### Finding Pion Positions In Target

The current algorithm of finding the pion position which stopped in target is
to assume the nearest point to the z-axis on the rebuilt track. How good is this method is the topic of the following work.
First, the positions of pions stopped in target were simulated following gaussian
distribution with different sigma. Using the above algorithm, we calculated
positions of the pions. Comparing these two results, we can get a rough idea
about how close our algorithm can give a result.

Second, we will try pion positions with distributions other than gaussian to see
how sensitive out algorithm is to the shape of the pion stop distribution.

### Some Results

Sigmas from 1 to 9 for x, y and z were studied. For x and y, the outputs were
obviously not gaussian, right now we just fit them with gaussian to get a rough
idea about relations of inputs and outputs. Samples of sigma equaling 5 were
included for x, y, and
z. In each graph, The left hand side graphs are without fitting while the right hand side ones were fitted with gaussian.
The relationships between FWHM(2.35*sigma) of output and that of input were also
included for x, y, and
z. In each graph, The upper one is without fitting while the lower one was fitted with linear function with p2 as the slope.

© 24 February 2000, Weidong LI, for the PIBETA collaboration