# A few questions on quarks, gluons and the strong force

I wanted to answer for myself some pretty fundamental questions pertaining to the strong interaction, color charge and quarks, but I'm sort of stumbling on a few. So I wanted to find the reason/evidence that for each of the following statements:

1. Quarks are fractionally charged

For this one I would say that because we see Baryons (+1,0) with integer charge, and we also observe through scattering experiments that Baryons are made from 3 quarks, quarks should therefore be fractionally charged...

1. Gluons carry colour charge

I would say gluon self-interactions...

1. There are three quark colours

Two up quarks found in the proton + Pauli exclusion principle?

1. Quarks are spin 1/2 fermions

And not sure!

If anyone could either say whether I'm along the right tracks and if I am, could also help me with my understandign for 4 that would be excellent!

Thank you!

Let´s go:

 From the DIS (Deep Inelastic Scattering) of eletron-proton, we can imagine that the photon exchanged in te process "sees" a parton (possible constituent of the proton) distribuition.

We can imagine a cross-section of photons and that constituents of the proton. And we can analyze two situations:

From a cross-section of longitudinal (scalar) helicity photons, $\sigma_{s}$ and a cross-section of transverse helicity photons, $\sigma_{t}$ we can stabilish a relation:

$$\frac{\sigma_{s}}{\sigma_{t}}$$

And experimentally, we know its values. From the theory, this rate goes to infinite if we are talking about a spinless constituent, and goes to zero (at high frequencies of the scattered photon) for a spin-half constituent. This is how we know that quarks are spin-half. (this answers 4)

 There is a excited state of the proton, called $\Lambda^{++}$. This particle is composed by 3 up quarks. As we know the principle of exclusion, we couldn't have 3 fermions in the same state unless there is a additional degree of freedom we are not taking into account.

This additional degree of freedom is the Colour charge. But the fact that we need 3 colours (3 kinds of charge) cames from the choice of the gauge group that describes the strong interactions, the SU(3).

And by this very choice, we have a non-abelian gauge symmetry wich means that our gauge bosons (in this case gluons) interact with each other, because in the non-abelian case:

$$F_{\mu \nu} = {\partial}_{\mu} A_{\nu} - {\partial}_{\nu} A_{\mu} - iq[A_{\mu},A_{\nu}]$$

The last term (the commutator) of $A_{\mu}$ and $A_{\nu}$ does not vanish and so the Lorentz invariant term in the Lagrangian $F_{\mu \nu}F^{\mu \nu}$ gives 3-field and 4-field interactions of the gauge bosons. (this answers 3 and 2)