 Seeing Interactions Drawing Feynman Diagrams

Feynman Diagrams Richard Feynman created a pictorial representation of particle interactions which now bear his name. (These were doodles to begin with but now are a powerful tool in particle physics.) The Feynman diagram is focused on the vertex (where two lines meet). The vertices all have the same basic structure. A quark or lepton enters a vertex, emits or absorbs an exchange particle, and a related quark or lepton then emerges from the vertex. The process is either quark– vertex–quark or lepton–vertex–lepton. This is the symbol for a photon

Some of the Rules These diagrams are NOT the tracks of the particles. The vertices show time ordering only. To the left of the vertex shows the particles before the interaction and to the right of the vertex shows the particles after. Each vertex has a arrowhead pointing towards the vertex and an arrowhead leaving it. This represents a same generation lepton-lepton transition or a same or neighboring-generation quark-quark transition.

photon This shows the electron-electron repulsion. The EM force is mediated through a photon! From a distance, this looks like the electrons are repelling each other. However, the Feynman diagram shows that an electron emits a photon and is pushed back to conserve momentum. The second electron also changed direction since it absorbed the photon.

Virtual Particles The photon that carries the information in the last example was emitted from a free electron. This certainly violates the conservation of mass-energy (inertia). However, Heinsenberg’s Uncertainty Principle states Measurements of the energy of a particle or of an energy level are subject to an uncertainty. The energy measurement must be completed within a certain time interval, Δ t. The uncertainty in the energy, Δ E is related to Δ t through: So the photon can exist, energy can be created (!), as long as it does not last longer than

Virtual Particles Since the photon is very quickly absorbed by the other electron, the energy “borrowed” is returned, (in time). Particles like this photon are called virtual particles. Virtual particles are particles that cannot be observed because they are absorbed as soon as they are created. They may violate conservations laws.

We have seen evidence, through the Bubble Chamber, that a photon can pair- produce an electron and a positron. What does this look like in a Feynman diagram? WRONG! Since every vertex has a arrowhead pointing toward it and one leaving Antimatter in Feynman diagrams

We have seen evidence, through the Bubble Chamber, that a photon can pair- produce an electron and a positron. What does this look like in a Feynman diagram? Any antiparticle, will have its arrowhead in the opposite direction.

What’s Wrong? What’s wrong with each of these Feynman diagrams? In both cases electric charge is not conserved.

Weak Interactions The weak interaction involves the emission or absorption of the W and Z bosons. The W particle carries either a positive or a negative electric charge between particles whereas the Z particle carries no electric charge. The W particle is a quark-changing or a lepton-changing particle. Gluons and photons carry no charge and do not change the particle flavour.

Weak Interactions d quark u quark What boson is this? Why? The charge before is -1/3. Afterward it is +2/3. -1/3 = +2/3 + x X= -1 It must be the W -

Weak Interactions d quark u quark Don’t confuse this with: W-W- d quark gluon What particle is leaving the vertex? A d quark of a different color. This is not a weak interaction

Weak Interactions e-e- νeνe W-W- Here is another example of a weak interaction.

Beta Decay Let’s see it:fun with quarks! Beta negative decay is the decay of a neutron into a proton emitting an electron and an antineutrino. Free neutrons will decay in this manner. What is the nucleus produced when calcium-46 decays through the emission of a beta particle?

A closer look at decays we have already seen The Ω - decays to produce a neutral xion ( Ξ 0 ) and a negative pion What is the quark makeup of the omega-minus? sss And the quark makeup of the neutral xion?uss ssssss ssss u What type of boson is this? u d Look at the charges at that vertex. Coming in: -1/3 Leaving: +2/3 So the boson is negative: W - π-π- Ξ0Ξ0

A neutral xion ( Ξ 0 ) decays, by weak interaction, into a neutral lamba ( Λ 0 ) and a neutral pion (π 0 ). The xion ( Ξ 0 ) is comprised of uss and the lamba ( Λ 0 ) is uds. The pion is (uu) sussus susu u u d What is the boson? W-W- A closer look at decays we have already seen

V π-π- K+K+ γ γ Λ0Λ0 P+P+ K0K0 Putting it all together A negative kaon (K - ) hits a stationary proton. K-K- e+e+ π-π- P+P+ Ω- Ω- e- e+e+ Ξ0Ξ0 This creates a K + and an omega-minus particle ( Ω - ). (A neutral kaon (K 0 ) is produced as well – as seen with the conservation of momentum.) The Ω - decays at W to produce a neutral xion ( Ξ 0 ) and a negative pion The neutral xion decays into a neutral lamba ( Λ 0 ) and a neutral pion. This pion decays very quickly into two photons. The two photons decay into electron- positron pairs while the lamba decays into a proton and a negative pion.

Strangeness In the weak interactions previously discussed, is strangeness conserved? The Σ - particle has a half-life in the order of s. The Σ 0 particle has a half-life that is in the order of s. That is 10 billion times shorter than the Σ - particle! They were called strange particles. A new quantum number called strangeness was used to make sense of their unusual properties.

Weak and Strange The Ω - decays to produce a neutral xion ( Ξ 0 ) and a negative pion What is the quark makeup of the omega-minus? sss And the quark makeup of the neutral xion?uss BeforeAfter S = -3S= -2 Strangeness is not conserved in this interaction

A neutral xion ( Ξ 0 ) decays, by weak interaction, into a neutral lamba ( Λ 0 ) and a neutral pion (π 0 ). The xion ( Ξ 0 ) is comprised of uss and the lamba ( Λ 0 ) is uds. The pion is (uu) BeforeAfter S = -2S= -1 Strangeness is not conserved in this interaction

Conservation of Strangeness BeforeAfter S = 0 Strangeness is conserved in this interaction Δ +  p + p - Δ + is comprised of uud. Strangeness is conserved ONLY in electromagnetic and strong interactions but is violated in weak interactions.

Strangeness Σ -  n + π - Σ 0  Λ 0 + γ Half-life: sHalf-life: s Σ - = dds n = udd π - = du Σ 0 = uds Λ 0 = uds BeforeAfter S = -1S = 0 BeforeAfter S = -1 This is a weak interaction since the strangeness is not conserved. It is therefore slow. This is not a weak interaction since strangeness is conserved. This decay takes place through the electromagnetic interaction and is therefore fast.

The Range of Interaction The range of an interaction can depend on the mass of the virtual particle. The fastest a virtual particle can travel is ‘c’. The range of the interaction will be R. The virtual particle will reach the second particle in a time no smaller than R/c. The energy exchanged will be in the order of mc 2. The uncertainties can be estimated to be: Δ E ≈mc 2 and Δ t ≈R/c Heisenberg's Uncertainty Principle produces: So

The Range of Interaction Why does the electromagnetic interaction have an infinite range? It is mediated by a massless photon! The weak interaction has a short range because it involves the massive W and Z bosons. The W boson has a mass of about 80 GeVc -2 it follows that R = m Note: the gluons are massless but the strong force is short ranged and it has to do with the fact that the gluons interact with each other.

Probability Feynman diagrams are not just pictures. It represents a very definite mathematical expression called the amplitude of the process. The square of the amplitude gives the probability of the process actually taking place. We will learn to assign to each vertex a quantity called the strength of the interaction. This has the symbol For the electromagnetic interaction, the basic vertex is assigned To find the amplitude of a process, multiple the amplitudes for each vertex. This means that the more vertices, the less likely the process is to occur.

Your tool kit: Real Particles Anti Particles BosonsParticles