Particle Physics
By: Akshay Bhatt
The plan
● Review of necessary physics background● The Standard Model of Particle Physics● Open questions in Particle Physics● Modern Experiments (i.e. the LHC)
What is Physics?
● Ancient Greeks: “Knowledge of Nature”● Physics aims to study “things” at a
fundamental level● The language of physics is mathematics
The Scales of Physics
What Particle Physics describes
● The basic building blocks of matter = particles
● The basic interactions between these particles = also particles
● The universe (a bunch of particles)
But before we can get to particles
● Classical Mechanics● Electricity/Magnetism● Special Relativity ● Quantum Mechanics● Quantum Field Theory (!)
Mechanics (1)
● Formal foundation by Isaac Newton● Want to understand equations of motion for
an object ● There exists a force between massive
bodies = Gravity
Mechanics (2)
● You give me , I will give you the equations of motion
● May need calculus!● Often work in terms of and ● How are forces felt?● There is a gravitational field!
Because you know I’m all about that field, ‘bout that field
Mechanics (3)
● We forgot about Energy!● This form is fixed by symmetry of physics● In-class exercise:
○ Suppose invariant under ○ Suppose invariant under 3D rotations
● Noether’s theorem: Symmetries ⇔ Conservation Laws
Mechanics (4)
● There is a more general way to determine dynamics that will be useful later on
● Axiom: minimizes a function called the “Lagrangian”
● Lagrangian is based on the energy of the system => fixed entirely by symmetries
● Moral: know the symmetries, and you are set!
E/M (1)
● Some objects have electric charge. Force between them is called “Coulomb Force”
● Opposite charges attract, like charges repel.● Force communicated by “Electric field”
E/M (2)
● Similarly, there is also a Magnetic Force and Magnetic Field.
● Electricity and Magnetism go hand-in-hand.● Maxwell’s equations. ● Together, E/M fields make up components of
a wave called the “Electromagnetic wave” ● Maxwell: Electromagnetic waves = light!
SR (1)
● Michelson-Morley Experiment: “If light is a wave, what does it propagate on?”
● Albert Einstein: “Nothing, you Dummkopfs”● Postulates of SR:
○ Laws of physics are the same in all inertial reference frames
○ The speed of light in free space has the same value in all inertial reference frames
SR (2)
● Time dilation: moving clocks tick slower● Length contraction: moving rulers are shorter● The notion of simultaneity is relative● Don’t worry though, causality is preserved!● There is a symmetry - Lorentz invariance! ● Space and time treated on equal playing
field
SR (3)
● Need to make changes to some of our mechanics formulas.
A quick note
● Einstein didn’t just stop there; he also adjusted Newtonian Gravity accordingly
● “General Theory of Relativity” ● Not going to be relevant for our discussions
I'm beginnin’ to feel like a physics god
QM (1)
● Very, very rich subject - only going to go over the bare essentials
● Matter made up of atoms = protons + electrons.
● Particles! (finally)
QM (2)
● Light comes in discrete energy packets● But this seems like a property of particles.● Hold up, is light a wave or a particle?● To that effect, can particles act like waves
then?
QM (3)
● To answer this deep question, I invite a guest lecturer to help me out!
QM (4)
● QM is indeterministic. Cannot precisely determine position, momentum, etc.
● Instead all we know about a particle is its wave-function
● We can calculate probabilities, and that’s it.
QM (5)
● The act of measurement will collapse the wavefunction to a specific value.
● But until then, particles exist in a probabilistic limbo.
● Schrodinger's cat: Another guest lecturer!
QM (6)
● Suppose system of two quantum particles with combined wave-function
● These are indistinguishable particles● We must have equal probabilities
QM (7)
● Two kinds of particles: bosons and fermions● All quantum particles have an additional
property known as “spin”● Like an intrinsic angular momentum, but not
quite. ● half-integer spin = fermions● integer spin = bosons
QFT (1)
● Finally we are in a position to study the merging of SR + QM = QFT!
● Deals with high energy quantum particles● Particles are really waves, which are really
fields. ● Forces are really fields, which are really
particles
QFT (2)
● All matter is particles ⇔ fields● Individual particles are seen as energetic
excitations of the underlying field, which permeates all of space-time
● All interactions are particles ⇔ fields● Particle exchange between bodies behaves
like a force, acts like a field
QFT (3)
QFT (4)
QFT (5)
● Most times, it’s convenient to think in terms of particles (we will do this)
● But to make calculations, we often make use of the field behavior
● So what are all these particles then???
Units
Electron
● Negatively Charged Matter particle● Fermion● Some non-zero mass (need to measure)
Photon
● Communicates electromagnetic force ● Same as old, familiar light!● Electrically neutral● Boson ● Zero mass
QED
● How does Quantum Electrodynamics work?● Remember that “Moral” from before? Find a
symmetry!● It turns out there is a symmetry here due to
charge conservation ● Mathematicians call this symmetry “U(1)”● “1” = there is only one type of electric charge
Lets spice things up a bit
● When QM + SR were first combined, Dirac noticed something peculiar.
