Tim Wiser
Splash P2506
3 Nov 2012

• Standard Model of Particle Physics
– Particles, interactions, and the Higgs field
• Drawing Feynman diagrams
– These simple pictures are actually calculational tools for physicists!
• Particle colliders
– How they tell us what stuff is made of
• What’s left?
– Incompleteness of the Standard Model
• Q&A

• Atoms (~100 elements)
• Protons (p), neutrons (n), and electrons (e-)
• p, n made of quarks (up & down type)
• All the matter around us is made of u, d, e-
• But there’s more!
• 6 quarks and 6 leptons, plus antiparticles

• Four fundamental forces:
– Gravity
– Electromagnetism
– Strong force
– Weak force
• Gravity is by far the weakest, and it’s different than all of the others. So we will ignore it today!

• In the Standard Model, all forces work the same way: by exchanging particles.
– E&M: photon
– Strong force: gluon
– Weak force: W, Z bosons
• Two electrons can “toss” a photon back and forth between them, and repel each other as a result.

e-/e- repulsion

• You might think that exchanging particles can only result in repulsive forces.
• But the exchanged particles are not “real”…
• Virtual particles can move left but carry rightward momentum!
• Kind of like throwing a boomerang…

• There are three rules in particle physics:
– Conserve energy
– Conserve momentum
– Conserve charges (electric, and more…)
• As long as those rules are satisfied, everything that is allowed WILL happen with some probability!
• Feynman diagrams automatically obey the 3 rd rule.
“Calculating” the diagram tells us the probability.
• There are usually lots of diagrams for the same process, so we will need to add them all together.

• QED is the simplest part of the Standard
Model. There is only one possible Feynman vertex:

• Let’s say we want to see how two electrons
“scatter” off of each other. We need to draw all Feynman diagrams with two electrons in and two electrons out.
• We already saw one:

How can we possibly deal with an infinite number of
Feynman diagrams??

• Fortunately for us, the more complicated the diagram, the smaller its value!
• Each vertex multiplies the probability by a small number (in QED, 1/137)
• Every loop divides the probability by about
25,000!
• So, we only need to think about the simplest possible diagrams.

• It’s not against the rules to have electron lines go “backwards in time”
• Such electrons would act exactly like oppositely-charged particles moving forward in time—antimatter!
• (This doesn’t make time travel possible.
Sorry!)

• If a photon has enough energy (rule #1!) it can produce an electron and its antiparticle, the positron.
• (It turns out that this can only happen if the photon hits something first, due to rule #2.)

• If we read the diagram the other way, we see that an electron and positron can “annihilate” and produce a photon.
• (Well, actually two photons—we need to conserve momentum!)

• Besides the fact that we have detected electrons, positrons, and photons and they work just like QED says…
• QED predicts the “g-factor” of an electron to be almost, but not quite, 2.
– Prediction: 2.0023228 (1 loop)
– Measured: 2.0023193
• If you add in the 2-loop correction, they agree to 10 decimal places!

• For a while, scientists thought that these were elementary particles like the electron and photon.
• If that were true, g p
=2 and g n
=0
• But…
• Experimentally, g p
=5.6 and g n
=-3.8
• This can only happen if the proton and neutron are made of smaller particles!

• We only have one good way of finding out what’s inside of particles…
• Smash them together!

• When we started smashing protons and neutrons together, we started discovering all sorts of new particles:
– 8 mesons: 3 pions, 4 kaons, and the eta
– 8 baryons: p, n, 3 sigmas, 2 xis, and the lambda
• But as we built bigger, better colliders we found even more: there are now hundreds of mesons and baryons known.

• We wanted to find what protons and neutrons were made of…
• But we found a bunch of composite particles like them instead!
• We can explain the structure of hadrons (mesons and baryons) if we guess that there are three
“quarks”—up, down, and strange.
• But we’ve never seen quarks by themselves, so the force that holds them together must be really strong!

• Mesons:
• Baryons:

• In fact, there is a way for this all to work…
• Three quarks: up, down, and strange
• In addition to electric charge, “color charge”
– Call them red, green, and blue
• Force carrier particle: gluon

• Because gluons themselves have color charge, the force between two quarks doesn’t get weaker as they get further apart!
• If you pull hard enough, you will just create new particles until everything is color neutral.
• This explains why we see mesons (quarkantiquark pairs) and baryons (three quarks or three antiquarks) but never quarks or gluons by themselves.

• If we never see quarks or gluons in nature, why are they useful?
• It turns out that QCD gets weaker at high energies!
• So we can describe collider physics with quarks and gluons…
• which “hadronize” as they leave the collision point.
• The resulting bunches of hadrons are called jets.

