Undergrad Particle Creation function of beam energy

[Albertgauss]

TL;DR

As you crank up the beam energy in particle accelerator, what particles are possible at each energy

This seems like it should be an easy and obvious thing to look up, but I had the hardest time finding it. Is there any graph which shows, as I increase the beam energy of a particle accelerator, what particles can be produced at each energy? Just looking for something ballpark here. Obviously there are a ton of hadrons and mesons, but maybe just the most important/famous/etc particles would appear on such a graph.

 

[mfb]

For electron-positron colliders it's relatively easy: If the particle can be created in isolation (e.g. Z boson) then the collision energy needs to be its mass, if it is created in pairs (e.g. everything with quarks) then you need twice that energy. For every process you can just add up the mass of the produced particles: That's how much energy you need (speed of light squared as conversion factor).
If we skip the low energy region (where a lot of different things happen): 3 GeV for particles with charm quarks and tau, 10 GeV for particles with bottom quarks, ~90 GeV for the Z boson, ~160 GeV for W bosons, ~215 GeV for the Higgs boson (as the production of Z+H is the first relevant process), 350 GeV for top quarks. LEP reached 209 GeV, they just missed the Higgs.

For hadron colliders things are more complicated. The theoretical minimum is still the same but in practice you need much more energy to get a relevant production rate. These calculations are done particle by particle so you can often find cross sections ("production probabilities") as function of collision energy. Here are some cross sections

 

[Meir Achuz]

For any center of mass energy, W, the particles that can be created have to satisfy
\sum_i M_i\ge W, and the conservation laws of charge, etc.
For a fixed target, the lab kinetic energy is given in terms of the center of mass energy by
(KE)_{\rm lab}=[W^2-(M+m)^2]/2M. (Derive this.)

 

[Albertgauss]

Excellent. I understand. I knew the particles created needed to be at least mc2, but I didn't know if there was any other requirement (of course, I understand all the necessary laws must be conserved).

One last question:

Once a reaction has the minimum mc2 to create the particle, are there ever higher energies (or a range of energies) beyond this minimum energy that creates the most particles?

Just to make things easy, suppose a particular hadron or meson has a mc2 of "1", but if I tuned my beam energies to say "3" or "4", would I get some energy that would create the most particles of mc2 of "1"? I'm using simple numbers here because I'm just interested in a qualitative, ballpark answer.

 

[mfb]

In electron-positron colliders there can be an ideal energy.

• For the Z that's simply the Z mass.
• For ZH the ideal energy is about 270 GeV. Lower and the phase space is very small (both particles need to be nearly at rest relative to each other), higher and other processes are more likely. Here is a plot.
• For B mesons the ideal energy is the $\Upsilon(4s)$ resonance, which usually decays to pairs of B mesons. You might get more again at very high energy, but at least it's a strong local maximum.

For hadron colliders more is better - outside the low-energy region all the reactions get more likely with more energy.

 

[Meir Achuz]

Generally, the more the center of mass energy (W), the more particles are created.
However, if W equals the energy of a short-lived resonance, there is a large jump in particle creation.
For instance, when electrons collide with protons, pion production jumps when W approaches the mass of the \Delta resonance.