# Event selection cuts and cross section relation

I was working on experimental HEP project where I am bit confused. I generated 1000 MC events with say "x" cross section and without selection cuts. Now suppose I put some selection cuts while writing the C++ code for the data analysis of these events. Because of this, the number of events now drops down, say "y" (<1000) which is logical but while doing any computation should I write the cross section now as (y.x)/1000 ?

• Do you want to say "cross section, given cuts x" , or "over all probability"? That changes the answer. Commented Aug 10, 2017 at 13:38
• @Floris I meant that say 10pb is the cross section of 1000 events without selection cuts. Now, I write a C++ code where I put a selection cut which reduces the events to 900. So now, should I also normalize the cross section to 900*10/1000 = 9pb and use this value for further analysis instead of 10pb?
– kg__
Commented Aug 10, 2017 at 13:41
• If you are looking for the probability of an event that matches your cut (e.g. "scatters by at least 10°"), then yes - you have just calculated that that probability is (obviously) smaller than the probability of "any" scatter, including the ones you don't care about Commented Aug 10, 2017 at 14:16
• @Floris Should I equate probability with cross section and conclude that my new cross section after selection cut is 9pb?
– kg__
Commented Aug 10, 2017 at 14:19

## 1 Answer

The particular cross section is fixed by the physics of the interaction. A Monte Carlo modelling the data has all the possible channels and phase space defined by construction. In the experiment one cannot access all the phase space, due to the experimental limitations.

The transition probability per unit time for the interaction under study is given by the specific quantum mechanical model ,used in the generator of the MC events.

When the MC data fit the part of the cross section available to the detectors, one extrapolates to the full cross section , assuming that the model is perfect.

So if your experiment covers lets say an angle between two particles of 90 degrees, the Monte Carlo is used to extrapolate to the full crossection 360 degree phase space. Suppose you found 2 events within the experiment's phase space, and the MC extrapolates another 3. Then the cross section for the interaction gives five events, of which two detectable by the experiment. Thus the theoretical cross section is measured by the use of the Monte Carlo events.