FYSC24 Particle Physics

four fundamental forces/interactions and what they couple to

gravity (everything), weak (fermions), electromagnetic (charged particles), strong (quarks, gluons)

length contraction

objects appear shorter to an observer at rest when they are moving at relativistic speeds (~ speed of light)

time dilation

the time experienced by something traveling at relativistic speeds is shorter than for something at rest

4-vectors

• zero:th component is the time-like component (for momentum we often have (E, px, py, pz))

• lorentz invariant, meaning they are the same in lorentz space (after going through a lorentz transform). the square of a momentum 4-vector is the mass squared, which is a manifestation of this

standard model

like a periodic table of particles that make up all (luminous) matter and correspond to the 4 fundamental interactions (all affected by gravity, the other 3 are divided). they are the smallest constituents of matter

also divided up into different generations, where each generation has increasing mass and decreasing stability. all three generations are fermions

leptons

electron, muon, tau + antiparticles and corresponding neutrinos

can be observed on their own

have electric charges and interact electromagnetically as well as weakly (except neutrinos that are charge- and massless and only interact weakly)

quarks

come in flavors up, down, charm, strange, top, and bottom + antis. u, d, s are the light quarks and c, b are the heavy quarks (t heaviest)

build up hadrons (for simplicity we often say that the top quark is too heavy to form a hadron)

interact strongly

always found bound in composite, colorless states, since quarks have color and therefore cannot be observed alone

force carriers

photon - EM (charged particles)

gluon - strong (colored particles)

Z and W bosons - weak (flavored particles)

if a photon is involved in the interaction, it must be electromagnetic

if a neutrino is involved, it must be weak

conservation laws - how to see which interactions are allowed

• energy and momentum

• electric charge

• baryon number (more like quark number)

• lepton number of each family (ex anti/electron and anti/electron neutrino is one family)

• quark flavor - only conserved in EM and strong interaction!

• color charge

feynman amplitude

M

the absolute squared gives us important physical quantities of the interaction

what you get by multiplying the coupling constant of each vertex in a feynman diagram

leading order feynman diagram

the feynman diagram with least amount of possible vertices, also the one with the largest amplitude out of all possible orderings - therefore becomes most likely and energetically favored

why is the weak force weak?

the weak force carrier are the Z and W bosons - which, compared to the massless photons, are extremely massive (m_Z = 91 GeV/c²) and therefore require much more energy to create

these interactions will then work as long as the very massive particle only exists for a short amount of time (comes from Heisenberg ???????)

therefore, the mass or energy in for example e-/e+ annihilation must be much higher than it is normally for the interaction to happen with the weak force instead of electromagnetically, which is of course extremely unlikely (however, for high E/m collisions, like top quarks, the probability for weak decay becomes much higher)

the coupling constant for weak force vertices are also much smaller than coupling constant for, let’s say, EM

what’s special about the W boson?

it’s the only force carrier to also carry a charge, which means that it is able to change the type of particle

ex a vertex with an electron neutrino, W, and an electron

it does the weak interactions that are flavor-changing charge current (alter particles’ flavor as well as their charge)

what’s special about the Z boson?

it can’t do flavor-changing neutral currents (FCNC:s are very supressed/impossible in the standard model)

neutrinos

uncharged, undetectable particles (bc we can only really detect charge)

for energy conservation to be true, there must be a third particle inside nuclei which are neutral and very light

neutrinos of electron flavor will interact differently with electrons compared to those of muon or tau flavor; those use the Z boson since we can’t change particle type then

come from nuclear reactors, accelerators, space (cosmic rays, stars, supernovae (rare)), decay of radioisotopes in the earths crust

neutrino oscillations

neutrinos oscillate between different flavor states (electron, muon, tau) which in turn are linear combinations of three different mass states, and since the masses of each state is different, their wavefunctions will have different frequencies (the masses travel through space at different speeds). this gives rise to wave packets (superposition) wherein some packets will have higher probability for the neutrino to occupy a certain mass state

neutrinos are detected as different flavor states, but they propagate as linear combinations of mass states

lepton quark symmetry

for leptons, weak interactions work between all leptons in the same generation in the same way, and they all have the coupling constant g_w - for quarks, there is a similar coupling constant, but it is not identical

however, compared to leptons, quarks can also do cross-generational transitions

cabibbo favored

in-generational transition, most energetically favorable

for a cabibbo-favored quark transition, the coupling constant will be = g_w * cos(cabibbo angle)

cabibbo supressed

cross-generational transition, less energetically favorable

coupling constant is = g_w * sin(cabibbo angle)

isospin

a quantum number that works similarly to spin and relates to the up- and down quark content of a particle

the strong force is invariant under rotations in isospin-space

mathematically it works very similarly to spin, but it is not at all related to angular momentum or any actual type of spin, and is a dimensionless quantity

making mesons

we combine flavors in the same way that we would combine spin, and we use isospin to distinguish between different flavors (so we get linear combinations)

isotriplet

an isospin state which has three different states possible within itself, so that all these three states would result in the same isospin

?????????????

isosinglet

an isospin state which has only one state available to it ??????????

the spin statistics theorem

a generalized version of the pauli exclusion principle

bosons (integer spin) have symmetric wave functions under particle exchange:

\Psi_21 = \Psi_12

fermions (half-integer spin) have antisymmetric wavefunctions instead

\Psi_21 = -\Psi_12

the hadron wave function

spin part x flavor part x space part x color part

the space part is always symmetric, but the color part is always antisymmetric, which ensures that a baryon will (no matter its quark content) always have an antisymmetric wave function

gluons are freaky (quantum chromodynamics)

gluons have both color and anticolor, and since they are the carriers of QCD/strong force they can interact with themselves!

confinement

an unconfirmed “law of nature” that says that the only free particles we can see have to be colorless, meaning we can’t observe a lone quark since it has a color charge

asymptotic freedom

when probing with high energy (= at a small length scale) quarks and gluons will behave like free particles, since the strong force is weaker relatively

or, a better explanation:

at very short distances, the strong force becomes weaker, and at even shorter distances (equivalent to very high energies) quarks and gluons act like free particles

screening effect

in quantum electrodynamics, we have annihilation/pair production when a photon becomes an electron and a positron. there exists a similar situation for quantum chromodynamics/strong force, where a gluon can become a quark and an antiquark (or the quarks annihilate into a gluon)

strong force coupling, running coupling

in the strong force, coupling “constants” aren’t constant but depend on the energy (as 1/length) that they are probed at - an example of how asymptotic freedom manifests

as the energy increases, the coupling constant (alpha) will decrease exponentially

at high energy, the strong coupling falls

jet

hadron remnants left behind from a quark/gluon reaching its final state and hadronizing

the way that we detect gluons and quarks is from seeing these jets

how do you measure the mass of a meson?

measure the energy and momentum of outgoing muons

why? because of 4-vectors

p_x² = m_x² = (p_1 + p_2)², where x refers to the meson, 1 and 2 to the muons

building blocks of particle accelerators

the source of (charged) particles; ex spallation source, electron gun…

E-fields to accelerate the particles

B-fields to guide the particles