identification

identification is used to identify the particle type of each track. This is particularly important for the hadrons ($\pi^\pm$, $K^\pm$, and $\proton/\pbar$) because they interact similarly in matter. These particles are identified by examining the light and its distribution.

The identification algorithm (called ²³) used in FOCUS is based on likelihood ratios between the various particle hypotheses. The particle possibilities considered for each track are $e^\pm$, $\pi^\pm$, $\kaon^\pm$, and $\proton/\pbar$.²⁴ For each of these four hypotheses the likelihood, $\mathcal{L}$, is calculated by observing the status of the cells within the cone of the particle. The probability that a particle associated with a track of known momentum²⁵ will fire a particular cell is computed using Poisson statistics. This calculation is based on the predicted number of photons striking the cell under each particle hypothesis. An accidental firing rate is also included in this calculation to model spurious hits; this cell-by-cell correction factor depends on the beam intensity on an event-by-event basis. The accidental firing rates are typically less than 1% except for cells close to the uninteracting beam.

The product of the firing probabilities for all relevant cells in the three detectors is computed to form $\mathcal{L}$. The value $W_\mathrm{obs}(i) \equiv -2 \ln \mathcal{L}$ is calculated for each particle hypothesis i. identification is performed by cutting on the difference between two likely hypothesis. For example, a typical cut separating a kaon from a pion is

$$W_\mathrm{obs}(\pi) - W_\mathrm{obs}(\kaon) > 3~.$$ (11)

(The fact that we are using a negative log likelihood means we expect $W_\mathrm{obs}(\pi)$ to be larger than $W_\mathrm{obs}(\kaon)$ for a kaon.)

This identification method has distinct advantages over the standard method of particle identification using threshold detectors, which simply determines the on/off status of the cells and return a simple yes or no for consistency with a given particle hypothesis. First, discrimination between two hypotheses can be extended beyond the threshold momentum ranges. Second, using this likelihood approach, the cuts can be more carefully selected and tuned for a particular physics analysis since there is a continuous value to cut on rather than simple on/off values for each particle hypothesis. The algorithm is fully described in Wiss:citadl_design_memo.