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 process in which the pions are produced occurs close to the \Lambda_{qcd} 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?