# Understanding SU(3) & Quarks: Proton Structure & Multiplets

• faen
In summary, the conversation discusses the fundamental representation of SU(3) and how it relates to the structure of protons and the concept of multiplets. The participants also touch on the importance of maintaining color neutrality in quark combinations.

#### faen

Can anyone please explain to me how quarks are the fundamental representation of SU(3)?

Why is a proton exactly uud and not another combination of quarks?

What is a multiplet?

Hi,

I'll pick the short one
faen said:
Why is a proton exactly uud and not another combination of quarks?
This is not true : the valence part of the proton, which determines its quantum numbers (so its unique identity) is exactly uud, but there is more to the proton. There is an infinite tower of additional Fock state, or if you will as much vacuum fluctuations as you can wish for if you look "close enough" (at short distances).

but why is it not let's say just u or uuudd? Those combinations also correspond to the protons isospin so why just uud? the baryon number and charge seems to be defined after knowing that it is the combination of 3 quarks which determine the proton state.

faen said:
but why is it not let's say just u or uuudd? Those combinations also correspond to the protons isospin so why just uud? the baryon number and charge seems to be defined after knowing that it is the combination of 3 quarks which determine the proton state.
We always proceed by trials and errors. You can not expect that we knew historically about quarks before we knew about protons. Given quarks, the minimal combination considering all quantum numbers is uud. That is what we call valence part of the wavefunction.

uuudd does not satisfy colour neutrality.

malawi_glenn said:
uuudd does not satisfy colour neutrality.

true. if one of the d's is a dbar, then it's a pentaquark, those mythical particles that we thought we found a few years back.

blechman said:
true. if one of the d's is a dbar, then it's a pentaquark, those mythical particles that we thought we found a few years back.

also one u must be u-bar in order to maintain colour neutrality.

malawi_glenn said:
also one u must be u-bar in order to maintain colour neutrality.

no - you can have the color combination r+g+b+c+cbar (where c is any color). that's the pentaquark.

ah yeah of course, stupid me.. and I supposed to be a Hadron Physicsits:P

faen said:
Can anyone please explain to me how quarks are the fundamental representation of SU(3)?

Why is a proton exactly uud and not another combination of quarks?

What is a multiplet?

Which SU(3) are you referring to? SU(3)_c (color) or SU(3)_f (flavor)? It makes a difference...

## 1. What is SU(3) in relation to particle physics?

SU(3) is a type of mathematical group that is used to describe the symmetries of the strong nuclear force, which is one of the four fundamental forces in particle physics. It is used to understand the behavior of particles known as quarks within the theory of quantum chromodynamics (QCD).

## 2. How does SU(3) relate to the structure of protons?

Protons are made up of three quarks, which are held together by the strong nuclear force. SU(3) is used to describe the symmetries of this force and how it interacts with quarks, allowing us to better understand the structure of protons and other particles.

## 3. What is the significance of quark multiplets?

Quark multiplets are groups of particles that have similar properties and interact with each other in a consistent way. Understanding these multiplets is important in studying the behavior of quarks and how they form different types of particles.

## 4. How does the concept of color charge relate to SU(3) and quarks?

Color charge is a property of quarks that describes their strong interactions. Similar to how electric charge can be positive or negative, color charge can be red, green, or blue. SU(3) is used to describe the symmetries of these color charges and how they interact with each other.

## 5. What are some real-world applications of understanding SU(3) and quarks?

Understanding SU(3) and quarks has led to advancements in our understanding of the strong nuclear force, which has practical applications in fields such as nuclear energy and particle accelerators. It also helps us understand the behavior of matter at a fundamental level, leading to developments in technology and materials science.