Particle physics - exercise 1d solution

Repository

• Madanalysis 5: https://launchpad.net/madanalysis5
• @lemouth's exercises: https://github.com/BFuks/mad5-utopian-exercises

Introduction

This post is my implementation of @lemouth's fourth exercise in his series aiming at getting voluntary contributions from software developers and Utopian-io to help in producing open-source software providing physics analysis testing new theories stretching beyond the Standard Model.
The objectives of the project are described in @lemouth's first post in this series.

View of the CMS endcap through the barrel sections.
Image credits - Julian Williams on Wikipedia]

Post Body

For this last exercise, @lemouth introduced us to the concept of cutflows.

A cutflow is a list of event selection strategy which ensure that selected events meet certain criteria to ascertain signal quality and ensure that minimum characteristics are satisfied for the target of the experimentation.
For example, events must present a large amount of missing energy to be candidates for the search for Dark Matter.

Cutflows must also kill undesirable background events while keeping signals of interest as untouched as possible. Losing signal in the process is unavoidable but must be kept to a minimal level.

As always for these exercises, the Madanalysis5 framework is relied upon to extract event information from sample files and provide the analysis development with key programmatic utilities such as calculating transverse momentum and missing energy.

Missing Energy

With this exercise we were also introduced to the concept of missing energy.
This is the energy not detected during experimentation but is expected with the laws of conservation of energy and momentum.

Missing energy is in principle carried by particles that do not interact with the electromagnetic and strong forces and, for this reason, is difficult to detect.

This energy can be carried in large parts by neutrinos but can also be taken as a a clue that may go towards validating new theories beyond the Standard Model

While the total amount of energy involved in an event is hard to measure, the energy carried in the transverse direction of the beam axis is initially zero. For this reason the energy measured in the transverse direction (ET) also indicates the amount of missing energy (MET) by applying the principle of conservation of energy.

Search for Dark Matter

In the research paper at the center of this exercise, the writers describe how Dark Matter (DM) may be produced in proton-proton collisions in the Large Hadron Collider and how this Dark Matter may result in a large amount of missing transverse momentum p_T^miss.

The paper also provides in its introduction the summary of a couple of different models predicting the production of DM particles along with a single photon with large transverse momentum.

The analysis thus focuses on selecting events with large missing transverse energy and a signal photon with large transverse momentum.

As always, some cleaning up of the sample events is to be implemented in order to get rid of particle detection overlap and ensure object isolation.

Cutflow Implemented in this Exercise

The cutflow described in section 3 of the research paper is as follows. Each selected event must pass the following cuts:

• Missing transverse moment p_T^miss must be at least 170 GeV.
• At least one photon with transverse momentum p_T^γ greater than 175 GeV and pseudo-rapidity |η| < 1.44
• Minimum opening angle between missing transverse momentum and any of the four highest transverse momenta jets greater than 0.5 (for jets with p_T > 30GeV and |η| < 5)
• Signal photon p_T^γ and p_T^miss are separated by at least 2 radians.
• electrons and muons with p_T > 10 GeV must be separated from signal photon with ΔR > 0.5

From the above, I added the following cuts to the Initialize method:

  Manager()->AddCut("pTmiss");
  Manager()->AddCut("dPhi(pT(miss), pT(jet))");
  Manager()->AddCut("pt_photon > 175 & |n| < 1.44");
  Manager()->AddCut("dPhi(pT(miss), pT(photon))");
  Manager()->AddCut("DR(electron, signal_photon)");
  Manager()->AddCut("DR(muon, signal_photon)");

The Execute method was then updated with the following steps:

Apply cut for p_T^miss:

  if(!Manager()->ApplyCut(event.rec()->MET().momentum().Pt() > 170,
                          "pTmiss"))
  {
    return true;
  }

Extract jets (see above):
Note that I preserved the code from the last exercise with regards to generate histograms.

  bool found = false;
  std::vector<const RecJetFormat*> signal_jets;
  for (auto &jet : event.rec()->jets())
  {
    if (jet.pt() > 30 && jet.abseta() < 5)
    {
      if (!found)
      {
        Manager()->FillHisto("pt_jets", jet.pt());
        Manager()->FillHisto("n_jets", jet.eta());
        found = true;
      }
      signal_jets.push_back(&jet);
      cout << "Adding jet - Pt = " << jet.pt() << ", |n| = " << jet.eta() << endl;
    }
  }

