What is a Fiducial Cross Section?

[ChrisVer]

I have come across the term quiet often, but I find it difficult to explain it to myself (or others) and even interpret it...
So what is a fiducial cross section?
Is it the measured cross section once you factor out the detector acceptance and the different cut-efficiencies (mainly motivated by Eq.7 or Sec.6 of this paper https://arxiv.org/pdf/1307.5865.pdf )... However I am slightly confused with terms like 'fiducial volumes' and things like that or how this (in the end) becomes model-independent.

 

[mathman]

• 
  In particle physics
• Fiducial cross section, in particle physics experiments, a cross section for the subset of a process in which the distinctive process signatures are visible within the sensitive regions of the detector volume. The definition now commonly means a cross section with kinematic and other selection cuts consistent with the sensitive detector acceptance applied, but in which detector inefficiencies are corrected for within that volume. These corrections are typically derived by applying the fiducial cuts on collections of simulated collision events, with and without detector simulation, and inverting the resulting detector transfer function. Fiducial cross sections are favoured for many purposes because they minimise extrapolation into experimentally invisible phase space, and are hence maximally model-independent.
• ------------------------------
• From Wikipedia

 

[ChrisVer]

Some example questions from that definition:
Why should it be a subset of a process? In fact from how many sets does a process consist of?
What is that volume in which the inefficiencies are corrected?
"detector transfer function"?

 

[mfb]

Why should it be a subset of a process?

It is the part you can measure, that is necessarily a subset of all particles. With realistic detectors it is even a strict subset, e. g. you never get full 4 pi solid angle coverage.

In fact from how many sets does a process consist of?

That question doesn't make sense.

What is that volume in which the inefficiencies are corrected?

The measurable part, e. g. particles flying into the direction of the detector. There you can know "okay, my efficiency is 50%, so there are twice as many particles as I observe". For particles that don't even fly into your detector you cannot do this. They are outside your fiducial phase space.

"detector transfer function"?

The efficiencies and migration effects.