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Counting pions in the strong field setting.

In the strong field setting, to identify pions directly one needs to require a $C2$ firing (see Fig. 3.5 and discussion of the Cherenkovs in Subsection 3.4.4). However, it is desirable to avoid the uncertainty associated with the Cherenkov's efficiency, which would have entered the game had $C2$ been required to fire. Notice that sorting out $p$ ($\bar{p}$) off-line by vetoing $C1$ and $C2$ and using $TOF$ can be done cleanly and reliably even in the strong field settings. Having done that, we are left with a sample of $K$ and $\pi$. For this sample, we can obtain distributions with respect to the kinematic variables of a $\pi$ by applying a pionic acceptance correction . Then, we obtain inefficiency-corrected, clean $K$ distributions with respect to the pionic $y$ and $k_T$, where a pionic acceptance correction is used. Finally, we subtract the kaon component in the distributions:

$$\frac{\,dN(\pi)}{\,dy_{\pi}} = \frac{\,dN(\pi+K)}{\,dy_{\pi}} - \frac{\,dN(K)}{\,dy_{\pi}}$$ (30)

Clearly, the $y$ above can be replaced by any kinematic variable.