A photon is detected as energy in the electromagnetic calorimeter, with little energy in the hadronic calorimeter, and no track pointing at the calorimeter cell. Isolation cuts are used to reduce the backgrounds, mainly from pi-zero decays.

PGS finds photons by starting with a a calorimeter cluster seed, and then imposing cuts. To be considered as a seed cluster, the calorimeter cell must pass a cut on transverse energy, E_T=E_cal sin \theta. Photons can be found out to an eta of 3.0, as described in the Detector Parameters.

• The E_T of the photon > 5 GeV

Once the candidate calorimeter cell is identified, PGS checks for other nearby activity. This is how experiments distinguish true photons from those arising from decays of pi⁰ ‘s in jets, e.g.

1. The total transverse calorimeter energy in a (3×3) grid around the candidate photon (excluding the candidate cell) is defined as ETISO. PGS then imposes:
   • ETISO / E_T(candidate) < .1
2. The total number of tracks with P_T > 0.5 GeV within a Delta R = \sqrt{ \delta \eta² + \delta \phi²} < 0.40 cone is defined as NISO. The total P_T of these tracks is denoted PTISO. These must satisfy:
   • PTISO < 5 GeV
   • NISO < = 1
3. There is a further cut on the tracks pointing to the calorimeter cell. This distinguishes candidate photons (no track) from electrons (track).
   • P_T(candidate track) < 1 GeV.
4. Finally, the ratio of the energy deposited in the hadronic calorimeter to the energy deposited in the EM calorimeter is defined as HADEM. This must satisfy:
   • HADEM < 0.125

Note that HADEM is given as part of the Olympics output. In principle, you might use this information to modify the cuts in some way.

An electron is detected as energy in the electromagnetic calorimeter, with little energy in the hadronic calorimeter, with an isolated track pointing at the calorimeter cell. Electron isolation cuts are used to reduce backgrounds, mainly from a charged pion track pointing at a calorimeter cell with a photon from a pi-zero decay.

Leptons are a very important sign of potential new physics, since, naively, QCD processes don’t generate leptons. But this isn’t really true. Jets generate leptons, or apparent leptons, in several ways. First, a charged pion overlaid on a pi-zero, which decays to two photons, can look just like an electron: a track with electromagnetic energy. Most of the time there’s hadronic energy too, which disfavors identifying this as an electron, but fluctuations happen and sometimes the hadronic energy isn’t registered. So we get a “fake” electron. It’s harder to fake muons, but not impossible. Of course, a fake electron will generally be inside, or near, a jet, since other hadrons typically will accompany the pion-fake-electron. So if we demand the electron be isolated — that there be no nearby tracks or energy in the calorimeter — we are probably looking at a real electron. Probably.

Another way to get an electron or muon is from the production of a bottom or charm quark, which has a certain probability of decaying to a lepton. Such a lepton typically is also inside a jet formed from the rest of the shower of particles that are created as the bottom quark discovers it is confined. But the kick from the bottom quark decay tends to knock the leptons out of the jets a little bit, and occasionally they will be isolated enough to be indistinguishable from “prompt” leptons from W bosons, or Z bosons, or other new sources. Again, an isolation requirement reduces, though it does not eliminate, the chance of mistaking a prompt lepton from one that comes from a nearby heavy quark jet.

Lepton isolation requirements are generally different for electrons and muons, and in any case the efficiency with which a detector detects muons and electrons will be different. Do not expect the numbers of muons and electrons to be equal, even within a standard model calibration sample! Instead, you need to learn something about how the lepton isolation efficiency affects signals in order to draw correct conclusions about the underlying physics.

As in the case of the photon, a candidate electron must statisfy

• E_T > 5 GeV

Electrons can be found out to an eta of 3.0, as described in the Detector Parameters. In addition, it must pass the isolation cuts below.

1. The total transverse calorimeter energy in a (3×3) grid around the candidate electron (excluding the candidate cell) is defined as ETISO. PGS then imposes:
   • ETISO / E_T(candidate) < .1
2. The total P_T of tracks with P_T > 0.5 GeV within a Delta R = \sqrt{ \delta \eta² + \delta \phi²} < 0.40 cone is defined PTISO. In this case, this excludes the leading electron track. It must satisfy:
   • PTISO < 5 GeV
3. There is a cut on the ratio of the calorimeter cell energy to the P_T of the candidate track, EP:
   • 0.5 < EP < 1.5

A muon leaves little energy in the calorimeters, has a track, and travels all the way to the muon-detection system outside the calorimeters.

At present, PGS does not impose any cuts on a muon, except for asking it to leave a track. This results in an important source of muons that do not arise from high-pT events: the semi-leptonic decays of heavy quarks. In particular, transitions of the type b → c mu nu_mu and c → s mu nu_mu can occur within a jet. PGS will still report these as muons. Muons are found in PGS4 out to eta of 2.4, as described in the detector parameter file.

