Appropriate bin size given an energy resolution

[antrobot]

Homework Statement

A new particle with the mass of 317 GeV and natural width which is much smaller than the mass resolution of the detector is under investigation. It decays into two photons with equal energies, which are detected in the electromagnetic calorimeter. If one searches the particle over a range of 50 GeV to 600 GeV, would a bin size of 30 GeV be appropriate? If yes, why? If no, which bin size would you suggest?

Homework Equations

resolution of the calorimeter
$$\frac{σ(E)}{E} = \sqrt{(0.1^2 / E + 0.02^2)}$$

The Attempt at a Solution

I have calculated the resolution, using E = m/2 = 317/2 from the photons:

$$\frac{σ(E)}{E} = \sqrt{(0.1^2 / 317/2 + 0.02^2)} = 0.0215 => 2.15\%$$

From here I'm not sure how to proceed. If I multiply by the energy of the particle I would get $$σ(E) = 0.015 \cdot 317 GeV = 6.8 GeV$$. I would argue that 30 GeV is quite wide based on the resolution 6.8, but still ok, but I'm not even sure if what I'm doing is correct. Thank you for your help in advance!

 

[mfb]

The photon energy will be lower than the particle mass.

Your peak would be in a single bin or maybe two bins. You don't see a peak that way.
You can check what e.g. ATLAS and CMS did when searching for peaks in the diphoton mass spectrum. The excess around 750 GeV got a lot of attention before it disappeared with more data.

 

[antrobot]

Thank you very much for you answer, that was helpful! I have tried to understand a couple of those papers regarding the excess at 750 GeV and also other diphoton mass spectra channels during the Higgs search. Unfortunately, I didn't always find the information I was after. For the 750 GeV excess they used 40 GeV bins. If I compare it to the most easy case where both photons would get half of the energy, they would have 375 GeV. Then it depends on how large the width of the particle is, but this would still mean that they would observe it only in one bin, which they basically did. CMS performed a search with 20 GeV bins and also found an excess but not as large as ATLAS. The resolution of both experiments is much smaller than the bin width, why wouldn't they just go as low as the resolution allows? Regarding my homework: your argument was only regarding the energy of the photons, but I have to include the resolution as well and I'm not sure if I'm doing the right thing?

 

[mfb]

For the 750 GeV excess they used 40 GeV bins.

Where did you see 40 GeV bins?
The analyses were done unbinned, and plotted with smaller bins, to avoid issues with bins that are too large.

 

[antrobot]

Where did you see 40 GeV bins?
The analyses were done unbinned, and plotted with smaller bins, to avoid issues with bins that are too large.

I found this article, where some people were discussing the results from ATLAS and CMS: http://paperity.org/p/75529578/phenomenology-of-a-750-gev-singlet

On page 2 you can find a table with the bins, and the background and signal events. Could you send me a link to the original paper? I have trouble to find it.

 

[mfb]

The original papers are directly linked at the Wikipedia page, for example:

ATLAS and CMS

The collaborations didn't share the unbinned data, so theorists used the plots to extract yields, these are necessarily binned then, but the original analyses were unbinned.

 

[antrobot]

The original papers are directly linked at the Wikipedia page, for example:

ATLAS and CMS

The collaborations didn't share the unbinned data, so theorists used the plots to extract yields, these are necessarily binned then, but the original analyses were unbinned.

Thank you very much, but that still doesn't answer the questions:

1) Why and how is the resolution important for the decision of how to bin the data? Or why not just bin it with the resolution bin width?

2) If the natural width of the particle is smaller than the resolution, then it would be visible in one bin no matter how small the bin width is, so it could as well stay 30 GeV?

 

[mfb]

Making the bin wider than your peak just means you include more background without getting more signal in it. You reduce your sensitivity. In addition, even if you still get a significant excess, you don't know where in your bin the peak is.
If you have to do a binned analysis in a peak search, make the bins smaller than the typical detector resolution.

This is different from differential cross section measurements where you want your bins to be significantly wider than the detector resolution to avoid too much bin migration.

2) If the natural width of the particle is smaller than the resolution, then it would be visible in one bin no matter how small the bin width is, so it could as well stay 30 GeV?

No, if your experimental resolution is 5 GeV and you make 2 GeV bins it will appear in many bins and make a nice peak shape.