CMS Data Analysis School Tracking and Vertexing Short Exercise - Tracks as particles

Overview

Teaching: 10 min
Exercises: 10 min

Questions

• Can we consider a track as a particle?

• Can I use an alternative to the muon object?

• Can I define the invariant mass of two tracks?

Objectives

• Being familiar with the tracks, particle and identification concepts.

• Plot distributions of variables related to a muon resonance.

Unlike calorimeter showers, tracks can usually be interpreted as particle 4-vectors without any additional corrections. Detector alignment, non-helical trajectories from energy loss, Lorentz angle corrections, and (to a much smaller extent) magnetic field inhomogeneities are important, but they are all corrections that must be applied during or before the track-reconstruction process. From an analyzer’s point of view, most tracks are individual particles (depending on quality cuts) and the origin and momentum of the particle are derived from the track’s geometry, with some resolution (random error). Biases (systematic offsets from the true values) are not normal: they’re an indication that something went wrong in this process. The analyzer does not even need to calculate the particle’s momentum from the track parameters: there are member functions for that. Particle’s transverse momentum, momentum magnitude, and all of its components can be read through the following lines (let’s name this new file kinematics.py and create it in TrackingShortExercize/):

import DataFormats.FWLite as fwlite
import ROOT
import math

events = fwlite.Events("/eos/user/c/cmsdas/2023/short-ex-trk/run321167_ZeroBias_AOD.root")
tracks = fwlite.Handle("std::vector<reco::Track>")

for i, event in enumerate(events):
    event.getByLabel("generalTracks", tracks)
    for track in tracks.product():
        print track.pt(), track.p(), track.px(), track.py(), track.pz()
    if i > 20: break

Question 1

Now we can use this to do some kinematics. Assuming that the particle is a pion (pion mass = 0.140 GeV), calculate its kinetic energy.

Answer

import DataFormats.FWLite as fwlite
import ROOT
import math

events = fwlite.Events("/eos/user/c/cmsdas/2023/short-ex-trk/run321167_ZeroBias_AOD.root")
tracks = fwlite.Handle("std::vector<reco::Track>")

for i, event in enumerate(events):
    event.getByLabel("generalTracks", tracks)
    for track in tracks.product():
        print track.pt(), track.p(), track.px(), track.py(), track.pz()
        print "energy: ", math.sqrt(0.140**2 + track.p()**2)
    if i > 20: break

Additional information

Identifying the particle that made the track is difficult: the mass of some low-momentum tracks can be identified by their energy loss, called dE/dx, and electrons and muons can be identified by signatures in other subdetectors. Without any other information, the safest assumption is that a randomly chosen track is a pion, since hadron collisions produce a lot of pions.

Let’s look for resonances. Given two tracks,

if len(tracks.product()) > 1:

one = tracks.product()[0]
two = tracks.product()[1]

the invariant mass may be calculated as

total_energy = math.sqrt(0.140**2 + one.p()**2) + math.sqrt(0.140**2 + two.p()**2)
total_px = one.px() + two.px()
total_py = one.py() + two.py()
total_pz = one.pz() + two.pz()
mass = math.sqrt(total_energy**2 - total_px**2 - total_py**2 - total_pz**2)

However, this quantity has no meaning unless the two particles are actually descendants of the same decay. Two randomly chosen tracks (out of hundreds per event) typically are not.

To increase the chances that pairs of randomly chosen tracks are descendants of the same decay, consider a smaller set of tracks: muons. Muons are identified by the fact that they can pass through meters of iron (the CMS magnet return yoke), so muon tracks extend from the silicon tracker to the muon chambers (see CMS quarter-view below), as much as 12 meters long! Muons are rare in hadron collisions. If an event contains two muons, they often (though not always) come from the same decay.

Normally, one would access muons through the reco::Muon object since this contains additional information about the quality of the muon hypothesis. For simplicity, we will access their track collection in the same way that we have been accessing the main track collection. We only need to replace generalTracks with globalMuons. Add the following loop to kinematics.py.

events.toBegin()
for i, event in enumerate(events):
    if i >= 15: break            # only the first 15 events
    print "Event", i
    event.getByLabel("globalMuons", tracks)
    for j, track in enumerate(tracks.product()):
        print "    Track", j, track.charge()/track.pt(), track.phi(), track.eta(), track.dxy(), track.dz()

Run this code on the run321167_Charmonium_AOD.root file that you can copy with:

cp /eos/user/c/cmsdas/2023/short-ex-trk/run321167_Charmonium_AOD.root $TMPDIR

Notice how few muon tracks there are compared to the same code executed for generalTracks. In fact, you only see as many muons as you do because this data sample was collected with a muon trigger. (The muon definition in the trigger is looser than the globalMuons algorithm, which is why there are some events with fewer than two globalMuons.) See in the Appendix an application for the Muon and Tracks objects usage in the CMS tracking efficiency computation.

Question 2

As an exercise, make a histogram of all di-muon masses from 0 to 5 GeV. Exclude events that do not have exactly two muon tracks, and note that the muon mass is 0.106 GeV). Create a file dimuon_mass.py in TrackingShortExercize/ for this purpose.

More…

The solution combines several of the techniques introduced above:

import math
import DataFormats.FWLite as fwlite
import ROOT

events = fwlite.Events("/eos/user/c/cmsdas/2023/short-ex-trk/run321167_Charmonium_AOD.root")
tracks = fwlite.Handle("std::vector<reco::Track>")
mass_histogram = ROOT.TH1F("mass", "mass", 100, 0.0, 5.0)

events.toBegin()
for event in events:
    event.getByLabel("globalMuons", tracks)
    product = tracks.product()
    if product.size() == 2:
        one = product[0]
        two = product[1]
        if not (one.charge()*two.charge() == -1):  continue
        energy = (math.sqrt(0.106**2 + one.p()**2) +
                  math.sqrt(0.106**2 + two.p()**2))
        px = one.px() + two.px()
        py = one.py() + two.py()
        pz = one.pz() + two.pz()
        mass = math.sqrt(energy**2 - px**2 - py**2 - pz**2)
        mass_histogram.Fill(mass)

c = ROOT.TCanvas ("c", "c", 800, 800)
mass_histogram.Draw()
c.SaveAs("mass.png")

The histogram should look like this:

If so, congratulations! You’ve discovered the J/ψ!

Key Points

• Tracks give us a direct handle on actual particles, thus they can easily be used to reconstruct other particles in the event