ARSSUM Study ( May 10th 2007) :
The purpose of this study (proposed by Jeff) is to find an alternative method to extract the Cerenkov efficiencies for LD2 at 687 MeV using the ARSSUM signals ( ADC ). In this case, I used 3 different types of data , LD2 at 687 and 362 MeV and LH2 at 362MeV, in order to separate the pion and the electron distributions by various fits.
My first step was to take the ARSSUM in the elastic locus for LD2 at both energies and scale one with respect to the other on the 6 to 12 pe range ( where the electron signal is dominant )
The figure 1 shows a plot where I fit the 2 distributions in that region with an exponential function. I did a fit of one of the distribution with all the parameters free, and I did a fit of the second distribution with the resulting function with only one free parameter that is a scaling factor, we can see that the agreement is quite good :
The second step was to fit both the 2 distributions after rescaling over the whole range of pe's. For my fit, I just used several gaussians until I get some good agreement ( 12 free parameters ,needs to be improved). Then, I did the subtraction of the 2 resulting functions and I tried to fit it with 3 gaussians ( black and grey curves on the figure respectively ). I am not sure about the accuracy of this method but that s how I got something close to the pion distribution.
On figure 2 , the blue curve is LD2 @ 687 MeV , the red curve is LD2 @ 362MeV and the black and grey curves are "blue - red" . I used the grey curve as my pion distribution.
The Third step was to take the LH2 data @362 MeV ( very few pion ) and apply ToF cuts to get an even better electron purity. In this case I fitted the ARSSUM with a Poisson distribution ( "convoluted" with a gaussian ) + a gaussian for the pedestal. I was impressed by the good agreement. See next figure :
The final step was to take the pion distribution ( grey curve on figure 2 ) and the electron distribution ( black curve above ) and combine them together to fit the LD2 data @687MeV as shown on figure 4. The blue curve is electrons, the red curve is pions, and the black curve is the total fit. Note that I have 5 free parameters in this case : the scaling of the pion distribution(p13) , a shape factor for the pedestal of the electron distribution, the mean of the poisson distribution(p5), the width of the 1pe signal for the electron (p4) distribution and the scaling factor of the electron distribution(p3).