Remove jets electrons overlap:
I used here the JetCleaning method provided by Madanalysis on electrons (not necessary on muons).

  for (auto &electron : event.rec()->electrons())
{
    double eta = electron.abseta();
    double pt = electron.pt();
    double iso_var = PHYSICS->Isol->eflow->sumIsolation(electron,
                                                        event.rec(),
                                                        0.4,
                                                        0.,
                                                        IsolationEFlow::ALL_COMPONENTS);
    if( (eta > 1.44) and (eta<1.57) ) continue;
    if(eta > 2.5) continue;
    if(iso_var>0.15*pt) continue;
    if (pt>10) electrons.push_back(&electron);
}
  signal_jets = PHYSICS->Isol->JetCleaning(signal_jets, electrons, 0.2);

Clean muons:

  for (auto &muon : event.rec()->muons())
  {
    double eta = muon.abseta();
    double pt = muon.pt();
    double iso_var = PHYSICS->Isol->eflow->sumIsolation(muon,
                                                        event.rec(),
                                                        0.4,
                                                        0.,
                                                        IsolationEFlow::TRACK_COMPONENT);
    if(eta > 2.4) continue;
    if(iso_var>0.20*pt) continue;
    if (pt>10) muons.push_back(&muon);
  }

Check that at least one photon meets p_T^γ > 175 GeV and |η| < 1.44:

 if(!Manager()->ApplyCut(
    std::none_of(event.rec()->photons().begin(), event.rec()->photons().end(),
                 [](const RecPhotonFormat& photon) { return photon.pt() > 175 && photon.abseta() < 1.44; }),
    "pt_photon > 175 & |n| < 1.44"))
  {
    return true;
  }

Isolate signal photon:
This was done using Table 3 selection criteria in the research paper with the same implementation as in the last exercise.

Verify opening angle between missing transverse momentum and signal photon is greater than 2 radians:

  if(!Manager()->ApplyCut(signal_photon->dphi_0_pi(event.rec()->MET().momentum()) < 2,
                          "dPhi(pT(miss), pT(photon))"))
  {
    return true;
  }

ΔR between electrons/muons (with pT > 10 GeV) and signal photon:

  if(!Manager()->ApplyCut(
    std::any_of(event.rec()->electrons().begin(), event.rec()->electrons().end(),
                  [&signal_photon](const RecLeptonFormat& electron) {
                    return electron.pt() > 10 && electron.dr(signal_photon) > 0.5;
                  }),
      "DR(electron, signal_photon)"))
  {
    return true;
  }

  if(!Manager()->ApplyCut(
    std::any_of(muons.begin(), muons.end(),
                  [&signal_photon](const RecLeptonFormat* muon) {
                    return muon->pt() > 10 && muon->dr(signal_photon) > 0.5;
                  }),
      "DR(*muon, signal_photon)"))
  {
    return true;
  }
  return true;
}

Note that while doing this exercise I discovered the std::none_of and std::any_of methods provided by the C++ standard library.
These proved any to reduce the code size and make it more explicit.

Execution on Sample File

At the time of this writing @lemouth hasn't had the chance yet to provide a suitable sample file.

As I'm due to go abroad for a few days pretty soon I release this code without being to execute it against such file.

Resources

• Particle physics @ Utopian-io - Designing an LHC search strategy for unraveling new phenomena - @lemouth's fourth exercise.
• Search for new physics in the monophoton final state in proton-proton collisions at √ s = 13 TeV
• Madanalysis 5
• Missing Energy - Wikipedia
• Standard Model - Wikipedia

Madanalysis Credits:
E. Conte, B. Fuks and G. Serret,
Comput. Phys. Commun. 184 (2013) 222
http://arxiv.org/abs/1206.1599

E. Conte, B. Dumont, B. Fuks and C. Wymant,
Eur. Phys. J. C 74 (2014) 10, 3103
http://arxiv.org/abs/1405.3982

B. Dumont, B. Fuks, S. Kraml et al.,
Eur. Phys. J. C 75 (2015) 2, 56
http://arxiv.org/abs/1407.3278

Series Backlinks

• Particle Physics - @lemouth exercise 1a
• Particle Physics - @lemouth exercise 1b
• Particle physics - exercise 1c solution (CORRECTED)