Physics Department,
University of California,
One Shields Avenue,
Davis, CA 95616
Computing the efficiency correction for the TPC is
complicated by the momentium resolution. (see
resolution page) In order to understand the effect of momentium
resolution on the efficiency correction, I used the following simple
model.
A non square (1by1.7 mt(GeV)) responce matrix is made with
a flat input distribution (0to2 mt(GeV)). Each input is smeared by a
gaussian in the form
gauss = rnd(1)/5*random+random
where rnd is a random number from a normal distribution,
random is the number from the input distribution. This gives a very rough
simulation to the real TPC responce, but it only has the momentium
resolution in it so that can be studied qualitativly without tracking
loss, split tracks, etc...
Another distribution is made from a different random seed
that simulates the shape of the real data. This is then corrected with
the TPC responce matrix that is discribed above. The plot below shows the
result.
correction (fit bins 15 30)
The top 2 plots are the simulated data and the output.
The left is the two distributions, and the right is the ratio. If the
correction is perfect the correction would be the same as the right
plot.
The bottom shows the correction calculated from the flat
distribution responce matrix. Compairing the corrections, it is clear
that the high Mt range is different, although the low Mt range is similar.
The high Mt is effected by how the distribution is extended so it can be
used in the responce matrix. The tail extension here is from an
expodential fit to the bins 15 through 30 and the tail is basied on
that fit.
The next plot shows the same as the above except the tail
extenison is removed. The thing to note is the correction becomes worse
as expected. The tail correction is important to the high Mt only.
correction no tail extension
This plot is again the same except the tail extension. Here the tail is
over sized. It is simply the last value extened out to fill the vector.
Here we see the correction go the other way.
correction with large tail extension
Finally I moved the fit range to the last five bins. The modeled
distribution is not expodential or it would not matter where I fitted it.
This gives a resonable result. The correction is about what it should be.
I guess this shows that the choice of extension has a significat impact on
the higher Mt corrections.
correction, exp tail extension (fit bins 35 to 40)
The particles lost in the simple simulation are shown below. These are
the tracks that extend beyond the edge of the histogram. This loss
corresponds to a flat distribution that makes the responce matrix. The
loss for the non-flat distribution would be less.
correction, exp tail extension (fit bins 35 to 40)
Nuclear Physics Group
