# Fiducial volume in collider/detector physics

I'm trying to make some sense of ATLAS measurements for a personal project to learn how to use Pythia, and part of my work requires me to recreate the distribution for Z boson decay. I encountered the term 'fiducial volume', and I am wondering what it is, because I couldn't find an answer online.

So, what is fiducial volume in the context of particle phenomenology? Is it the region of phase/energy space that is of interest?

Or does it have to do with hypothesis testing?

• short answer: yes, it's the region of phase/energy space that is of interest.
– Shep
Commented Mar 17, 2015 at 17:55

In some detector experiments,

1. The response at the periphery of the detector is poorly understood.
2. The majority of background events interact in the periphery of the detector. The periphery of the detector is the final shielding.
3. Some parts of the detector may be broken.

In such cases, results from such parts of the detector are ignored. The results are drawn entirely from the fiducial volume (the reliable, central area of the detector) in which neither 1. nor 2. apply.

Occasionally, however, fiducial volume might refer, metaphorically, to an interesting volume of phase space of objects produced in a collision, in which 1. and 2. don't apply.

ATLAS has no experiment-wide definition of "fiducial", it basically means sensitive to signal.

The definition is confusing because, unlike most experiments, ATLAS (and CMS, D0, CDF, etc) doesn't just define the physical area where the experiment is sensitive, they also define collision properties. This means the definition of fiducial isn't limited to the detector volume. Instead it's roughly defined as the parameter space of events where you can expect to measure your signal.

Unfortunately this may depend on what you're trying to measure. Other "fiducial cuts" may include:

• $p_\mathrm{t}$ of objects (jets, leptons, etc)
• $\eta$ of objects
• Various relationships among the objects in the detector (i.e. missing transverse energy, etc)

Further confusing matters, some groups within the experiment choose to omit the term "fiducial" entirely; the financial volume may just be referred to as the "signal region". So while in the most general sense it means the place where your signal is strong, the term should never appear without a more precise definition.

This presentation (NB: PDF) has a "jargon" page that states,

• Fiducial (Webster's):
1. Taken as a standard of reference
2. Founded on faith or trust
3. Having a nature to be trusted
• Fiducial Volume (Particle Physics):
4. The volume used to make physics measurements
5. The volume where the detector is assumed to be well understood

With the following diagram (slightly modified for formatting purposes),

So basically the fiducial volume is the volume of the observatory at which a specified number (typically 90%) of events are to be accepted, and will be smaller than the total volume. For the particular case of Super-Kamiokande, it has a total volume of 50 kton and a fiducial volume of 22 kton.

• in the DM/neutrino experiments, the edges of the detector is basically a final layer of shielding. What about at the LHC, though? What's wrong with the edges? I can guess, but I don't know for certain. Commented Mar 17, 2015 at 15:02
• @innisfree: I don't know for sure, but I imagine that it is probably more of a S/N ratio there (e.g., $\propto(N_{obs} - N_{bkg})$) than the edges for neutrino experiments. (I missed the "ATLAS" bit when I first read the question and answered based on what I knew about SK). Commented Mar 17, 2015 at 15:08
• Oddly, we're starting to see more experiments applying statistical methods to make some of the originally excluded volume count at reduced weight. See, for instance, the third KamLAND paper. Commented Mar 17, 2015 at 15:23
• @dmckee Could the background/detector behaviour (however poor) in the bad regions be modelled just like it is in the fiducial region? it might have very little statistical power, but the same methods could apply? Commented Mar 17, 2015 at 15:45
• @innisfree More or less. The driving factor is how well you know the backgrounds so this kind of analysis comes after you have already understood the easy part of the detector. Commented Mar 17, 2015 at 18:54