$\pi^{\pm}/K^{\pm}$ separation

After the calibration constants (TWC), optimized on $\mu$-pair events, were applied to hadronic events, sizeable deviations from zero for the $\delta t$ residuals were observed. In particular the deviations were found to be momentum dependent and different for each of the hadron species. Deviations were observed as large as two sigma away from zero for low momentum tracks identified as kaons and protons by other detector subsystems. Further investigation revealed that the observed momentum and hadronic species dependence could in fact be reasonably modeled by a single linear function in terms of the track's velocity, see the left side of Fig. . A velocity or $\beta$ parameterization was then applied in the TOF reconstruction algorithm to correct for this effect. The $\beta$ parameterization was determined from an analysis of a large sample of hadronic events. In the right side of Fig. we show the momentum distribution of the $\delta t$ residual after the application of the $\beta$ correction. The large $\delta t$ systematics observed earlier were largely removed over the relevant momentum range and for each of the hadron types. Further study is planned to establish the origin of the velocity dependence in the $\delta t$ distribution. Fig. shows the TOF resolution averaged over all counters and $z$ as a function of momentum for each hadron species.

Figure: Systematics of TOF $\delta t$ residuals. The figure on the left shows the $\beta$ dependence of the $\delta t$ residual after application of the $\mu$-pair optimized calibration constants but before the $\beta$ correction for each hadron species. The figure on the right shows the distribution of the residuals as a function of momentum after application of all calibration constants.

Figure: The TOF resolution, averaged over all counters and $z$, as a function of momentum for each hadron species.

Figure shows the mass distribution for each track in hadron events, calculated using the equation

$$mass^2 = \left( \frac{1}{\beta^2} - 1\right) P^2 = \left(\left( \frac{c T_{obs}^{twc}}{L_{path}}\right)^2 - 1\right) P^2$$ (5)

where $P$ and $L_{path}$ are the momentum and path length of the particle determined from the CDC track fit assuming the muon mass, respectively. Clear peaks corresponding to $\pi^{\pm}$, $K^{\pm}$ and protons are seen. The data points are in good agreement with a Monte Carlo prediction (histogram) obtained by assuming $\sigma_{TOF}$ = 100 ps.

Figure: Mass distribution from TOF measurements for particle momenta below 1.2 GeV/c.

The identification power of $\pi^{\pm}/K^{\pm}$ separation is shown in Fig. as a function of momentum. The identification power is defined as

$$\sigma_{\pi^{\pm}/K^{\pm}} = \frac{T_{obs}^{twc}(K) - T_{obs}^{twc}(\pi)}{\sqrt{\sigma_K^2 + \sigma_{\pi}^2}},$$ (6)

where $\sigma_K$ and $\sigma_{\pi}$ are the time resolution for $K$ and $\pi$, respectively, at each momentum. This demonstrates clear 2$\sigma$ separation for particle momenta up to 1.25 GeV/c.

Figure: $\pi^{\pm}/K^{\pm}$ separation by TOF.