To identify “true muons”, an isolation cut is usually placed on muons, usually placing a limit the total hadronic activity near a muon. While PGS4 does not do that by default, the output includes some information about whether or not the muon is isolated in the hadem column for the muon. At this point, it is up to the user to decide how to treat muon isolation. Cuts can be placed using your favorite analysis software (an example using Chameleon is in the template file.)

Alternately, a "data cleaning" script is included on the webpage that will use this information to make a default set of muon isolation cuts if desired. If one calls

clean_olympics -muon lhcdata.in lhcdata.out

The script will go through the lhcdata.in file looking for muons that fail the isolation cut. As far as the cleaning script is concerned, the muon can fail the isolation cut in two ways:

• If ptiso, the summed p_T in a R=0.4 cone around the muon (excluding the muon itself), is ptiso > 5.0 GeV
• If etrat, the ratio of E_T in a 3×3 calorimeter array around the muon (including the muon’s cell) to the p_T of the muon is etrat > 0.1125.

If the muon fails the isolation cut in either of these ways, the cleaning script will combine it with the jet that is closest in Delta R (recorded in the whole number place in the btag column). The script will remove muon from the event record, and will add its four-vector to that of the jet. The jet’s eta, phi and p_T are modified appropriately, and the number of tracks in the jet is incremented by 1.1 in the “cleaned” event record. This makes it easy to see how many muons reside in a given jet. An enterprising user might try to develop a heavy-flavor tag based on this information.

Users may prefer to not run the cleaning script to preserve the muon information, in which case they should consider imposing their own isolation cut after the fact. It should be recognized that this cleaning script is a very crude implentation of muon isolation, and thoughts about more sophisticated treatments are welcome. For example, you could use the information that there is a jet nearby with a b-tag or a large track multiplicity as a part of a veto. You might also wish to try playing with the ptiso and etrat veto levels. A different combination mechanism, perhaps based on kT distance, could also be implemented.

Remember, unless you run the cleaning script, there are no isolation cuts placed on muons, and you should take this into account! (btw: One of the reasons not to remove muons from the event is that a user might wish to try and see whether a muon pair reconstructed a Z-boson. Even if the muons accidentally are close to hadronic activity, one could be fairly certain that the muons are “real”, and not from semi-leptonic decay of heavy jets.)

The current version of PGS implements a kT algorithm.

Jets are the most common and most problematic objects in hadronic collider physics. Crudely, jets are defined to be a collection of particles as detected by the calorimeters that are either spatially clustered (in azimuth and pseudorapidity) or clustered via some invariant measure (such as a pairwise invariant mass).

For the PGS detector simulations used here, in contrast to the previous version used in the Olympics which used cone-jets LINK, jets are defined using a cluster-based kT algorithm. Detailed background on kT algorithms can be found, e.g., here.

Basically, a kT clustering algorithm proceeds in the following steps:

• It calculates the distance between any two clusters pairs (i,j) = d_ij
• It calculates the distance between any cluster and the beam = d_{i Beam}
• Then comes merging:
  • If the smallest d_ij is less than the smallest d_{i Beam} then objects i and j are combined, and distances are recalculated.
  • Else the object i with the minimum d_{i Beam} is called a jet and removed from the list.
• This repeats until all clusters are in jets.

The particular implementation of the kT algorithm in PGS4 uses the following distance definitions:

• d_ij=min(pT²_i, pT²_j) * (Delta R_ij)²/R_cone²
• d_{i Beam} = pT_i²

with R_cone=0.5.

The jet 4-vector is defined treating each cell within the jet as a massless particle. As noted above, the kT criterion for associating particles to jets is scaled by a spatial cone size, which has been set to R_cone=0.5. The kT jets, however, are not restricted into a fixed spatial cone size and do collect neighboring particles outside of the cone.

Sometimes this is called “b-tagging”, since the main goal of tagging is usually to detect bottom quarks, but in fact significant numbers of charm quarks get detected this way also. The key feature of bottom and charm quarks is that they both live just long enough to usually decay at a measurable distance from the initial collision point. When a hadron containing a bottom or charm quark decays after travelling a few millimeters from the collision point, the charged particles created in the decay can form a “displaced vertex”, or at the very least, they do not point back to the collision point — they have a nonzero “impact parameter”. The decays also can produce muons (which are harder to fake than electrons, so they are preferentially used) which are close to the jet. The observation within a jet of a displaced vertex, tracks with nonzero impact parameter, and/or a single muon all give evidence that a heavy quark was somewhere in the jet. It is expected that about 50 (15) percent of jets containing bottom (charm) quarks will be “tagged” at LHC, while about 1 percent of other jets are tagged by accident — “mistags”. However, one cannot take these numbers at face value. First, adjustments in the tagging algorithm can increase or decrease all three tagging rates; certain analyses may need very pure samples, demanding very “tight” tagging requirements, whereas others may need high statistics, in which case “loose” requirements would be used. Second, a single number is not a proper estimate of a tagging rate; the tagging probabilities for bottom, charm, and non-heavy-flavor jets are dependent on where the jet’s transverse momentum and pseudorapidity (among other things, such as the luminosity.)

