# Exercise 8: Pick a physics cut 
**(15 minutes)**

Go back and run the macro you created in {ref}`Exercise 5 <scatterplot-c>`. If you've
overwritten it, you can copy my version and copy-n-paste the relevant
lines to your code:

    > cp ~seligman/root-class/AnalyzeExercise5.C $PWD
    > cp ~seligman/root-class/AnalyzeExercise5.h $PWD

:::{note}
The chi2 distribution and the scatterplot hint that something
interesting may be going on.

The histogram, whose limits I originally got from the command
`tree1->Draw("chi2")`, looks unusual: there's a peak around 1, but
the x-axis extends far beyond that, up to chi2 > 18. Evidently there
are some events with a large chi2, but not enough of them to show up on
the plot.

On the scatterplot, we can see a dark band that represents the main peak
of the chi2 distribution, and a scattering of dots that represents a
group of events with anomalously high chi2.

The chi2 represents a confidence level in reconstructing the particle's
trajectory. If the chi2 is high, the trajectory reconstruction was poor.
It would be acceptable to apply a cut of "chi2 < 1.5", but let's see
if we can correlate a large chi2 with anything else.
:::

Write a macro to create a scatterplot of **`chi2`** versus **`theta`**. It's
easiest if you just copy the relevant lines from your code in 
{ref}`Exercise 7 <trig-functions-c>`; there are files AnalyzeExercise7.C and .h in my area if it will help.

:::{note}
Take a careful look at the scatterplot. It looks like all the large-chi2
values are found in the region theta > 0.15 radians. It may be that our
trajectory-finding code has a problem with large angles. Let's put in
both a theta cut and a chi2 cut to be certain we're looking at a sample
of events with good reconstructed trajectories.
:::

Use an `if` statement to only fill your histograms if chi2 < 1.5 and
theta < 0.15. Change the bin limits of your histograms to reflect these
cuts; for example, there's no point to putting bins above 1.5 in your
chi2 histograms since you know there won't be any events in those bins
after cuts.

:::{note}
It may help to remember that the symbol for logical AND in C++ is
`&&`.

A tip for the future: in a real analysis, you'd probably have to make
plots of your results both before and after cuts. A physicist usually
wants to see the effects of cuts on their data.

I confess: I cheated when I pointed you directly to theta as the cause
of the high-chi2 events. I knew this because I wrote the program that
created the tree. If you want to look at this program yourself, go to
the UNIX window and type:

    > less ~seligman/root-class/CreateTree.C
:::