add matching ep

_episodes/05-Matching.md

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+---
+title: "Matching trigger objects"
+teaching: 10
+exercises: 0
+objectives:
+- "Learn how to access the trigger information stored in MiniAOD and NanoAOD"
+- "Learn what is trigger objects and how to access them"
+- "Measure trigger efficiency using the tag-and-probe method"
+---
+
+## Match trigger objects to offline objects
+
+Trigger objects are physics objects(electrons,muons,jets,MET..etc) reconstructed at HLT and are used for making HLT decisions of each HLT path.
+Offline objects are reconstructed offline, which in general has more precise reconstructions.
+If we want to know whether an offline object(e.g. a muon) is responsible for firing the HLT, we can look for a trigger muon within a certain `dR` of the offline muon.
+
+### Collection names 
+We can learn from the example in the `analyze` function in `SingleMuTrigAnalyzerMiniAOD.cc.` 
+The offline objects are reconstructed primary vertices (offlineSlimmedPrimaryVertices) and offline-reconstructed muons (slimmedMuons). 
+The trigger object is `trigMuons`, which we obtained from the `TriggerObjectStandAloneCollection` from last episode. 
+Here we are not interested in primary vertices per se, we just need to get them because later we will use them in identification of "tight" muons.
+
+### Matcing by momentum direction `dR`
+
+> Take a look at lines 231-286 in SingleMuTrigAnalyzerMiniAOD.cc, where you can find two for loops that iterate over the offline muons.
+{: .callout}
+
+Since the second for loop is inside the first one, together these two for loops are going over all possible pairs of offline muons. 
+The first muon in each pair is called "tag", and the second is called "probe", for reasons that will soon become apparent. 
+Inside the loop, several selection criteria are placed on muons, such as cuts on pt and eta, tight identification, and isolation requirements.
+
+Now that we have both trigger-level muons and offline-reconstructed muons, we can compare them with each other. 
+In order to do this, we need to figure out which trigger muon corresponds to which offline muon. This is called *trigger matching*.
+In the code, trigger matching is performed both for tag muons ([lines 245-248](https://github.com/FNALLPC/LPCTriggerHATS/blob/master/ShortExerciseTrigger/plugins/SingleMuTrigAnalyzerMiniAOD.cc#L245-L248)) and probe muons ([lines 277-280](https://github.com/FNALLPC/LPCTriggerHATS/blob/master/ShortExerciseTrigger/plugins/SingleMuTrigAnalyzerMiniAOD.cc#L277-L280)). 
+For tag muons, the matching code looks like this:
+~~~
+   bool trigmatch_tag = false;
+   for (unsigned int itrig=0; itrig < trigMuons.size(); ++itrig) {
+      if (ROOT::Math::VectorUtil::DeltaR(muon_tag->p4(),trigMuons.at(itrig)) < dr_trigmatch) trigmatch_tag = true;
+   }
+~~~
+Since reconstruction of muon trajectory is less precise in HLT than in offline reconstruction, there might be a small difference between the directions of the trigger muon and the offline muon, even if they correspond to the same original real muon. 
+Therefore a DeltaR cone of 0.2 is used to geometrically match the trigger object and the offline object (`dr_trigmatch = 0.2`).
+
+Finally, if the two muons pass the selections in the code, and the tag muon passes the trigger matching, the invariant mass of this dimuon system is calculated and saved in a histogram:
+~~~
+     LorentzVector dimuon = LorentzVector(muon_tag->p4() + muon_probe->p4());
+     hists_1d_["h_mll_allpairs"]->Fill(dimuon.M());
+     if (verbose_) cout << " - probe dimuon mass: " << dimuon.M()  << endl;
+     if (dimuon.M() < 81. || dimuon.M() > 101.) continue;
+     hists_1d_["h_mll_cut"]->Fill(dimuon.M());
+~~~
+
+> Use the `TBrowser` to open the file `histos_SingleMuTrigAnalyzer.root` and have a look at the histogram `h_mll_allpairs`, which shows the dimuon invariant mass distribution of muon pairs that passed the selections. 
+> Can you explain the shape of the distribution?
+{: .challenge}
+
+{% include links.md %}
+