KID and pion fake rate

The $K/\pi$ identification is carried out by combining information from three nearly-independent measurements:

• $dE/dx$ measurement by the CDC,
• TOF measurement, and
• measurement of the number of photoelectrons ($N_{pe}$) in the ACC.

As in the case of EID, the likelihood function for each measurement was calculated and the product of the three likelihood functions yields the overall likelihood probability for being a kaon or a pion, $P_K$ or $P_{\pi}$. A particle is then identified as a kaon or a pion by cutting on the likelihood ratio ($PID$):

$$PID(K) = \frac{P_K}{P_K+P_{\pi}}$$ (1)

$$PID(\pi) = 1 - PID(K) ~.$$ (2)

The validity of the $K/\pi$ identification has been demonstrated using the charm decay, $D^{\ast +} \rightarrow D^0 \pi^+$, followed by $D^0 \rightarrow K^- \pi^+$. The characteristic slow $\pi^+$ from the $D^{\ast +}$ decay allows these decays to be selected with a good $S/N$ ratio (better than 30), without relying on particle identification. Therefore, the detector performance can be directly probed with the daughter $K$ and $\pi$ mesons from the $D$ decay, which can be tagged by their relative charge with respect to the slow pion. Fig.  shows two dimensional plots of the likelihood ratio $PID(K)$ and measured momenta for the kaon and pion tracks. The figure demonstrates the clear separation of kaons and pions up to around 4GeV/$c$. The measured $K$ efficiency and $\pi$ fake rate in the barrel region are plotted as functions of the track momentum from 0.5 to 4.0 GeV/$c$ in Fig. . The likelihood ratio cut, $PID(K) \geq 0.6$, is applied in this figure. For most of the region, the measured $K$ efficiency exceeds 80%, while the $\pi$ fake rate is kept below 10%.

Figure: Likelihood ratio $PID(K)$, versus momenta for daughter tracks from $D^0 \rightarrow K^- \pi^+$ decays, tagged by the charge of the slow $\pi^+$'s. The open circles correspond to kaons and the cross points to pions.

Figure: $K$ efficiency and $\pi$ fake rate, measured with $D^{\ast +} \rightarrow D^{0}(K \pi) + \pi^+$ decays, for the barrel region. The likelihood ratio cut $PID(K) \geq 0.6$ is applied.