size="220"
  caption=""
}%
</td></tr></table>

---+!! Run-by-run luminosity, bunch, and tower based pileup offset information

In order to determine the dependence of the average calorimeter energy, and thus the tower based offset correction, we list all of the quantities of interest in the table below. The plots these numbers are derived from are in the Notes section below. 

|  *Data Period*  |  *[[http://atlas-runquery.cern.ch/query.py?q=arq_110519175250oiis][Run Number]]*  |  *Luminosity*  |||  *&lt;mu&gt;*  |  *RMS(mu)*  |  *Bunch Spacing*  |  *Average Bunch Train Length*  |  *Slope of tower based &lt;Jet ET Offset&gt; vs. NPV (GeV / Vertex) AntiKt4,AntiKt6*  |||||||
|^|^|  Recorded *[1/pb]*  |  [[https://atlas-datasummary.cern.ch/lumicalc/results/1a7810/result.html][L1_J15]] *[1/nb]*  |  [[https://atlas-datasummary.cern.ch/lumicalc/results/931fc4/result.html][EF_zerobias_NoAlg]] *[1/nb]*  |^|^|^|^|  0&lt; &#124;eta&#124; &lt; 0.3  |  3&lt; &#124;eta&#124; &lt; 0.8  |  0.8&lt; &#124;eta&#124; &lt; 1.2  |  1.2&lt; &#124;eta&#124; &lt; 2.1  |  2.1&lt; &#124;eta&#124; &lt; 2.8  |  2.8&lt; &#124;eta&#124; &lt; 3.2  |  3.2&lt; &#124;eta&#124; &lt; 4.5  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=B2&fnt=data11_7TeV][B2]]  |  178044  |  4.7  |  3.5  |  3.1  |  |  |  75ns  |  1727ns  |  0.35, 0.65  |  0.37, 0.69  |  0.39, 0.77  |  0.37, 0.75  |  0.42, 0.89  |  0.54, 1.2  |  0.35, 0.80  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=B2&fnt=data11_7TeV][B2]]  |  178109  |  6.5  |  4.8  |  4.3  |  |  |  75ns  |  1727ns  |   |  |  |  |  |  |  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D1&fnt=data11_7TeV][D1]]  |  179710  |  4.3  |  4.4  |  2.1  |  5.9  |  1.4  |  50ns  |  1651ns  |  0.50, 0.92  |  0.51, 0.95  |  0.53, 1.0  |  0.49, 0.99  |  0.58, 1.2  |  0.71, 1.6  |  0.36, 0.86  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D2&fnt=data11_7TeV][D2]]  |  179804  |  7.4  |  5.4  |  3.7  |  6.4  |  1.5  |  50ns  |  1701ns  |  0.51, 0.94  |  0.52, 0.97  |  0.54, 1.1  |  0.51, 1.0  |  0.58, 1.2  |  0.73, 1.6  |  0.38, 0.86  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D3&fnt=data11_7TeV][D3]]  |  180124  |  7.6  |  5.3  |  3.8  |  5.1  |  1.2  |  50ns  |  1704ns  |  0.44, 0.79  |  0.46, 0.84  |  0.46, 0.91  |  0.44, 0.87  |  0.52, 1.1  |  0.64, 1.4  |  0.35, 0.86  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D3&fnt=data11_7TeV][D3]]  |  180139  |  7.7  |  3.4  |  3.8  |  6.1  |  1.1  |  50ns  |  1704ns  |  0.47, 0.84  |  0.47, 0.86  |  0.48, 0.93  |  0.45, 0.89  |  0.53, 1.1  |  0.65, 1.4  |  0.38, 0.88  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D4&fnt=data11_7TeV][D4]]  |  180153  |  8.8  |  6.0  |  4.4  |  5.4  |  1.2  |  50ns  |  1704ns  |  0.44, 0.79  |  0.46, 0.85  |  0.48, 0.91  |  0.46, 0.89  |  0.53, 1.1  |  0.65, 1.4  |  0.40, 0.87  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D4&fnt=data11_7TeV][D4]]  |  180164  |  19.1  |  9.8  |  9.6  |  5.8  |  1.3  |  50ns  |  1704ns  |  0.50, 0.91  |  0.51, 0.94  |  0.54, 1.0  |  0.49, 0.98  |  0.58, 1.2  |  0.72, 1.5  |  0.40, 0.88  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D5&fnt=data11_7TeV][D5]]  |  180225  |  17.1  |  10.2  |  8.5  |  5.3  |  1.1  |  50ns  |  2833ns  |  0.36, 0.67  |  0.38, 0.70  |  0.39, 0.75  |  0.39, 0.76  |  0.45, 0.93  |  0.57, 1.2  |  0.38, 0.84  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D6&fnt=data11_7TeV][D6]]  |  180309  |  9.5  |  2.9  |  4.8  |  6.7  |  0.9  |  50ns  |  2833ns  |  0.38, 0.71  |  0.41, 0.74  |  0.40, 0.80  |  0.40, 0.79  |  0.47, 0.97  |  0.58, 1.3  |  0.40, 0.87  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D6&fnt=data11_7TeV][D6]]  |  180400  |  14.5  |  2.8  |  3.5  |  6.2  |  1.0  |  50ns  |  3318ns  |  |  |  |  |  |  |  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=D7&fnt=data11_7TeV][D7]]  |  180481  |  21.1  |  4.2  |  5.4  |  6.0  |  1.1  |  50ns  |  3318ns  |  0.38, 0.68  |  0.38, 0.70  |  0.39, 0.75  |  0.39, 0.76  |  0.45, 0.92  |  0.57, 1.2  |  0.35, 0.83  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=E1&fnt=data11_7TeV][E1]]  |  180636  |  24.1  |  5.1  |  6.6  |  5.8  |  1.1  |  50ns  |  3318ns  |  0.35, 0.64  |  3.36, 0.66  |  0.37, 0.72  |  0.37, 0.71  |  0.43, 0.87  |  0.54, 1.1  |  0.36, 0.77  |  
|  [[https://atlddm10.cern.ch/tagservices/RunBrowser/runBrowserReport/runBrowserReport.php?pn=E1&fnt=data11_7TeV][E1]]  |  180710  |  12.1  |  1.8  |  6.8  |  7.1  |  0.9  |  50ns  |  3084ns  |  0.34, 0.60  |  0.33, 0.63  |  0.35, 0.68  |  0.35, 0.69  |  0.40, 0.81  |  0.51, 1.1  |  0.35, 0.78  |  

