# Energy reconstruction in calorimeter

Hi guys, I have some general questions and was hoping some of you might be able to answer them.

Does anyone know what it means to be "collinear unsafe" and "infrared unstable" when referring to energy reconstruction in calorimeters?

Also why do theorist prefer collinear and infrared safe data?

Why does is infrared- and collinear-safety to all orders of perturbative QCD?

Hi guys, I have some general questions and was hoping some of you might be able to answer them.

Does anyone know what it means to be "collinear unsafe" and "infrared unstable" when referring to energy reconstruction in calorimeters?

Also why do theorist prefer collinear and infrared safe data?

Why does is infrared- and collinear-safety to all orders of perturbative QCD?

Hello Kenith,

you might be interested by this (rather old) paper about jets building at Tevatron :
http://arxiv.org/PS_cache/hep-ex/pdf/0005/0005012v2.pdf
In particular, in section 2, they explains with drawings collinear and infrared instabilities on jets.

on page three:
The algorithm should not only be infrared safe, in the sense that any infrared singularities do not appear in the perturbative calculations, but should also find solutions that are insensitive to soft radiation in the event.

What exactly are infrared singularities, and why do they not appear in perturbative calculations? Figure one in that paper illustrates infrared sensitivity. Presence of soft radiation leads to then merging of the jets. What is this not preferred? Any would do theorists not prefer this? It seems to me that there is no problem reconstructing one jet instead of two with half the energies.

The algorithm should not only be collinear safe, in the sense that collinear singularities do not appear in the perturbative calculations, but should also find jets that are insensitive to any collinear radiation in the event.

Again, changing the seed threshold and splitting seed energy between towers would create more/less jets, however, the energy reconstrcted would still be the same had there been a jet vs had there been two jets with 1/2 the energy.

Could someone explain this?

Staff Emeritus
I think two things are confused here. First, energy reconstruction in a calorimeter has nothing whatsoever to do with jets, jet algorithms, and infrared and collinear safety. Energy reconstruction has to do with relating the voltage (e.g.) that you actually measure to the energy that was deposited and ultimately produced that voltage.

The second thing is jet algorithms, and here infrared and collinear safety is important in comparing what was measured to theoretical predictions. While you don't need to know about this to measure the energy, you do need to know about this if you want to use this to say something about theories.

A good introduction is CTEQ's http://www.physics.smu.edu/%7Eolness/cteqpp/handbook/handbook.pdf" [Broken].

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how do infrared and collinear safety play into theoretical predictions? Why these not preferred when comparing data to theory?

what are infrared and collinear singularities?

Staff Emeritus
Did you read the references? If not, I suggest you do. If you did, and didn't understand them, you might want to tell us your background so the answer can be pitched at the right level.

nrqed
Homework Helper
Gold Member
what are infrared and collinear singularities?

When calculating Feynman diagrams, (think for example of a one loop diagram with a photon emitted before a vertex and then reabsorbed after the vertex), there are divergences when the photon momentum goes to zero. This is an infrared divergence. On the other hand, the tree level diagram with a photon (or any number of photons) emitted with an energy smaller than the resolution of the detector must also be included. These diagrams contain a collinear singularity. The two singularities cancel out.

lets specifically talk about infrared and collinear problems that arise in jet algorithms since that is what the paper talks about.

infrared instability comes from the fact that addition of soft radiation can change the cone configuration. collinear instability comes from the fact that changing a pt cut for seeds will produce different cone configurations. however, i do not see how these detector and coding issues play into theoretical calculations. feynman diagrams are unrelated to algorithm problems...

Staff Emeritus
feynman diagrams are unrelated to algorithm problems...

You say that with such authority!

feynman diagrams are unrelated to algorithm problems...
I would strongly disagree with that. The resolution of most infrared divergences lies utlimately in the detectors resolutions. After all, there is no way to distinguish between an electron and a collinear pair eletron-photon, and it is not unreasonable that the cross-section blows up in strict collinear limits. So when you want to make a useful Feynman diagram calculation, you need to know what the resolution will be in the end, and the resolution is also strongly determined by the best algorithm you have at hand...

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If I may give you an advice, nrqed gave you a non-trivial fact about pure QED collinear singularities. Before embarquing to understand what happens in QCD, you may want to understand QED first. Just a hint. My 2 cents...

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You say that with such authority!

i say it so someone can say i'm wrong and why!

Ok, so what i've been trying to do in the post is to ask for an explanation in baby terms what all these big words means. the paper throws around terms like infrared and collinear safety like they are talking to someone working at CDF. well... i dont what these terms mean at all. reference me to a paper, i still wont know what it means, because it is implied that the reader understands parts of it.

now, having said that, is my idea of collinear and infrared safety correct?

kenith said:
infrared instability comes from the fact that addition of soft radiation can change the cone configuration. collinear instability comes from the fact that changing a pt cut for seeds will produce different cone configurations. however, i do not see how these detector and coding issues play into theoretical calculations. feynman diagrams are unrelated to algorithm problems...

If so, how does this play into theory? Since I only know about collinear and infrared in the sense of jet reconstruction (thats what the paper was about), how does reconstructing 2 jets (say jet A and jet B) that are close in eta-phi space different than clustering both (jet A and jet B) as one jet? I mean, reconstructed energy stays the same.

I would strongly disagree with that. The resolution of most infrared divergences lies utlimately in the detectors resolutions.

what is resolution and what is infrared divergence?

After all, there is no way to distinguish between an electron and a collinear pair eletron-photon, and it is not unreasonable that the cross-section blows up in strict collinear limits.

what is a collinear pair? and what are collinear limits? see, when you say collinear, all i think about is a change in pt cut for stable cone seeds.

Staff Emeritus
i say it so someone can say i'm wrong and why!

I think this is a pretty lousy way to learn something - to say incorrect things with authority hoping someone will correct you. I think many people will simply decide that it's not worth the time.

Frankly, I don't think you have the background to understand the answer to the question you are asking. Your initial question showed a confusion between jet finding and energy reconstruction, along with a sentence that isn't even English: "Why does is infrared- and collinear-safety to all orders of perturbative QCD?" It's missing a verb. At least. You don't know what resolution is, or what it means for two particles to be colinear.

Don't take this the wrong way - it was two years into graduate school before I could even calculate radiation correctly in QED, so you wouldn't be expected to know this.

could you give a qualitative description? i'm more interested in the physical ideas instead of being bogged down in QED

i guess all i would like is a definition. and also an answer to whether my definition is correct at all.

also, i dont know whether what i'm saying is right, since i dont know whats right and whats wrong, i try to make a picture in my mind of the physical process that is happening... but if all you do is reference me to papers above my level, say that i shouldnt be expected to know this... how is this beneficial to me? all i'm asking for is a physical description and all the posts have been just very unrelated to the subject matter.

Staff Emeritus