Reconstruction of Tau Candidates

4.1 Reconstruction of Tau Candidates

In almost all hadronic decay modes of taus, charged and neutral pions are the dominant decay products. Charged pions deposit energy in the electromagnetic and hadronic layers of the calorimeter, and leave tracks in the tracking detector. Neutral pions decay into two photons which will deposit most of their energies in the electromagnetic layers of the calorimeter. A tau which decays hadronically will have many similarities to a jet from strongly interacting particles.

However, there are some major differences between tau jets and typical hadronic jets. Most taus produced from the decay of heavy particles like W or Z bosons are fairly energetic and have high boost factors resulting in decay products that are mostly collinear with the taus themselves. Jets from tau decays have a narrower radius than jets from hadronization of strongly interacting particles. They are also expected to have a small number of tracks, between one to three, associated with them, which result from the charged pions. The total sum of energy for the remaining tracks surrounding the tau is expected to be small.

The DØ tau reconstruction algorithm [49] finds and builds tau candidates from three primary elements:

1. Calorimeter cluster, which is reconstructed by a simple cone algorithm. The tau cone algorithm use a radius of R < 0.5. A co-axial cone of radius R iso < 0.3 is used to defined tau calorimeter isolation variables.

2. Electromagnetic sub cluster(s), which is reconstructed using by the nearest-neighbor algorithm and is expected to come from neutral pions in tau decays.

3. Track(s), which are expected to come from the charged pions in tau decays. The tau track matching algorithm follows these steps in matching a tau calorimeter cluster with tracks:

(a) All tracks with transverse momentum greater than 1.5 GeV in a cone of radius 0.5 about the centroid of the calorimeter cluster are considered as candidates for the tau tracks. They are sorted in order of decreasing transverse momentum.

(b) The first track (the one with the highest p T ) is always attached to the tau. (c) Up to two more tracks can be assigned to the tau if the tracks’ z−position are within 2

cm from the first track at closest approach. (d) A second track is added if the invariant mass of the first and the second track is less

than 1.1 GeV. (e) A third track is added if the invariant mass of the three tracks is less than 1.7 GeV and the total sum of their charges is either +1 or −1.

There is a possibility for tau candidates to have two tracks with charges sum to zero. Since this analysis requires the tau to have charge sign opposite that of the charge of lepton, such tau candidates are rejected. Tau candidates with two tracks that have a net charge of +2 or −2 are retained, and assigned a unit charge of the same sign with the total charge, i.e. +1(−1) for taus with charge +2(−2).

The tau identification sorts the reconstructed tau candidates into three types:

1. Type 1: One track without associated electromagnetic sub cluster. This type of tau

candidates is expected to come from the decay τ − →π ν τ .

2. Type 2: One track with associated electromagnetic sub cluster. This type of tau candidates is expected to come from the decay τ −

→π − Nπ 0 ν

τ , where there are N ≥ 1 neutral pions.

3. Type 3: Two or three tracks. This type of tau candidate is expected to come from the decay

τ − →π π + π Nπ 0 ν τ , where there are N ≥ 0 neutral pions.

Figure 4.1: Three tau decay types as defined by DØ tau reconstruction algorithm.

Figure 4.1 illustrates all three types. Notice the distinct feature of each tau decay type, in particular how each type gives different signatures in the central tracking detectors, electromagnetic, and hadronic calorimeter.

After the reconstruction stage, tau candidates contain candidates from real taus and other objects (fake taus). The primary source of fake taus is hadronic jets. Other physics objects which can also be reconstructed as fake taus are electrons and muons. Further selection criteria are then required to separate real taus from fake taus.