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?

Matter-Antimatter Asymmetry

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.