What is the reason for the specific number of quarks in baryons and fermions?

[Schrodinger's Dog]

You'll have to excuse my ignorance I am fairly new to physics, having only the sort of predegree level of maths knowledge and a few ideas.

How do we come to the conclusion that baryons have 3 quarks and fermions have 2? Is there a mathematical reason for this? I assume this is proven or bourne out by experimental data too? I just remember reading that these fundamental particles come in these pairings and can see why it works as regards charge and spin but I could just as easily say there are 6 quarks or 12? Or I could say there are an infinite number of quasi quarks or they don't exist or whatever?

So obviously my preposterous other theories are false, how do we maintain the ideas that there are up down down, is it something to do with the weak force? Or is there something more fundamental that leads us to this conclusion.

 

[jtbell]

How do we come to the conclusion that baryons have 3 quarks and fermions have 2?

You mean mesons, not fermions.

Is there a mathematical reason for this? I assume this is proven or bourne out by experimental data too?

These particular combinations were originally proposed because they can explain the way that the various baryons and mesons can be classified according to their properties. This is rather similar to the way that QM's description of the atom can explain the way that the various elements can be classified according to their properties in the periodic table.

We also have more direct evidence for quarks in that particles scatter off each other in high-energy collisions in ways that we can explain (as far as we know) only by assuming they are made up of more fundamental particles that actually perform the scattering. This is rather similar to the way that Rutherford scattered alpha particles off of atoms and used the results to deduce that an atom must have a small, massive nucleus.

To measure the behavior of individual quarks in a baryon or meson, we often use leptons (neutrinos, electrons or muons) as our scattering "probes", because they are themselves fundamental pointlike particles, as far as we know. When I was a graduate student long ago, I worked on a neutrino-scattering experiment which (among other things) studied the quark structure functions of protons and neutrons, i.e. the functions which describe the probability that each quark carries a certain amount of the proton's/neutron's momentum in a collision.

So far, only two- and three-quark combinations fit experimental data, except perhaps for recent data that seem to indicate the existence of five-quark combinations ("pentaquarks"). I don't know what the status of that data is now.

 

[Schrodinger's Dog]

Sorry yes, just reading something about fermions and made a slip.

Thanks good answer, very clear.