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I have a proton, how do I know that it is made of 2 up quarks and 1 down quark or if it is made of 3 anti-down quarks, each with different color charges?

This question is also applicable to the antiproton, is it made up of 2 antiup and 1 antidown or of 3 down quakrs?

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You're welcome to improve on the edit I made to your post, but please don't use MathJax for things that aren't math. Quark types, when spelled out, should be written as normal text; they are not mathematical symbols. I'll roll that edit back, but again, you're welcome to make further changes as long as they actually improve the post. –  David Z Aug 5 '13 at 18:27
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@dmckee The OP mentioned antidown quarks, so they would have a +1 charge. (Also I thought $ddd$ was the $\Delta^-$; is $\omega^-$ just another notation for that, or is there something else going on?) –  David Z Aug 5 '13 at 18:41
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2 Answers 2

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Basically, it's because the proton has spin $\frac{1}{2}$, which means the quarks' spins need to be split: two in one direction (let's say up) and one in the other direction (down). But having two quarks with opposite spins and different colors but the same flavor (antidown) violates the Pauli exclusion principle. So there can't be a spin-$\frac{1}{2}$ baryon made of three of the same flavor quark.

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I'm confused by that second sentence. If they have different spins and colors, how does Pauli exclusion apply? And how is $\mathrm{uud}$ any more permissible under this argument than $\mathrm{\bar{d}\bar{d}\bar{d}}$? –  Chris White Aug 7 '13 at 16:43
    
I'm a little confused about that myself, but I think the result should come out of projecting all possible states of the proton onto a completely antisymmetric subspace. I tried to work through that calculation for this answer but it quickly became very tedious (and I wasn't even sure I was doing it right... if I figure it out, I'll add it in). Regardless, I've heard this stated in many places. –  David Z Aug 7 '13 at 20:01
    
@DavidZ: I read in Wikipedia that having the same flavor will produce a 3/2 spin, but why? –  Hakim Jun 4 at 20:19
    
@حكيمالفيلسوفالضائع that's because the spins have to be in a symmetric state, which effectively means they all add up. Though as I mentioned above, the calculations to show this are rather tedious. –  David Z Jun 4 at 20:58
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The Standard Model which has been decided upon after a thorough experimental observation of the interactions of particles at the micro level, i.e. the space and energy dimensions where quantum mechanics reigns, has as a main pillar the quark model.

spin 1/2 baryon

The quark model started with the above observation: that if the particles were plotted in two dimensions using their spins and their quantum numbers ( isotopic spin, strangeness, etc) a beautiful symmetry emerged, which also ordered the particles according to their masses.This symmetry was found to be mathematically represented by the representations of the special unitary group , SU(3). The 3 means that there are 3 basic units which can be permuted to fill up the points of the representations. These were whimsically named "quarks".

This plot is the baryon spin 1/2 plot of which the proton is a member. There are a number of other representations where the data from hadronic resonances fit well, and even a prediction was made that the omega minus should exist because all the other members of the decuplet were experimentally seen already.

decuplet

It was found, and it established the quark model, and nobel prizes were awarded to the researchers at the frontier of this work.

All quarks are assigned a baryon number of 1⁄3. Up, charm and top quarks have an electric charge of +2⁄3, while the down, strange, and bottom quarks have an electric charge of −1⁄3. Antiquarks have the opposite quantum numbers. Quarks are also spin-1⁄2 particles, meaning they are fermions.

Mesons are made of a valence quark−antiquark pair (thus have a baryon number of 0), while baryons are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavours of quark (which form an approximate SU(3) symmetry). There are generalizations to larger number of flavours.

Now if you look at the plot of the ground state baryon octet, you can see that it does not matter what we call them, it is the symmetry that establishes their quark content. Thus the proton, which is the name of the particle with the lowers mass in this representation, can be nothing but the building block of the solid matter we exist on. We call it a proton, its constituents quarks with given names. If one changed the quark content, one would have a different name, it would be a different particle and not the lowest energy state in the stable representation.

The proton has to add up to baryon charge of 1, your speculative quantum numbers cannot do that by the definition of quarks and their position in the SU(3) representations. Anti quarks add up to anti baryons, and the proton is not an antibaryon by definition.

The representations are restrictive by experimental measurements, and one cannot throw quarks like dice, because the whole quark representation is constrained , and the names of the particles are convenient, but are really a one to one correspondence with the quark content by construction of the mathematics that nature is using.

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The fact that protons are the lightest-mass baryons is good and in some ways sufficient, but it seems we should be able to distinguish $p = uud$ from $\bar{\Delta}^+ = \bar{d}\bar{d}\bar{d}$ (or however one denotes the antiparticle of $\Delta^-$) based just on (iso/regular) spin. Yes, one could say we observe $\bar{\Delta}^+$ to have $I_3 = +3/2$, $J = 3/2$, and that we observe $p$ to have $I_3 = +1/2$, $J = 1/2$. But then why can't $\bar{d}\bar{d}\bar{d}$ have quantum numbers matching the proton? –  Chris White Aug 7 '13 at 20:57
    
Because it adds up to baryon number -1 (that is what the anti means) and the proton has baryon number +1. It cannot be the anti proton because of the spin, that is why the deltas are in the 3/2 multiplet whereas the proton and neutron is in the 1/2. I am trying to say that the concept of "quark" that has been annointed to the status of "particle" rests entirely on the SU(3) representations which magically order all these measurements into coherent subgroups. One cannot choose quarks a la carte. They have to fit in the representations that established their existence. –  anna v Aug 8 '13 at 3:23
    
@ChrisWhite the above was for you. It is not enough to find three quark quantum numbers to say that they exist as baryons. They have to be found in one of the SU(3) representations. The delta has the four charge expressions and fits in this slot of the 3/2 representation. It is the symmetry representations that define the quark content and not the inverse. That is what was so exciting back in the early sixties, that the boring plethora of hadron resonances had such a beautiful framework. –  anna v Aug 8 '13 at 3:50
    
@annav All what you show is what the proton, by definition, is. Not what it may be. –  Hakim Nov 23 '13 at 11:50
    
The definition comes from the identification of the lowest energy stable charged particle which generates matter as we know it. We call it a proton. You could call it a zumba forall the difference it could make , but the identification comes from the quark content and the matter stability ( experimental). From the doublet you could say it is the neutron if we did not know experimentally that the stable component of matter is charged. –  anna v Nov 23 '13 at 12:01
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