The heavy flavor tagging in PGS4 is based completely on a vertexing algorithm. There are two types of tags “tight tags” (corresponding to btag=2.0 in the Olympics output), and loose tags (corresponding to btag=1.0 in the Olympics output). Tight tags have a lower efficiency, but also a lower fake rate.

The parameterization is based on callibration data from CDF. PGS cheats to look to see whether there is really a charm quark or a b-quark near the jet in question. Then based on this “true-type” it chooses whether to assign a b-tag. PGS only assigns heavy flavor tags out to an eta=2.0.

For loose tags (btag=1.0):

• b-jets are assigned a heavy flavor tag with probability nearing .5 in the central region for high energy jets.
• c-jets are assigned a heavy flavor tag with probability 0.26 times that of b-jets
• u,d,s and glue jets are assigned a loose tag with probability of a percent.

For tight tags (btag=2.0):

• b-jets are assigned a heavy flavor tag with probability nearer to .4 in the central region for high energy jets.
• c-jets are assigned a heavy flavor tag with probability 0.22 times that of b-jets
• u,d,s and glue jets are assigned a heavy flavor tag with probability approximately 10^-3

Note that all of the above are functions of eta(jet) and the ET(jet). The efficiencies for charm and b jets are roughly constant for small eta, but efficiencies fall off dramatically after eta of around 1.0. Generically, efficiencies decrease as the ET of the jet decreases, and asymptote for jets with E_T around 150 GeV.

Tau leptons decay about one third of the time to either an electron or a muon plus neutrinos. In this case, they cannot be distinguished from electrons or muons and appear in the detector as objects of electron and muon type.

The most common hadronic decays of the tau are to a neutrino plus

• a charged pion
• one charged pions and one or two pi-zeros (each of which decays to two photons)
• two pions of one charge and a third of the opposite charge

In the first two cases a single charged track, distinguished from an electron by its energy deposition in the hadronic calorimeter, is the result – a “1-prong” tau. Any hadronic or electromagnetic energy is clustered in a very narrow cone surrounding the charged track. In the third case, three tracks result – a “3-prong” tau. Thus, what appears in the detector is a very narrow jet, with invariant mass no greater than 2 GeV, and with 1 or 3 tracks. Such an object is unlikely to be an ordinary QCD jet, though fake taus do occur.

Hadronically decaying taus can be found out to an eta of 2.0, as described in the detector parameters file. The search for a tau candidate begins in the calorimeter. A candidate cell must satisfy

• E_T(cluster) > 10 GeV

PGS then searches for an associated track. The track must lie within 10 degrees.

• P_T(track) > 3 GeV

Since hadronically decaying taus are generally much thinner than jets, a tau candidate is vetoed if it is too wide. To determine whether it is too “wide”, PGS defines two cones. The small cone, which contains tracks potentially associated with the tau, and a isolation cone (Delta Theta(isolation cone)=30 degrees), which contains activity that potentially indicates that the candidate object is not in fact a tau. The size of the small cone depends on the energy of the tau candidate:

• Delta Theta (small cone) = (5.0 GeV/ E_tau) radians

If there is a track (or a pi⁰) within the isolation cone, but not the small cone, then PGS says the candidate is not a tau.

The tau is also distinguished from electrons by examining ECUT=ratio of the energy in the hadronic calorimeter to the energy of the leading track (near zero for electrons, near one for taus). ECUT must satisfy:

• ECUT > .15

Other cuts:

1. The tau charge is +/- 1 (the charge if found by summing up the charge in the small cone)
2. The number of tracks in the small cone is 1 or 3.
3. The invariant mass of the object in the small cone is less than 1.8 GeV.

In the PGS program, Missing-Et is defined as the vector sum of the directed transverse energy deposited in all of the calorimeter cells — this combines, ideally, the momenta of all photons, electrons, hadronically-decaying taus, unclustered energy, and jets — and adding to this the transverse momenta of any muons, whose energy is measured using the muon detection system. The magnitude of the resultant vector is the “missing transverse energy”.

A caution: muon detection works only out to |pseudorapidity|=2.4, whereas the calorimeter extends to |pseudorapidity|=5, so muons at large |pseudorapidity| (very near the beampipe) can cause additional missed transverse momentum.