Experimental Signatures of Neutral Pion Decay at High Energies

[bcrowell]

A neutral pion decays into two gammas. In the rest frame of the pion, these are back to back and have energies of 67 MeV. I'm interested in the case where the pion's energy in the lab frame is on the order of a few hundred MeV. Can anyone point me to any source of information on what kind of experimental signature you would get from this in a laboratory experiment? These two gammas would probably interact through pair production, so then you'd have some high-energy electrons and positrons. After that, do you get a further cascade of gammas? Charged particles?

 

[Orodruin]

You would measure the energy and direction of the ensuing EM cascade. This gives you a handle on the photon 4-momenta and computing the invariant mass you get a peak at the pion mass. @mfb should be able to give more details.

 

[mfb]

An electromagnetic shower is the most likely result - a cascade of pair production and bremsstrahlung. Below 1 MeV pair production doesn't work any more and ionization becomes dominant, at even lower energy for the electrons bremsstrahlung becomes neglible and interactions with the outer electrons dominant, and so on until everything is dissipated down to a few eV.

The experimental signature are usually those eV processes: scintillation, excitation of electrons/holes in semiconductors, other processes that produce photons, ... everything within the range of the electromagnetic shower of the high-energetic processes. The calorimeter measures the total energy deposited.
A good detector can see the direction of this shower and extrapolate it back to the interaction vertex, but in collider experiments you often know the interaction point anyway.

A few hundred MeV for the pion should allow to see the photons as separate showers. This is different at the LHC, for example, where the showers overlap significantly.

 

[bcrowell]

Cool, thanks, Orodruin and mfb!

Am I correct in imagining that at least some (maybe all?) of the annihilation gammas in such a cascade would be produced from positrons annihilating at rest in the lab frame, so that you would see some multiplicity of 511 keV gammas, and there would be a sharp peak at that energy? This is what we see for gammas in the ~2-10 MeV range, but my experience doesn't extend to hundreds of MeV.

 

[Vanadium 50]

Very few. You would need a positron to stop (or nearly stop) via ionization before anihilating.

 

[bcrowell]

Very few. You would need a positron to stop (or nearly stop) via ionization before anihilating.

Hmm...that's what normally happens at lower energies (2-10 MeV gammas). Does that not happen with higher-energy positrons?

 

[Vanadium 50]

At high energies the other processes (brehm, compton, pair production, anihilation) play a relatively larger part than ionization.

 

[snorkack]

Do fast positrons readily slow down to produce more pairs on collisions with nuclei and electrons?
Like, if a fast positron collides with an electron, the results include:
1) elastic collision
2) braking radiation e⁺+e^-->e⁺+e^-+hnu
3) annihilation e⁺+e^-->2hnu or 3hnu, according to spins
4) pair production e⁺+e^-->2e⁺+2e^-
So, what is the branching ratio of 4 to 3, at energies where 4 is allowed?

 

[Vanadium 50]

It varies with energy. The PDG has a plot, I'm sure.

 

[ChrisVer]

This is different at the LHC, for example, where the showers overlap significantly.

Well I think you can still sort things out even for overlapping showers by either using a set of good classifiers and so the most information possible from the whole EM system. At least that's what some algorithms are for...

These two gammas would probably interact through pair production, so then you'd have some high-energy electrons and positrons

Again this in ATLAS can be resolved by tracking the electron positron pair if the conversion takes place before reaching the electromagnetic calorimeter. Otherwise if it happens within the detector, you get the electromagnetic showers [and that's the way you detect the gammas]

 

[mfb]

At high energies the other processes (brehm, compton, pair production, anihilation) play a relatively larger part than ionization.

They don't kill the positrons - apart from annihilation but that has a small cross-section at high energies. You still get the 511 keV photon pairs, but somewhere in a ton of other particles. I am not aware of any attempt to isolate those 511 keV photons. Even if a calorimeter would be granular enough for that - what would you gain?

Well I think you can still sort things out even for overlapping showers by either using a set of good classifiers and so the most information possible from the whole EM system. At least that's what some algorithms are for...

Both CMS and ATLAS have finely granulated first calorimeter layers to see two peaks instead of one, I know, but the showers still overlap for pions at relevant energies, which makes a reconstruction of their invariant mass tricky. It has been done (examples: ATLAS pp, CMS PbPb), but mainly with lower-energetic pions.

Photon conversion in the tracking system helps with tracking, of course.