Option J: Particle physics J3 Quarks This part of Option J has already been covered in Option D5 Quarks. It is replicated here without any changes

Option J: Particle physicsJ3 QuarksThis part of Option J has already been covered in

Option D5 Quarks.

It is replicated here without any changes.

J.3.1 List the six types of quark.

J.3.2 State the content, in terms of quarks and antiquarks, of hadrons (that is, baryons and mesons).

J.3.3 State the quark content of the proton and the neutron.

J.3.4 Define baryon number and apply the conservation of baryon number.

J.3.5 Deduce the spin structure of hadrons (that is, baryons and mesons). Only an elementary discussion in terms of ‘spin up’ and ‘spin down’ is required. See D.4.4 above for details.

Option J: Particle physicsJ3 Quarks

List the six types of quark.

You have already been introduced to the six quarks:

Quarks participate in the strong force whose carrier is the gluon.


Quark

Flavor Symbol Charge

Up u + 2/3Down d - 1/3

Strange s - 1/3

Charm c + 2/3

Bottom b - 1/3

Top t + 2/3

Antiquark

Symbol Charge

u - 2/3d + 1/3

s + 1/3

c - 2/3

b + 1/3

t - 2/3

State the content, in terms of quarks and antiquarks, of hadrons (that is, baryons and mesons).

A hadron is a particle that participates in the strong force.

Since quarks participate in the strong force, and since baryons and mesons are made of quarks, baryons and mesons are hadrons.

A baryon is made of three quarks (qqq). An antibaryon is made of three antiquarks (qqq).

A meson is made up of a quark and an antiquark (qq):


FYIA single quark cannot be isolated. We will talk about quark confinement later. Basically, confinement states that you cannot separate a single quark from a hadron.

State the quark content of the proton and the neutron.

A proton is a baryon made up of two up quarks and a down quark. p = (uud).

A neutron is a baryon made up of one up quark and two down quarks. n = (udd).


EXAMPLE:

Show that the charge of a proton is +1, and that the charge of a neutron is 0.

SOLUTION:

The charge of an up quark is +2/3.The charge of a down quark is -1/3.Thus

Proton = uud : +2/3 + +2/3 + -1/3 = +1.

Neutron = udd : +2/3 + -1/3 + -1/3 = 0.

Define baryon number and apply the conservation of baryon number.

The baryon number of a quark is +1/3. The baryon number of an antiquark is -1/3.


quark (q) or antiquark (q) baryon number B

Quark: B = +1/3Antiquark: B = -1/3

PRACTICE: What is the baryon number of a proton and an antiproton?SOLUTION: Proton = uud : +1/3 + +1/3 + +1/3 = +1.Antiproton = uud : -1/3 + -1/3 + -1/3 = -1.PRACTICE: What is the baryon number of a meson?SOLUTION: A meson has the quark makeup (qq) so that it has a baryon number of +1/3 + -1/3 = 0.

FYIBaryon number is conserved in all reactions.

Deduce the spin structure of hadrons (that is, baryons and mesons).

The spin of a quark (or antiquark) is spin up ( = 1/2) or spin down ( = -1/2).


quark (q) or antiquark (q) spin

Spin up +1/2 or Spin down -1/2 or

PRACTICE: Deduce the possible spin structures of a baryon:SOLUTION: A baryon is (qqq): Possibility 1: +1/2 + +1/2 + +1/2 = +3/2. Possibility 2: +1/2 + +1/2 + -1/2 = +1/2. Possibility 3: +1/2 + -1/2 + -1/2 = -1/2. Possibility 4: -1/2 + -1/2 + -1/2 = -3/2.

FYIRecall that fermions have odd multiples of ½ as their spin and obey the Pauli exclusion principle.


