elementary particles
Which are the matter particles and how do we classify them?
Leptons: electron, muon, tau + corresponding neutrinos
Quarks: up, down, strange, charm, bottom, top
- first three: light quarks, second three: heavy quarks
All of them are spin-1/2 fermions and they’re further classified into families/generations.
elementary particles
Which are the interaction particles? Which interactions to they mediate?
Photon: EM-interaction, massless
W(+/–), Z bosons: weak interaction, massive
Gluon: strong interaction, massless
Higgs-boson: gives mass to elementary particles (exc. photons and gluons), massive
interactions as particle exchange
What does a particle interaction mean in practical terms? What’s the problem with this? What’s the solution?
It means the exchange of mediator particles carrying just the right amount of the various quantum numbers.
Problem: when a particle is exchanged the energy and the momentum can’t be conserved simultaniously, which leads to serious contradictions from a classical perspective
Solution: Heisenberg’s uncertainty principle. The interaction can violate energy conservation for Δt ~ ħ/ΔE span of time
interactions as particle exchange
What does the range of interaction of particles mean? What determines it?
Range of interaction: inverse of the mass of the lightest mediator particle
- so the determining factors are Heisenberg’s uncertainty principle and therefore the lightest mediator particle
- Compton-length: Δx = cΔt, the particle can go as far as it would in Δt time if it had c velocity
interactions as particle exchange
What determines the strength of interactions?
The likeliness of absorption or emission which is described by the coupling constant.
- the larger the coupling, the higher the chance
natural units
What are the natural units?
ħ = c = 1, e = 1
- e is also dimensionless
- c —» [m] = [E] (unit of mass = unit of energy)
- ħ —» [t] = 1/[E] (unit of time = unit of inverse energy)
- ħc —» [l] = [t] = 1/[E] = 1/[m] (unit of length = unit of time = …)
- ħc = 197 MeV for the conversion
building up matter
How do the elementary particles build up the known matter? How are mesons and baryons constructed?
- quarks —» hadrons: strong interaction
- hadrons —» nuclei: strong interaction
- nuclei + electrons —» atoms: EM interaction
Construction of hadrons: same quark content but different spin/angular momentum state means different mesons, different quark content means different hadrons
building up matter
What’s the lightest baryon and why is it stable?
It’s the proton, which ensures the stability of ordinary matter. It’s stable exactly because it’s the lightest: there’s nothing for it to decay into because of the conservation of baryon number.
stable and unstable particles
Which are the stable particles and what are some properties of the unstable ones?
Stable particles: protons, electrons, neutrinos, photons
Unstable particles: everything else
- lifetime: typical mean time it takes a particle to decay
- decay width: inverse of lifetime, energy dimension
- decay channel: particles decay through different modes and each mode is a channel
- partial width: characterization of each channel
- branching ration/fraction: the relative probability of a decay happening in a certain channel
- exponential decay law: insert képlet
- energy conservation is independent of the frame of reference: the sum of the decay products cannot exceed the initial particle’s mass
decays and conservation laws
How can we tell which process governs which interaction?
By lifetime: strong —» EM —» weak (increasing lifetime from left to right)
- also corresponds to the strength of the interaction decreasing with the increasing lifetime
- signature particles: (anti)neutrinos (weak), photons (EM), pions (strong)
By conservations laws: all interactions conserve electric charge, baryon number and lepton number, but not all conservation laws are valid for all interactions in general
- generally they’re related to the symmetries of the systems through Noether’s theorem
decays and conservation laws
What conservation laws are there and how can we categorize them? Which elementary interaction conserves them?
Particle-type conservation laws:
- baryon number
- strangeness, charm, beauty, upness, downness, topness
- lepton number, individual lepton numbers, lepton family number
- electric charge
Approximation of flavour symmetries: only the masses distinguish the different flavoured quarks in terms of the strong interaction, isospin can be introduced (more on a different card)
Discrete symmetries:
- parity: spatial inversion
- charge conjugation: exchange of particles with antiparticles
- time reversal: inversion of the direction of time
decays and conservation laws
What is isospin and what does it represent?
It’s a type of internal symmetry (formulated analogously to spin), meaning it acts in the internal space spawned by the up and down component of the quark state.
- different flavoured quarks can be “rotated” into each other without physical effects: rotational symmetry
- completely different from spacial symmetries (only mathematically identical)
- it manifests through multiplets (like the degeneracy of the energy levels): I = (I1, I2, I3), I3 = -I,…,I, I3 = (1/2)(baryon number + S)
- only conserved by the strong interaction