---+++!!Notes:

   * [[http://atlas-runquery.cern.ch/query.py?q=arq_110519175250oiis][Trash.AtlasRunQuery result for these runs]] (cached), including trigger information, luminosity and LHC info.
   * The "Average Bunch Train Length" is a weighted average, accounting for the probability that a given event is in a given bunch train.  (We assume that all bunches are equally intense, which is not a very good approximation.)  
      * Thus, the probability of an event occurring within the first 400ns of a bunch train is just the ratio of 400ns to this average length.
   * The luminosities are calculated using iLumiCalc:
      * [[https://atlas-datasummary.cern.ch/lumicalc/results/1a7810/result.html][iLumiCalc results page for L1_J15]].
      * [[https://atlas-datasummary.cern.ch/lumicalc/results/931fc4/result.html][iLumiCalc results page for EF_zerobias_NoAlg]].
      * [[%ATTACHURL%/data11_7TeV.periodAllYear_DetStatus-v13-pro08-02_JetEtMiss-OFFSET.xml][GRL for only these runs]].
         * This is a derivative of the =data11_7TeV.periodAllYear_DetStatus-v13-pro08-02_JetEtMiss.xml= GRL obtained from [[http://atlasdqm.web.cern.ch/atlasdqm/grlgen/CombinedPerf/JetEtMiss/JetEtMiss_v01/][the GRL generator page here]]).
%IMAGE{"OffsetAnalysis_mu_L1J15_ZB_overlay.png"
  type="frame" 
  align="center"
  size="320"
  caption="Overlay of the average mu per LB distribution for the runs listed above separately for the L1_J15 and ZeroBias triggers. The mean and RMS of each distribution is also listed."
}%

