Standard model - Physics Feynman diagram PDF

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Physics Feynman diagram...

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THE STANDARD MODEL The particles in our universe can be broken down into fundamental blocks, as presented in the diagram below. When dealing with questions on particles, we need to consider the following conservation laws: 1. Conservation of charge 2. Conservation of baryon number 3. Convservation of lepton number 4. Conservation of strangeness The assigned values of each of these properties are also included in the diagram.

PARTICLES

FERMIONS

GAUGE BOSONS (EXCHANGE

They obey the Pauli’s Exclusion Principle – two fermions cannot be in the same place at the same time. Further divided into: Charge Baryon no. up charm top +2/3e +1/3 dow strange bottom -1/3e n

Gluon Photon (γ) W-, W+, Z0 Graviton

Mediated force Strong nuclear Electromagnetic Weak nuclear Gravity

Felt by particles: Quarks Charged particles Quarks and leptons Particles with mass

PARTICLES/FORCE CARRIERS) They do NOT obey the Pauli’s Exclusion Principle – two or more bosons CAN be in the same place at the same time. Strange, I know.

1

1 10-2 10-16 10-41

QUARKS

AND Strangeness: LEPTONS -1

H

Charge Lepton no. 0 +1 1 Relative strengths of the four fundamental forces. The particular values vary depending on the source, electron muonfor the tauweak-1e especially nuclear force (10-6 – 10-16). This is due to the fact that the two nuclear forces exhibit a

ve

vμ

vτ

rather complicated dependence on distance r between the two particles, rather than a simple F ∝1 /r 2 like for gravity. Therefore, the relative strength will depend on the distance at which we are measuring it. However, the order presented here is correct and the numbers at least approximately correct.

Higgs boson – responsible for giving particles mass (well, not quite, but you don’t need to know more)

All leptons have lepton number +1. All baryons have baryon number +1/3. All quarks have strangeness 0, apart from the strange one (as the name suggests…): -1.

On top of that, each particle above has its own ‘antiparticle’, usually (but not always!) denoted with a bar on top, e.g. u´ . The properties of antiparticles are simple: just change the sign of the value. For example, the baryon number of an anti-top quark will be -1/3, strangeness of antistrange quark is +1 and the lepton number of a muon antineutrino is -1. We can also combine the fundamental particles into groups: Hadron: a particle made of 2 or more quarks. It has the following subtypes: Baryon: a particle made of exactly 3 quarks. A proton and a neutron are hadrons and also baryons, as they consists of, respectively: uud and udd quarks. Meson: a particle made of one quark and one antiquark, e.g. π+: u ´d , π0: u u´ or d ´d , π−: d u´ .

Feynman Diagrams Feynman diagrams are a useful representations of what happens during an interaction between fundamental particles. In those diagrams, fermions are denoted as a straight line, while bosons (usually) as wiggly lines. For example, this is how two electrons repel each other as they feel the electromagnetic force and exchange its boson – the photon.

We can check that all 4 conservation laws are obeyed. We have a total charge or -2e on the left side (before the interaction, i.e. before the photon) and -2e on the right side, so that’s fine. Same with lepton number, +2 on both sides. Baryon number: electrons are not baryons, so this stays 0. Strangeness: only strange quark is -1, so that’s fine as well. You should stop thinking of the arrows on these diagrams as indicating the direction. Here, they only indicate whether we are dealing with a particle or an antiparticle. For example, this is how an electron and its antiparticle, the antielectron (more commonly known as positron), annihilate by producing a photon:

The arrow to the left on the positron does NOT mean it is somehow ‘going to the left’ of the picture. The two particles meet just as in any other collision and turn into a photon. So, to reiterate the point, the arrow to the left is just a representation of an antiparticle on the Feynman diagram. You need to be careful about the time convention. Some textbooks (and I’ve seen IB questions like that) use the convention where the time is flowing upwards. Just rotate any given diagram in this document by 90 degrees to the left to see what it would look like in this convention. In this case, an antiparticle would have an arrow going downwards. So, more generally, one should say that antiparticles have arrows going against the time direction. The diagram below represents beta-decay.

