# Quark Structure of Particles & Antiparticles: Rules & Order

• neelakash
In summary, the conversation discusses the rule for determining the quark structure of an antiparticle based on the structure of the particle. It also addresses the question of whether the order of letters in the quark symbol has any significance. The expert suggests reading on the Fonda-Ghirardi tensor representations for SU(3) to find the answer.
neelakash
I am asking this question because I did not get it clarified in any of the books I have read.
What is the rule for having the quark structure of an antiparticle given the structure of the particle?Is it always OK to put bar on the quark symbols of the corresponding particle?

Specifically,I know proton is represented as $$\ u \ u \ d$$ and antiproton as
$$\bar{u}\bar{u}\bar{d}$$

Is it true that since neutron is $$\ u \ d \ d$$, we must have anti neutron:
$$\bar{u}\bar{d}\bar{d}$$?

Another thing: Is there any rule for the order of letters while writing the symbol for a particle?In other words, uud or udu or duu---do they mean the same?

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In a hadron, all quarks in the anti hadron shall be anti, just as you did with the neutron.

Another example, the anti-particle to the $$\pi ^+$$, Quark content: $$u \bar{d}$$, Is $$\pi ^+$$, Quark content: $$d\bar{u}$$. Since $$\bar{\bar{u}} = u$$ etc.

The "rule" is to start with all quarks in the same generation, e.g (u and d) then (c and s) then (b and t). Then in the same gruop you start with the positive charged quark. Then you have the anti-quarks in the end.

For example, the D meson: $$D^+ = c\bar{d}$$

But I think different conventions exists, the important things are the total quark content, Mass, Spin etc. Those are the quantities that determines the physics.

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The "rule" is to start with all quarks in the same generation, e.g (u and d) then (c and s) then (b and t). Then in the same gruop you start with the positive charged quark. Then you have the anti-quarks in the end.

For example, the D meson:

But I think different conventions exists, the important things are the total quark content, Mass, Spin etc. Those are the quantities that determines the physics.

I see.Thanks.

neelakash said:
Another thing: Is there any rule for the order of letters while writing the symbol for a particle?In other words, uud or udu or duu---do they mean the same?
The order has to be correlated with the other degrees of freedom.
For instance, in the proton, the two u quarks must be in the symmetric spin one state.
If you change uud to udu, then the spin wave function has to be similarly permuted.

clem said:
The order has to be correlated with the other degrees of freedom.
For instance, in the proton, the two u quarks must be in the symmetric spin one state.
If you change uud to udu, then the spin wave function has to be similarly permuted.

That does not make sense. It is a difference of writing the representation of the hadron by its quark content as uud , and by writing its state as: |p> = 1/sqrt(18){2|uud> + 2|udu> + ... etc.

malawi_glenn said:
That does not make sense. It is a difference of writing the representation of the hadron by its quark content as uud , and by writing its state as: |p> = 1/sqrt(18){2|uud> + 2|udu> + ... etc.
The quark order must be consistent with the spin order. For instance, for the proton
(using a for spin up and b for spin down), a suitable wave function is
|p>=uud(2aab-aba-baa)/\sqrt{6}.
If the quark order is changed to udu, then the last two spins must also be interchanged to give |p>=udu(2aba-aab-baa)/\sqrt{6}.

but as I said, you are talking about the wave function. The OP asked about the "REPRESENTATION". In the representation, you don't write the whole wave function, you write the quark content, spin, mass etc.

And if you want the whole wave function, |p>=uud(2aab-aba-baa)/\sqrt{6} is not good enough, it has 9 terms

malawi_glenn said:
but as I said, you are talking about the wave function. The OP asked about the "REPRESENTATION". In the representation, you don't write the whole wave function, you write the quark content, spin, mass etc.

And if you want the whole wave function, |p>=uud(2aab-aba-baa)/\sqrt{6} is not good enough, it has 9 terms
Only Neelakash knows what he asked.
I don't know what Malawi means by "representation"
If you just mean the number of each type of quark, the order doesn't matter.
If you mean something more, then the quark order must be correlated with the spin order in each term.
You could write the wave function I gave three permuted times, but then would you do every calculation three times? What I wrote is all you need.

Neelakash meant : "Specifically,I know proton is represented as $$\ u \ u \ d$$
and antiproton as
$$\bar{u}\bar{u}\bar{d}$$"

So what both him and me means with representation is that when looking in particle tables etc, you often only finds the quark content. So what he aksed is "uud and udu" the same particle? And my answer indicated that there are more things than just the quark content that matters, spin etc also plays role. For example the delta+ baryon has the same quark representation (uud) as p, but has a different wave function. So neither him or me was originally talking about wave function, we only disscussed the representation. And the representation follows the convention that I posted..

neelakash said:
I am asking this question because I did not get it clarified in any of the books I have read.
What is the rule for having the quark structure of an antiparticle given the structure of the particle?Is it always OK to put bar on the quark symbols of the corresponding particle?

Specifically,I know proton is represented as $$\ u \ u \ d$$ and antiproton as
$$\bar{u}\bar{u}\bar{d}$$

Is it true that since neutron is $$\ u \ d \ d$$, we must have anti neutron:
$$\bar{u}\bar{d}\bar{d}$$?

Another thing: Is there any rule for the order of letters while writing the symbol for a particle?In other words, uud or udu or duu---do they mean the same?

My suggestion is to read on Fonda-Ghirardi what is the tensor-Representations for SU(3).

regards
Marco.

Opps I'm sorry i meant Huang Kerson's Book, if i remeber righ... chapter 2 and the book was: Quark and leptons..

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## 1. What are quarks and what is their role in the structure of particles and antiparticles?

Quarks are fundamental particles that make up the building blocks of matter. They are the smallest known particles and are responsible for the structure and properties of all particles and antiparticles.

## 2. How many types of quarks are there and what are their names?

There are six known types of quarks: up, down, charm, strange, top, and bottom. These names are based on the properties and behavior of each type of quark.

## 3. What are the rules that govern the behavior of quarks in particles and antiparticles?

The rules that govern the behavior of quarks are known as the Standard Model of particle physics. This model describes the interactions of quarks with each other and with other particles through the four fundamental forces: strong, weak, electromagnetic, and gravitational.

## 4. How are particles and antiparticles related in terms of quark structure?

Particles and antiparticles have the same quark structure, except for the fact that they have opposite charges. For example, a proton (particle) is made up of two up quarks and one down quark, while an antiproton (antiparticle) is made up of two up antiquarks and one down antiquark.

## 5. Can quarks exist independently outside of particles and antiparticles?

No, quarks cannot exist independently outside of particles and antiparticles. Due to the nature of the strong force, quarks are always bound together in groups of two or three to form particles. This phenomenon is known as confinement.

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