   * While the run-by-run information is shown above, the average offset vs. NPV slopes will be used for the pileup uncertainty estimate for the summer conference. For reference, below are the average (over all 50ns runs) constituent multiplicity for AntiKt4 and AntiKt6 TopoTower jets: 
<table width="95%" border="0"><tr><td width="45%" valign="top">
%IMAGE{"nConst_vs_eta_akt4_ZeroBias.png"
  type="frame" 
  align="center"
  size="320"
  caption="Number of constituents for AntiKt4Tower jets with pT>20GeV in the ZeroBias stream, averaged over all 50ns runs listed above."
}%
</td><td width="45%" valign="top">
%IMAGE{"nConst_vs_eta_akt6_ZeroBias.png"
  type="frame" 
  align="center"
  size="320"
  caption="Number of constituents for AntiKt6Tower jets with pT>20GeV in the ZeroBias stream, averaged over all 50ns runs listed above."
}%
</td></tr></table>
   * With the average constituent multiplicities above and the average tower level E_T offset (below left), the average jet E_T offsets are shown below. 
<table width="95%" border="0"><tr><td width="30%" valign="top">
%IMAGE{"offset_tower_energy_et.png"
  type="frame" 
  align="center"
  size="275"
  caption="Average tower-level transverse energy offset derived from CaloTowers"
}%
</td><td width="30%" valign="top">
%IMAGE{"offset_jet_energy_et_akt4.png"
  type="frame" 
  align="center"
  size="275"
  caption="Average jet level transverse energy offset derived from AntiKt4Tower jets."
}%
</td><td width="30%" valign="top">
%IMAGE{"offset_jet_energy_et_akt6.png"
  type="frame" 
  align="center"
  size="275"
  caption="Average jet level transverse energy offset derived from AntiKt6Tower jets."
}%
</td></tr></table>

These plots can then be combined in a more useful form, the average jet transverse energy offset as a function of NPV for 7 eta bins, as shown below. These plots represent all of the 50ns data above modulo run 180400. 
<table width="95%" border="0"><tr><td width="45%" valign="top">
%IMAGE{"h_data_jet_energy_offset_vs_NV_fit_akt4_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Average jet level transverse energy offset derived from AntiKt4Tower jets as a function of NPV"
}%
</td><td width="45%" valign="top">
%IMAGE{"h_data_jet_energy_offset_vs_NV_fit_akt6_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="Average jet level transverse energy offset derived from AntiKt6Tower jets as a function of NPV"
}%
</td></tr></table>
---+!!2011 Jet Pileup uncertainty from the RMS bias between data and MC10a
While we are not in a position to provide a pileup offset correction, it is possible to characterize the uncertainty on the JES calibration due to pileup in the 2011 data. To do this, we compare the difference between the average change in jet transverse energy pileup offset per additional vertex (Average Jet ET offset/NPV) between 50ns 2011 data and currently, MC10a minbias events. This comparison is shown in the below plot, which is derived from the previous two plots as well as the analogous ones for MC10a. 
%IMAGE{"h_slope_eta_formatted_final.png"
  type="frame" 
  align="center"
  size="320"
  caption="Comparison of the average jet ET offset per NPV as a function of the pseudorapidity between 50ns 2011 Data and MC10a events. "
}%

With this information as well as the average number of vertices in the 50ns data and the width of this distribution, shown below, we can define a positive and negative RMS bias, defined as:

<latex title="RMSBias" size="small">
RMS\pm = (<offset>/NV(data) - <offset>/NV(MC10a))*( <NV> \pm RMS_{NV}-NV_{ref})
</latex>

Below are the calculated RMS biases between the 50ns data and MC10a for AntiKt4 and AntiKt6 Tower jets at EM scale for a %$NV_{ref}=3$%, chosen because for this number of vertices, the average calorimeter tower energy is closest to zero, %$<NV>=\lambda$% and %$RMS_{NV}=\sqrt{\lambda}$%. Using the difference between the negative and positive bias with the current EM+JES calibration, a relative jet pileup uncertainty can be calculated for jets of various %$p_{T}$% in the defined %$\eta$% regions.  

<table width="95%" border="0"><tr><td width="30%" valign="top">
%IMAGE{"NVertices_fit.png"
  type="frame" 
  align="center"
  size="275"
  caption="Number of vertices in the 50ns data with a Poisson fit to extract the average and RMS"
}%
</td><td width="30%" valign="top">
%IMAGE{"h_RMS_akt4_slope_eta_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="RMS bias for AntiKt4Tower jets at EM Scale"
}%
</td><td width="30%" valign="top">
%IMAGE{"h_RMS_akt6_slope_eta_formatted.png"
  type="frame" 
  align="center"
  size="275"
  caption="RMS bias for AntiKt6Tower jets at EM Scale"
}%
</td></tr></table>

%ENDTWISTY%

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Topic revision: r6 - 2011-11-10 - JohnBackusMayes
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