# Muon detector efficiency?

## Main Question or Discussion Point

What is the typical efficiency (as a function of muon energy and/or rapidity) of a moun detector at an accelerator experiment?

More specifically I would like to know about the lower energy treshold: E.g. if a muon with energy of just some few GeV is produced in the collision process, what is the probability it will pass through the electromagnetic and hadronic calorimeters and finally reach the muon detectors and there be detected as a muon?

Even more specifically I'm interested in the detectors used at LEP2 (the Delphi detector to be even more precise), but I'm thankful for any comments on this subject!

## Answers and Replies

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Most detectors have a threshold of a few GeV. If you want to see the exact shape of the turn-on curves, you'll probably have to find the NIM article describing the detector you are interested in.

Most detectors have a threshold of a few GeV. If you want to see the exact shape of the turn-on curves, you'll probably have to find the NIM article describing the detector you are interested in.
Thanks for your reply Vanadium 50. I am definitley interested in more details about the energy dependence of the efficiency. (My results depend quite much on wheter I put in a sharp cutoff at say 2 GeV or wheter I place it at say 4 GeV instead.)
What does NIM stand for, and do you (or anyone else) know where I can find such an article (for the Delphi detector at LEP in specific)?

malawi_glenn
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EL: Have you tried here: http://delphiwww.cern.ch/ ?
Yes, but maybe I should look more closely. At least it says:
"Most muons of momenta above 2 GeV/c are expected to penetrate to The Muon Chambers", although I'd need more details.
(E.g. What is the more precise relationship between energy and probabilty to reach to moun detector. How much energy is typically lost on its way to the muon detector? And so on...)

malawi_glenn
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If you know what material they used for the EM-cal and H-cal then I think one can calculate that quite easy.

For what purpose do you want to know all of this?

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NIM = Nuclear Instruments and Methods. It's the standard journal for publishing papers on detector design and performance.

I disagree a bit with Malawi_Glenn. One can do the calculation, but it gives only a rough estimate. The problem is that near range-out the muons become non-relativistic, and a) the approximations of the calculation cease being valid, and b) the detection efficiency becomes more dependent on the detector design - specifically the response to wide-angle tracks.

malawi_glenn
Homework Helper
I disagree a bit with Malawi_Glenn. One can do the calculation, but it gives only a rough estimate. The problem is that near range-out the muons become non-relativistic, and a) the approximations of the calculation cease being valid, and b) the detection efficiency becomes more dependent on the detector design - specifically the response to wide-angle tracks.

That was why I asked him what the purpose of this knowledge was :-) If he only is interessted in a plain estimate, or if he is going to make a serious project etc.

A muon of momenta 2Gev when entering the muon chamer should still be ultra relativitistic right?

First, I appreciate your help Vanadium 50 and Malawi_Glenn!

For what purpose do you want to know all of this?
I'm doing a simple simulation of neutralino production at LEP, and want to compare my results with an already existing more detailed analysis. In models where the produced neutralinos typically decay into low energy muons (with that I mean muons below 10 GeV or so) my results deviate quite much from those of the detailed analysis, and I would like to understand why.
In my simulation I am right now simply assuming that the muon detector has a 100% efficiency in all directions it covers, and for all muon energies above a certain cutoff energy. (Below the cutoff I am assuming 0% efficiency.) The problem is that I don't really know where to put the cutoff (or even if it is an appropriate thing to do). By choosing it rather high (3-4 GeV) my results agree better with the exisiting analysis, so I was hoping for that such a cutoff would be a decent approximation of the detector efficiency. Changing the cutoff just 1 GeV up or down spoiles the agreement though.
Hence I would like to know in more detail how the muon detector really works.

NIM = Nuclear Instruments and Methods. It's the standard journal for publishing papers on detector design and performance.
Great, have to check that out (on monday when I'm back at work). I'm not an experimentalist you see, so that's probably why I hadn't heard of it.

A muon of momenta 2Gev when entering the muon chamer should still be ultra relativitistic right?
The thing is that I'm imposing cuts on the data collected by the "detector". One of the cuts is something like "discard all muons with energy less than 2 GeV". If a moun which initially has 3 GeV of energy looses some part of it before reaching the muon detector, this could make a big difference even if the detector is able to detect it. That's why I was asking about the typical energy loss on the way to the muon detector. (I do not take any such energy loss into account at the moment.)

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Staff Emeritus
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A muon of momenta 2Gev when entering the muon chamer should still be ultra relativitistic right?
Yes, but such a muon would have been 4-6 GeV when it was produced.

Yes, but such a muon would have been 4-6 GeV when it was produced.
This is very interesting for me. Do you have an idea of (or any feeling for) how much energy is lost during the passage through the callorimeters? A percentage of the initial energy, or more like a constant amount independent of the initial muon state?

Could one say that the muon detector will detect most of the muons that reaches it but that, due to energy losses on the way, only muons with an initial energy above some cutoff (2 GeV?) will ever get there?

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Staff Emeritus
2019 Award
Could one say that the muon detector will detect most of the muons that reaches it but that, due to energy losses on the way, only muons with an initial energy above some cutoff (2 GeV?) will ever get there?
A muon detector is located behind some material, and muons lose (typically) a fixed energy when traversing this material. For collider experiments, 1.5-4 GeV is typical. However, the threshold is a little higher than that (because low energy muons lose more energy) - so a detector configuration that causes a 100 GeV muon to lose 2 GeV of energy probably won't let a 2 or 2.2 GeV muon through.

A muon detector is located behind some material, and muons lose (typically) a fixed energy when traversing this material. For collider experiments, 1.5-4 GeV is typical. However, the threshold is a little higher than that (because low energy muons lose more energy) - so a detector configuration that causes a 100 GeV muon to lose 2 GeV of energy probably won't let a 2 or 2.2 GeV muon through.
Thank you Vanadium. This gives hope my simulation will actually work in the end. I will refine my calculations and see what happens.

Btw, do you know how the muon energy determination works?
For example, if a muon with an initial energy of 3 GeV looses 2 GeV on its way to the muon detector and hence only deposits 1 GeV there, what will the measured energy of that muon be?
Will it simply be measured just as 1 GeV, or can the energy lost on the way (e.g. in the electromagnetic calorimeter) be measured and taken into account and hence still give a readout of a 3 GeV muon?
(This is important for my simple detector part of the simulation.)

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