• In nature, we observe “flavor-changing” interactions
• Nuclear beta decay (n->p+e+?)
– d quark -> u quark
• How can we explain this? QED and QCD are
“flavor-blind”

• It looks like beta decay doesn’t conserve momentum!
• That’s ridiculous, there must just be an invisible particle as well.
• Call it a “neutrino” (quasi-Italian for little
neutral particle)

• To change from a d quark to a u quark, we must emit a charge -1 particle
• That particle must then emit an electron and an anti-neutrino.
• W boson (there is also a W + boson, of course.)
• To explain the “weakness” of the weak force, the W bosons must be heavy. (This will be important later!)

• A series of surprises, predictions, and experiments.
• Prediction: pion as nuclear force mediator
• Surprise: muon (a heavier electron!)
• Experiment: quarks are real
• Prediction: charm quark (confirmed!)
• Prediction: W and Z bosons (confirmed!)
• Surprise: 3 rd generation of matter

• Beta decay
• e + e -> μ + μ -
• π + -> μ + ν
μ
• K
0
-> K
0 bar

• High-energy tests
– Particle colliders
– Cosmic rays
• Precision tests
– g-2 experiments
– Rare particle decays

• 2 things come in, n things go out
• Higher energy means we can make heavier particles in the collision
• Two main types: linear (like SLC) and circular
(like LHC)

• The easiest particles to accelerate
• Since they’re elementary particles, easy to calculate and to measure the results
• Hard to make circular colliders (LEP was one)
• Lots of linear colliders, including one at SLAC!
• Link

• Countless hadrons
• Charm quark (in the form of the J/ψ meson)
• Tau lepton
• Precision measurements of W and Z bosons

• Protons and/or antiprotons
• Tevatron (p-pbar) and LHC (p-p) are the major
HCs
• Pros: high energy, can be circular (cheaper), strong interactions
• Cons: hadrons are composite, strong interactions

• Bottom and top quarks (Tevatron)
• W and Z bosons (SPS)
• Countless MORE hadrons

• Powerful electric fields speed up charged particles
• In practice, “RF cavities” are used
– Kind of like a tuned microwave oven…
• In a linear collider, we get one shot to accelerate
• In a circular collider, we can accelerate it over and over again

• Electric fields speed up the particles, but we use magnetic fields to focus and aim the beam
• Magnets have to be kept very cold so that the wires superconduct and produce very strong magnetic fields

• Finally, two beams of particles will collide with each other
• How do we see what is produced?
• Massive detectors around the collision point can track the paths of particles and measure their energies

• Large Hadron Collider
• At CERN, near Geneva, Switzerland
• 17 mile circumference, >150 ft underground
– Passes under both Switzerland and France
• 2 primary detectors, ATLAS and CMS
• 2 special-purpose detectors, LHCb and ALICE
• Several minor detectors

ATLAS

CMS

• The Standard Model as we have talked about so far makes a prediction:
• All elementary particles are massless!
– (Composite particles like hadrons can still have mass, though.)
• This is obviously not true…but the Standard
Model works so well, we have to try and save it.

• The SM has a property called “gauge symmetry” which describes the properties of the three forces
• Mass is incompatible with gauge symmetry!
• But removing gauge symmetry gets rid of all of the predictive power.

• In quantum field theory, particles are actually ripples of fields
• Most fields have the value of 0 in the lowestenergy state.
• If a field’s lowest energy state is not zero, then it is said to “break” a symmetry.
– The symmetry still exists, but it is ‘hidden’ at low energies.

• Peter Higgs* discovered the Higgs mechanism, where a field breaks a gauge symmetry. Then, the gauge boson (force-carrying particle) will become massive.
• This could be how the W and Z bosons get mass!
• *(It should really be called the Anderson-Higgs-Brout-Englert-Guralnik-
Hagen-Kibble mechanism.)

• Higgs realized that the presence of this field meant there would be a new boson that interacts with all massive particles.
• If we find the Higgs boson, we will finally complete the
Standard Model!
• But it won’t be easy: the Higgs interacts proportionally with mass of particles, so electrons, ups, and downs barely interact with it at all.
• Then, the Higgs will decay long before it reaches one of our detectors. We will only be able to see it indirectly.

• Production
– Gluon fusion
– Vector boson fusion
• Decay
– WW, ZZ
– bb
– 2 photons?

Announced July 4, 2012

• There are a few ways the SM is incomplete:
– Gravity
– Dark Matter & Dark Energy
– Lots of free parameters (unsatisfying)
– Fine-tuned (maybe not a problem?)
• So, we keep looking for new physics:
– Supersymmetry
– Extra dimensions
– Or something unexpected…

• The Particle Adventure
– http://www.particleadventure.org/
• Popular Science Books:
– Brian Greene (quantum physics, string theory)
– Lisa Randall (beyond SM physics)
– Sean Carroll (search for the Higgs, coming out soon)
• Take a physics class!
• Particle physics blogs
– Partial list at http://www.interactions.org/blogs/

• Contact me:
– tdwiser@stanford.edu