Reconstruction of a Photon: Photon Cut

A set of routines was used for the analysis of E838 data which were first developed by the RMC collaboration to identify real photons (26) from a pair of good tracks. These were used to identify a pair of tracks that would originate at the lead converter and project back to the target, constituting a photon that came from pion capture. The $xy$ and $z$ projection of the distance between the intersection points of the $e^+e^-$ tracks that formed a photon, $d_{xy}$ and $d_{z}$, were required to be within a certain distance. This requirement was kept fairly loose to minimize inefficiencies in the photon reconstruction due to increased curvature of the charged tracks from energy loss in the drift chamber.

Figure 5.5: The parameter R$_{close}$, is shown in a schematic diagram. The cross-sectional view of the cylindrical lead converter is shown as a circle. The parameter R$_{close}$, defined as the distance of closest approach of the photon from the center of the detector is determined by deriving the position vector $\vec{c}$ in the $xy$ plane.

Table 5.2: The photon cut parameters. Definitions of $d_{xy}$, $d_{z}$ etc. are given in Section 5.2.2.

$\quad$ Photon Cut	Cut Applied On	Parameter Requirement
$d_{xy}$	photons (wrap)	7 cm
	photons (non-wrap)	6 cm
Maximum allowed $xy$ distance
between conversion points
$d_{z}$	photons (wrap)	7 cm
	photons (non-wrap)	6 cm
Maximum allowed $z$ distance
between conversion points
$R_{close}$	photons (wrap)	8 cm
	photons (non-wrap)	8 cm
Maximum distance of closest
approach of the photon in
the $xy$ plane
$\Delta Z_{close}$	photons (wrap)	26 cm
	photons (non-wrap)	26 cm
Width of the cut based on the $z$
component of the photon's
position at target limit
$C$-sector cut	photons	$C$ counter
		intersection
Requirement on
track intersection
with $C$ counters	photon pair	time difference
and time coincidence		$\pm$ 20 ns
of two photons

A cut based on the distance of closest approach of a photon, $(R_{close}, z_{close})$ was applied. The radius of closest approach of the photon in the $xy$ plane, $R_{close}$ was found by determining the position vector $\vec{c}$ as seen in Figure 5.5. The vector $\vec{v}$ normal to the $xy$ plane is first obtained from the cross product $\vec{r}\times\hat{p}$ between the position vector at the conversion point of the photon at the lead converter $\vec{r}$, and the unit momentum vector of the photon $\hat{p}$. A cross product of the unit momentum vector $\hat{p}$ is then taken with the vector $\vec{v}$. The magnitude of the resultant vector $\vec{c}$ gives the distance of closest approach of the photon from the center of the detector in the $xy$ plane. A similar cut based on the width of the $z$ projection of the distance of closest approach, $Z_{close}$, was also applied.

While the intended purpose of $R_{close}$ and $Z_{close}$ cuts were to make sure that the reconstructed photon indeed originated from the target flask, in practice, the cuts are applied fairly loose, extending over the dimensions of the target flask in order to allow for limitations in the routine that fitted the charged $e^+e^-$ tracks.

Further, the pair of tracks that constituted a photon were required to intersect the $C$ counter that was fired. Two such photons were required to arrive within $\pm$ 20 ns of each other to distinguish and reject events that had one or both of the photons coming from later or earlier beam buckets. The details of the photon cut parameters are listed in Table 5.2.

Out of a total of of $3.1 \times 10^{11}$ pion stops in liquid hydrogen $2.3 \times 10^{6}$ photon pairs passed both the tracking cuts and photon cuts.