Percentage of neutral pions created

cambrian

When bombarding a target with a high energy proton beam, of the pions produced, what determines the percentage of them that are neutral?

mfb

It depends on your target material and the energy.
I would expect that about ~1/3 to ~1/2 of all produced primary (!) pions are neutral.

cambrian

Thanks mfb.

How do you know this? Let's say we had a liquid hydrogen target (so all proton targets). So we have an incoming proton with energy E interacting with a stationary proton. There will be some impact parameter, p. Given E and p (well - I would be messing with Heisenberg - but let's say we knew them within some small error) , is there a rule for determining what pions are produced?

Thanks again.

Bill_K

I believe at high energies such as at the LHC, details cease to matter, and the number of positive, negative and neutral pions produced is about equal.

mfb

At high energy, light quarks (especially up and down) and antiquarks are produced in large amounts, and combine to some hadrons afterwards. I would expect that "up anti-down", "down anti-up", "up anti-up" and "down anti-down" all have a similar probability, and form pi+, pi-, pi0, pi0, respectively. That approximation is not perfect, of course, as you have the initial valence quarks (2 up and 1 down in the beam, some variable composition in the target) and the quarks have a small mass.

Bill_K

But it's only the linear combination (up-antiup - down-antidown) that forms a pi0, right?

mfb

Right, therefore I wrote 1/3 to 1/2 - I would expect that the neutral pion counts twice, but I am not sure.

Vanadium 50

In the limit it's 1/3. This is from isospin symmetry. At 91 GeV, the measured number is 0.369 +/- 0.014.

ofirg

Even for for events with very high pt jets at the LHC ( 1TeV) the neutral pion has the slight egde mentioned by Vanadium 50(~37%) over the democratic case. I think this is because even if the collision happens at very high energies the hadronization proccess in which the pions are produced occurs close to the [itex]\Lambda_{qcd}[/itex] scale, so the mass difference still has an effect.

Vanadium 50

I think it's decays of heavier states, not mass differences, that slightly favor the pi0.

cambrian

Thanks everyone, That is very helpful.

What about at lower energies? If I have a 3 GeV beam, would you expect the % of pi0 to increase or decrease compared to the 91 GeV case?