The spin of a quark (or antiquark) is spin up ( = 1/2) or spin down ( = -1/2).


quark (q) or antiquark (q) spin

Spin up +1/2 or Spin down -1/2 or

PRACTICE: Deduce the possible spin structures of a meson:SOLUTION: A meson is (qq): Possibility 1: +1/2 + +1/2 = +1. Possibility 2: +1/2 + -1/2 = 0. Possibility 3: -1/2 + -1/2 = -1.

FYIRecall that bosons have even multiples of ½ as their spin (whole number spins) and DO NOT obey the Pauli exclusion principle.



Pauli says they can’t have identical quantum numbers. Their colors differ.

A proton has a quark structure of uud.

Each quark has a spin of ½.

If two of the three quarks has a spin of + ½ and the other a spin of – ½ the proton has a spin of ½.

J.3.6 Explain the need for color in forming bound states of quarks.

J.3.7 State the color of quarks and gluons.

J.3.8 Outline the concept of strangeness.

J.3.9 Discuss quark confinement.

J.3.10 Discuss the interaction that binds nucleons in terms of the color force between quarks.


Explain the need for color in forming bound states of quarks.

Two electrons repel, yet an electron and a positron (or proton) attract. To explain such interactions we use the model of “charge,” and give charges either a (+) or a (–) value.

Quarks, on the other hand, seem to show three types of charge, rather than two. A model using (+) and (-) numbers fails.

Instead, physicists use the color charge model because of the three primary colors red, green, and blue.


FYIPerhaps you recall from an art class that adding red, green and blue light produces white light. The color charge model requires all particles to be “white.”

State the color of quarks and gluons.

Just as (+) and (-) are used to explain the electromagnetic force, the three colors are used to explain the strong force.

Quarks come in red, green, and blue.Antiquarks come in anti-red, anti-green, and anti-blue.


FYINote that, for example, anti-red is the green-blue combo (cyan).Note that since all particles must be white, a baryon must have the color combo (qqq) and an antibaryon must have the color combo (qqq).A meson must have the color combo (qq), (qq), (qq).The color charge of a particle is zero (white).

State the color of quarks and gluons.

Gluons, the strong force carrier, have two colors and are not white (and thus have a non-zero color charge).

This gives gluons the ability to carry the strong force.

The complete theory of the color force is called quantum chromo dynamics (QCD).


quark

quark

quark

gluon

gluon

gluon

Outline the concept of strangeness.

The strangeness number S of a baryon is related to the number of strange quarks the particle has and is found using the formula


strangeness SS = #Antistrange quarks - #strange quarks

EXAMPLE: The lambda zero particle (0) is a baryon having the quark combo of (uds). What is its charge? What is its strangeness?

SOLUTION:

From a previous table the charges are u = +2/3, d = -1/3 and s = -1/3 so that the total charge is 0.

From the above formula S = #Antistrange quarks - #strange quarks

= 0 – 1 = -1.



The – is a hadron because it is composed of quarks.



The proton is composed of uud.



If X is sss, then the reaction can be written in terms of quarks as follows:

su + uud ds + us + sssThe left has an s, u, and d left.The right also has an s, u, and d left.The quarks are balanced on each side.

Discuss quark confinement.

Quark confinement means that we cannot ever separate a single quark from a baryon or a meson.

Because of the nature of the strong force holding the quarks together we need to provide an energy that is proportional to the separation.

Eventually, that energy is so vast that a new quark-antiquark pair forms and all we have is a meson, instead of an isolated quark!


Discuss quark confinement.


Origin

al

meson

Newly-

create

d

meson

Quark-

antiqu

ark pa

ir

create

d from

energy

neede

d

for se

parati

on

Discuss the interaction that binds nucleons in terms of the color force between quarks.

The residual color force of the gluons that hold the quarks together is what is known as the strong force.

Thus nuclear reactors and bombs represent only the residual energy in the gluon interaction between quarks.


Documents

Option J: Particle physics J3 Quarks This part of Option J has already been covered in Option D5 Quarks. It is replicated here without any changes