# Homework Help: Particle physics exam preparation

1. Feb 24, 2016

### Schwarzschild90

1. The problem statement, all variables and given/known data
See the PDF.

I would like some pointers as to what would be most relevant to talk about

2. Relevant equations
Amplitude, cross sections and decay rates.

3. The attempt at a solution
1) Particle classification: From the Eightfold way to the quark model

• Particles are classified approximately by their mass.
• There are two families of particles: Hadrons and Leptons. The hadrons being the heaviest and the leptons the lightest.
• Hadrons are further subdivided into baryons and mesons. Baryons being the heavier of the two. A distinguishing characteristic being that baryons are composed of three quarks and mesons of a quark and an antiquark.
• [Baryons] Eight baryons exist in all, and comprise six of the vertices of the baryon octet; the remaining two particles occupying the middle of the diagram. The Eightfold Way arranges mesons and baryons into the vertices of geometric shapes according to charge and strangeness.
• Protons are the most stable and in time all other baryons decay into the proton.
• [Antibaryons] Eight antibaryons exist in all. To get the an antibaryon, reverse the sign of all quantum numbers.
• [Mesons] contain a quark and an antiquark pair. The diagram form the pseudoscalar meson octet.
• [Leptons], as quarks, are categorized as elementary particles; their substructure being unknown.
• Six leptons exist in all. {electron, muon, tau} and their neutrinos. Leptons have an associated lepton number, [electron number], [muon number] and [tau number]. Leptons are subject only to the weak force.
• [The Baryon Octet] is a geometric model of the eight known baryons. The diagonal lines denote strangeness (-1, 0, 1), while the horizontal lines denote charge (-1, 0, 1). The intersection of these three lines form the vertices of a six sided shape and two particles constitute the center.

2) Neutral Kaons and the violation of CP
• What are neutral Kaons?
• Neutral kaons are composed of a strange antiquark and an up antiquark.
• If a complex phase term exists, then it will give rise to direct CP violation, which could explain why matter dominates antimatter in the universe. Proven for the CKM matrix and expected for the PMNS matrix.
• How can one distinguish the two types of neutral Kaons?
• The type of neutral kaon in question, can be found out, by studying the decay products.
• The neutral kaon decaying into two pions has positive CP violation, the one decaying into three pions, has negative CP violation.
• What is CP violation?
• Consider a beam of kaons. After a short while, it so happens that all the $K_s^0$kaons have disappeared, leaving just the $K_L^0$kaons. Thus, the $K_L^0$kaons do something they're not supposed to do.
• What is CP?

3) What is isospin? Isospin symmetry and its implications for nucleon-nucleon scattering.

• Isospin is a quantum number related to the strong interaction.
• Formally, it is not actually a spin, but it is mathematically related to spin and orbital angular momentum. Thus it can be coupled in the same manner.
• Properties of isospin
• It can be coupled as 1 or 0.
• It is a type of symmetry seen most commonly in baryons and fermions.
• Was invented to explain the properties of the neutron.
• Neutrons and protons are nearly identical in mass. It was proposed that the difference in mass could be attributed to the energy that the proton stores in the positive electric field.
• The strength of nucleons interacting is the same regardless of which nucleons are interacting. Neglecting the electromagnetic force.
• Multiplets are characterized as having same spin angular momentum and orbital angular momentum.

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2. Feb 24, 2016

### Staff: Mentor

Tau is heavier than a proton, for example.
And what about the elementary bosons?
Compare J/Psi and a proton...
Way more than eight.
What about the neutron in deuterium?
There is really good evidence that they do not have a substructure.

The topic is about baryons and quarks. Many of your points are about leptons, and you don't even list how many quarks we know.

That violates what you said above.
Phase term of what?
I don't think you mean "CP violation" here.
What are they doing?

I think the subtopic selection here is better.

What would be uncommon?

3. Feb 25, 2016

### Schwarzschild90

· A hadron is a composite particle made of quarks held together by the strong force.

o Now, baryons composed of three quarks and mesons are composed of a quark and an antiquark.​

· Now, what are quarks?

o Quarks are denoted as being elementary particles in the standard model, as a consequence of their substructure being unknown. Thus it assumed that they are not composed of other particles.​

o They come in six flavours: Up, down, bottom, charm and strange. Conversely, there are also six antiparticles.​

o Now, ordinary matter is composed of baryonic matter: up and down quarks and the electron, which is a lepton. The rest are of the elementary particles are considered by many to be exotic particles.​

· The Eightfold Way arranges mesons and baryons into the vertices of geometric shapes according to charge and strangeness.

o The Baryon Octet is a geometric model of the eight lightest baryons. The diagonal lines denote strangeness (0, 1, -2), while the horizontal lines denote charge (-1, 0, 1).​

§ Six baryons make up the six vertices of the baryon octet, with two particles occupying the middle of the diagram.​

§ The intersection of these three lines form the vertices of a six sided shape and two particles constitute the center.​

o The eight lighest mesons fill a similar hexagonal pattern, forming the pseudoscalar meson octet.​

§ Now, once again the diagonal lines denote charge (-1, 0, 1), while the horizontal lines denote strangeness (1, 0, -1).​

§ Now, Gell-Mann could just as well have assigned the proton and neutron a strangeness of 1, but he thought it seemed more natural to let the most familiar particles proton, neutron and pion, a strangeness of 0, in their respective geometrical models.​

o Now, not only hexagons are allowed in the Eightfold Way. There was also a triangular array, incorporating the 10 heavier baryons in a baryon decuplet.​

§ A decuplet is a word that means 10 of a kind.​

§ Now, once again the diagonal lines denote charge starting from the bottom (-1, 0, 1, 2), while the horizontal lines denote strangeness starting from the top (0, -1, -2, -3).​

§ The baryon decuplet was experimentally confirmed in 1964, when the particle comprising the lowest vertex of the baryon decuplet and having the exact properties that Gell-Mann had predicted years before, was discovered.​

· Why do hadrons fit into these bizarre paterns? The explanation was offered by the Pauli exclusion principle and quantum mechanics.

o Recall hadrons are composed of quarks. The down, up and strange quarks form a triangular “Eightfold-Way” pattern. Up has Q=2/3 and S=0, strange has Q=-1/3 and S=-1 and down quark has Q=-1/3 and S=0. The antiquarks form a reverse triangle, with the antistrange quark sitting at the top vertex.​

o Now, the baryon decuplet and the meson octet can be constructed by elementary arithmetic. We list the combinations of three quarks or quark-antiquark combinations to make the baryon table or meson table.​

o Now, the baryon octet can be counterintuitively gotten at, by handling spin.​

· Spin is an essential parameter in classifying particles. Particles of half integer spin are classified as fermions and particles of integer spin are classified as bosons.

o Spin classification determines the energy distribution in a collection of particles.​

o Integer spin particles obey Bose-Einstein​

o Half integer spin particles obey Fermi-Dirac statistics.​

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