Question

a) In a proton at one certain moment, the down quark has a strong color charge of red. What are the color charges of the two up quarks? (Type each color in lowercase with a space between each one.)

(d) In a pi meson at a certain time one quark has a red color. What is the color of the antiquark at that time?

Answer 1

A

Protons and neutrons are not fundamental. They are made of particles called quarks. There are a number of different types of quarks, called flavors. However, it takes only two flavors to make protons and neutrons: the up quark, , and the down quark, . The proton consists of two up quarks and one down:

Protons and neutrons are not fundamental. They are made of particles called quarks. There are a number of different types of quarks, called flavors. However, it takes only two flavors to make protons and neutrons: the up quark, , and the down quark, . The proton consists of two up quarks and one down:

There are six types of quarks, known as flavors: up, down, strange, charm, bottom, and top.^[4] Up and down quarks have the lowestmasses of all quarks.

The isospin of the proton and neutron then arises from the isospin of its quarks. Define and , making and the isospin up and down states at which their names hint. To find the of a composite, like a proton or neutron, add the for its constituents. This gives the proton and neutron the right :

The states and do not span a copy of the fundamental rep of inside

. So, as with color, the equations

'

B

Pions also fit into this model, but they require more explanation, because they are made of quarks and `antiquarks'. To every kind of particle, there is a corresponding antiparticle, which is just like the original particle but with opposite charge and isospin. The antiparticle of a quark is called an antiquark.

In terms of group representations, passing from a particle to its antiparticle corresponds to taking the dual representation. Since the quarks live in , a representation of , the antiquarks live in the dual representation . Since has basis vectors called up and down:

the space has a dual basis

called antiup and antidown. Similarly, since the standard basis vectors for are called red green and blue, the dual basis vectors for are known as anticolors: namely antired , antigreen , andantiblue . When it comes to actual colors of light, antired is called `cyan': this is the color of light which blended with red gives white. Similarly, antigreen is magenta, and antiblue is yellow. But few physicists dare speak of `magenta antiquarks'--apparently this would be taking the joke too far.

All pions are made from one quark and one antiquark. The flavor state of the pions must therefore live in

We can use the fact that pions live in to find out how they decompose into quarks and antiquarks, since

First, express the pions as matrices:

We know they have to be these matrices, up to normalization, because these act the right way on nucleons in :

Now, apply the standard isomorphism to write these matrices as linear combinations of quarks and antiquarks:

Note these all have the right , because isospins reverse for antiparticles. For example, , so .