● Recall Energy-Momentum relation in SR● When we add QM, the negative solution
cannot be ignored● Negative energy solution has physical
representation: antiparticle
Antiparticles
● Exact same properties, except opposite electric charge i.e. the positron
● particle + antiparticle = annihilation ● Fact: we live in a universe dominated by
matter● So where is all the antimatter?
Some thoughts
● Already we notice some general patterns○ Matter particles will be fermions○ Force particles will be bosons
● I didn’t include the proton or neutron○ There is a reason for this - they are not elementary!○ Let’s see why!
Quarks (?)
● Something troubling about a nucleus of protons + neutrons
● There must be a “very strong” binding force● Scattering experiments: each consists of
three composite particles● A physicist with a sense of humor: how
about we call them “quarks”
The first two quarks
● Proton + Neutron consist of “up” and “down” quarks
● These quarks are fermions● Their electric charges are +⅔, -⅓ resp. ● They have some non-zero mass ● Quarks feel the strong force
Gluons
● Some particle mediates the strong force ● Holds the quarks together “like glue”● We call it the Gluon● Electrically neutral● Bosons● Zero mass
Now for something strange
● In 1940’s cosmic ray, physicists saw other short-lived particles that looked like protons (kaon, lambda, etc.)
● These were composite particles - must be made of quarks as well
● Contain a third, heavier quark: the strange quark
So charming
● In 1970’s, high energy colliders produced very short-lived particles that seem to contain a fourth quark
● Dubbed the “charm” quark● Even more massive than and
Final two quarks
● Theorists predicted there should be two more quarks, but it took a while to experimentally confirm them.
● Top quark discovered in 1995 in Fermilab● These are both very, very massive quarks
QCD
● Why do only quarks feel the strong force?● Quantum Chromodynamics - there is an
analogy to electric charge for quarks called “color”. 3 different colors.
● Only quarks, gluons have color● We notice a symmetry! Mathematicians call
it “SU(3)”
Hadrons
● Hadrons = bound states of quarks○ Baryons = bound state of three quarks (all different
colors). ○ Mesons = bound state of quark, antiquark.
The Muon
● Cosmic ray experiments showed a new fundamental particle identical to the electron, but more massive
● Physicists called it a “muon”. ● All same properties of an electron except a
very short lifetime● Question: what does the muon decay to?
Another new particle!
● Neither QED/QCD describes muon decay, radioactivity, and other processes properly
● Problem: there is some missing energy in these decays
● Solution: this missing energy is carried by a very elusive particle called the “neutrino”
The Neutrino
● Electrically Neutral● Fermion● Virtually massless● Interact very, very weakly with other matter● There are neutrinos everywhere, you just
don’t feel them!
Another force!
● Physicists call the force involving neutrinos “the weak force”
● No such thing as weak charge● It really is very weak● For more complicated reasons, the
symmetry for the weak force is called “SU(2)”
Bosons
● Pair of particles that communicate the weak force
● Bosons● W is electrically charged, Z is neutral● Massive ● This explains why the weak force is so weak
The Tau ● Identical in properties to electron and muon,
but just heavier● Together, we refer to (electron, muon, tau)
family as Leptons● It turns out that there is a different neutrino
for each lepton (electron neutrino, muon neutrino, tau neutrino)
Mom, are we there yet?
● There is one problem. Why is the weak force so weak?
● Why do W, Z Bosons have mass?● Something must be giving it this mass● Higgs to the rescue! (and Englert, Brout,
Guralnik, Hagen, Kibble…) you mad, bros?
The Higgs Field
● Absolutely beautiful theory● Breaks the symmetry between QED and the
weak force - gives W,Z masses● But extends beyond this - gives all particles
their masses● Excitation of the field = Higgs boson● Experimentally confirmed at the LHC in 2012
You gotta be kidding me!
● What happened to gravity?????????????● It is so much weaker than the other forces,
we can essentially ignore it for experiments● That’s not a good enough answer though● Disclaimer: we don’t have a formal theory of
quantum gravity yet● Perhaps String Theory is the solution?
Extra dimensions
● Perhaps one reason gravity is so much weaker is that gravity propagates in an extra spatial dimension
● Looking for extra dimensions is an active area of research at the LHC
The Dark World
● It turns out Standard Model matter only makes up ~20% of the known universe
● Through gravitational attraction, astronomers see that the rest is some invisible form of mass = “dark matter”
● This is an open question - lots of theorists and experiments are working on it!
Cosmic Expansion
● The universe is expanding, and doing so in an accelerating pace!
● There is a non-zero energy encoded into space-time
● The Standard Model fails to predict this “vacuum” energy
Supersymmetry
● Why are all the forces so different? Is it possible to unify them into a single force?
● Supersymmetry does this in a beautiful way● Essentially, it is a symmetry between bosons
⇔ fermions● For every particle in the SM, there is a
corresponding superpartner particle. We are actively looking for them at the LHC.