It really depends. The Pauli exclusion principle states that no two fermions can occupy the same quantum state. The quantum state is usually defined by quantum numbers, in the case of a quark in a baryon, the important ones are flavour, colour and spin. Let's just consider a baryon and ignore antibaryons to keep the number of quantum states to a limit.

Each quark in the baryon must have a different colour quantum number (red, green and blue) so that they add up to zero colour charge. Lets assume that all three quarks are the same flavour (say up). Now we can see that all three quarks have different quantum states, but the spin has not yet been constrained at all. Each quark can be either 1/2 or -1/2. So The total angular momentum of the baryon in the ground state is either 1/2 (uud or udd) or 3/2 (uuu or ddd). The jp = 1/2 state forms at different group of baryons to the jp = 3/2 state; the two sets of baryons are degenerate.

In short, quarks of the same flavour in a baryon has nothing to do with the spins of those quarks.

Thanks Robert. I should clarify my question and restate what I am referring to. I wanted to find out if spin direction for quarks of the same flavour in a neutron (uud) or proton (udd), not delta baryons, must have opposing spin direction So for exampl, in a proton do the two up quarks have to be in opposing spin direction to the down quark; and likewise, do the two down quarks in a neutron have to be opposite in spin to the up quark. From what you have said above it sounds like that quark flavour is not related to spin direction for protons and neutrons.

But on this wikipedia page, it gives examples where quarks of the same flavour have the same spin direction; so that's why I am asking this question.

see link below under the sub-heading: 'Isospin symmetry of quarks'

https://en.wikipedia.org/wiki/Isospin#cite_note-greiner-5

Hi Mark, I now understand what you were asking and it's a good question...

Since protons are fermions, the total wavefunction of the 3 quarks must be antisymmetric when 2 quarks are exchanged. Since the colour charge wavefunction is antisymmetric, this implies that the combined spin, flavour and spatial wavefunctions must be symmetric. The spatial wavefunction for a proton or neutron in its ground state is symmetric (like the S orbital). Therefore the combined spin and flavour wavefunction must be symmetric.

Let's start by swapping the 2 ups (or downs). Clearly the flavour wavefunction is symmetrical, therefore the spin wavefunction must be symmetrical; i.e. they must both have the same spin.

Now let's consider swapping an up and a down. The flavour wavefunction is anti-symmetric, therefore the spin wavefunction must also be anti-symmetric.

So if you have two quarks of the same flavour in a baryon they will have the same spin. Thank you for the good question, it was a very interesting one once I understood it!

I would like to add the following in the discussion. What is known from the experiments

is the spin content of the proton in terms of its constituents namely various quarks , antiquarks, gluons. It is more or less clear now that substantial part of the spin

comes from gluons and some from orbital components as well.

We now know what is u quark contribution to proton spin, d quark contribution to proton spin (they are there in the literature). To get similar information for neutron

(that is , spin content ofthe neutron), we can use isospin symmetry that relates proton to neutron (it is an approximate symmetry but still works fine at somelevel).

This implies u quark contribution to proton spin is same as d quark contribution to neutron spin.

The flavor and spin part of proton (spin-up) wave function, shown in the wikipedia mentioned by Marc two days ago, can be rewritten simplified as,

|p(+)>= |uud>(|+-+>+|-++>-2|++->)+......

(|+> means spin-up.)

This means two u quark spins can be both parallel (|++>) and anti-parallel (|+-> or |-+>).

Note that complete wave function;

|uud>(|+-+>+|-++>-2|++->)+|udu>(|++->+|-++>-2|+-+>)+|duu>(|+-+>+|++->-2|-++>)

is symmetric for exchange of any quark pairs.

This is for simple quark model. But even if quark contribution to proton spin is small, I think the statement of "u quark spins can be parallel and anti-parallel" is still correct, since sea quarks and gluon contribution will make situation more random.

I guess, Marc's question from Wikipedia came from misunderstanding of description of Delta baryon.