# Exercise 7: Picking a physics cut 
**(15 minutes)**

Make a histogram of **`chi2`**, then a scatterplot of **`chi2`** vs
**`ebeam`**.

:::{hint}
If you've forgotten how to figure out the axis limits for **`ebeam`**,
look at {ref}`rdf-make-scatterplots` again for a clue.
:::

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

The chi2 histogram 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 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.
:::

Make a scatterplot of **`chi2`** versus **`theta`**.

:::{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.
:::

Repeat the above plots with a `Filter()` 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.

:::{tip}
You may ask which is better:

   - `.Filter("chi2 < 1.5").Filter("theta < 0.15")`

   - `.Filter("chi2 < 1.5 && theta < 0.15")`

On the relatively small scale of this example, it
doesn't make much of a difference. For a large-scale analysis, the
second expression is more efficient, since `RDataFrame` only has to
invoke the overhead of the `Filter()` method once (including compiling
the C++ expression within the quotes) instead of twice. 

I must 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 {ref}`UNIX window <terminal>` and type:

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