Analyse it carefully in terms of conservation laws. You might encounter a problem. In our first example, we treated the red wiggly line of a boson as the boundary between our left and right sides. However, this is not always true (in fact, rarely true) and we should instead look at the diagram from left to right. This way, we follow the time and so understand better what actually happens in a particular interaction – which particles are annihilated, which created. If you made the mistake, you might have thought that the left side of the diagram above is the one with d and u quarks, while the right side contains the electron and its antineutrino. This is wrong. So let’s follow the diagram from left to right. Beta decay is a two-step process. First, the down quark splits into a W- boson and an up quark. Then, the W- boson splits into an electron and an antineutrino (electron antineutrino to be precise). We need to check the conservation laws for both these stages separately. OK, let’s do that: 1) d quark changes to W- boson and an up quark.

a) baryon number: conserved, +1/3 for d and for u, 0 for Wb) lepton number: no leptons involved, so 0 for all particles c) charge: well, it’s -1/3 for a d quark. For the right side, we have -1 for the Wboson and +2/3 for the u quark. -1+2/3 = -1/3, so that’s conserved as well! d) strangeness: no strange quarks involved, so 0 for all particles. We can see that the first stage is possible. Now, let’s look at the second stage, which might be a bit harder, but don’t panic. 2) W- changes to an electron and an electron antineutrino. a) baryon number: no baryons involved this time, so 0 on both sides b) lepton number: this is where it gets interesting. W-, just like any boson, has lepton number 0. On the right hand side, we have an electron with +1 and an antineutrino. Is something wrong? No, because it is an antineutrino, its lepton number is -1 and so +1-1 = 0, so the lepton number is also conserved c) charge: W- has a charge of -1, so does an electron. Neutrinos do not have charge, so this is conserved as well. d) strangeness: 0 on both sides. We can now see that the second part is also possible, so the entire beta decay process is possible. This should not surprise you, because you have seen this process earlier in Chapter 7 and it does occur relatively frequently. Now, let’s look back on what this Feynman diagram actually means. Well, we have essentially turned a down quark into an up quark, the rest doesn’t really matter. A neutron consists of udd, so when the beta decay occurs, we will be left with uud, which is the configuration of a proton. That’s exactly what beta decay does – it turns a neutron into a proton.

QUESTIONS (answers given on the last page) 1. Consider the following Feynman diagram:

What could the identity of particle A be? a) u b) ´d c) d d) u´ 2. The reaction p+ + e- → n0 is impossible as it contravenes the law of conservation of: a) baryon number b) strangeness c) charge d) lepton number 3. A pion consists of an up quark and an anti-down quark. It decays into an antimuon and a particle Y, by emitting the exchange particle X as shown by the Feynman diagram:

What are the identities of X and Y? X

Y

a

Wo

e

b

Wo

ν μ

c

W+

e

d

W+

ν μ

ANSWERS 1. b) ´d On the left side, we have two particles colliding with each other. The charge of an up quark is +2/3, while on the right side the charge of W+ boson is +1. Therefore, we need to provide another charge of +1/3 on the left side to satisfy this conservation law. The only particles that have a charge of +1/3 are three of the antiquarks: antidown, antistrange and antibottom (check the first page for reference if needed). Among the answers given, we have antidown, so that has to be the correct answer. 2. d) lepton number We can easily check that all other laws are obeyed: a) baryon number: it’s 1 for a proton (a proton has 3 quarks, each of baryon number +1/3) and also +1 for a neutron (same reason) b) strangeness: no strange quarks involved, zero on both sides. c) charge: on the left side we have +1-1 = 0. On the right side, simply 0. d) lepton number: for proton, this is 0, for an electron, it’s +1. So on the left side we have total lepton number of +1. But on the right side, it’s 0 for a neutron. NOT obeyed. 3. d) Again, this is a two-step process, just like beta decay. Follow the diagram from left to right and check the conservation of charge. 1. An antidown quark and an up quark change into an unknown boson. In terms of charge, we have +1/3 + 2/3 = +1. So, the charge on the boson has to be +1. We know the answer has to be c) or d). 2. A W+ boson changes into an unknown particle and an antimuon. A normal muon has a charge of -1, but an antimuon has a charge of +1. So, the particle Y has to be neutral electrically – it has to be a muon neutrino. The answer is d)....