Lecture 01 Elementary Particle Physics - Prof. E....

Lecture 01

Elementary Particle Physics

Particle Astrophysics

Particle physics● Fundamental constituents of nature● Most basic building blocks● Describe all particles and

interactions● Shortest length scales available

● ~ 10-21 m

Astrophysics● Structure and evolution of the

universe● Composite objects at the largest size● Largest length scales

● ~1026 m

Particle Astrophysics● Combines the largest and smallest length scales● How do elementary particles and their interactions affect large

scale structure in the universe?● How can we use elementary particles as probes of cosmological

evolution?● What do astronomical observations tell us about fundamental

particles?

PHYS 6960 Lecture 01 3

Elementary Particles

What are the building blocks of nature?● Atoms● Subatomic particles: protons, neutrons, electrons● Sub-nucleonic particles: quarks● Force-carrying particles: photons, gluons, etc

● What is an elementary particle?Cannot be broken down into smaller constituents

● We cannot see “inside” it● No substructure● Point-like

● The study of elementary particles focuses on understanding what the fundamental particles are and how they interact

● New Physics is usually ascribed to new particles and/or new interactions


Detecting particles

We look for evidence of a particle interacting with a detector● Tracks

● Particle leaves a “trail” as it passes through material● Does it bend in B field? If so, which way?

● Energy● How much heat, light or ionization does a particle leave

● Topology● Different interaction with different materials for different particles


Describing Particles and Interactions

● Elementary particles are NOT classical● Point-like particles● Governed by quantum principles● We must describe EVERYTHING about a

physical system in quantum mechanical terms

A fundamental particle interacts with another fundamental particle by exchanging yet another fundamental particle

Or

● Composite particles (such as nuclei) can be described by their fundamental constituents

● The interactions can be described as a sum of the fundamental interactions

● This process can be coherent or incoherent


First Quantization

Schrodinger Equation:

H is total energy (KE + PE)

First quantization gives the relation:

Based on commutation relation:

From which we get the familiar form of the Schrodinger Equation:


What is First Quantization?

We treat the particles quantum mechanically, but the fields classically

Example: Hydrogen atom● Electron is treated quantum mechanically

● Follows uncertainty relation

● Wave function gives probability density for electron position

● Potential treated classically● Use Maxwell's equations

Result:Quantum description of electron

But NOT of the force (e.g. photon)

For particle physics we must go to the next step and quantize the field and interaction as well

→ Quantum Field Theory


Review of E&M

Recall the relation between the fields E, B, and their potentials, ϕ, A

● Maxwell's equations still satisfied● All of E&M can be summarized in 4 distinct quantities:● and the 3 components of ϕ A● We can combine these 4 quantities in a 4-vector● A

μ, with μ = 0,1,2,3

● A0 = , Aϕ

1 = A

x, A

2 = A

y, A

3 = A

z

● All of E&M can be written in terms of Aμ


Second Quantization

Fundamental interactions of matter and fieldsTreat matter AND fields quantum mechanically

● Quantum Field Theory quantizes Aμ in a similar way to the

construction of the Schrodinger equation● The quanta of the field are particles● For A, the quanta are photons

● Full discussion beyond the scope of this class● See Advanced Quantum Mechanics by Sakurai

● With the Schrodinger equation, we had quantum particles (e.g. electrons) interacting with classical fields (e.g. electrostatic field)

● Now we have quantum fields● Electrons interact with photons


Forces and Interactions

In classical physics, and 1st quantization, a force is derived from a potential:

In QFT, this is replaced by the concept of interactions In QED, two charged particles interact by the exchange of photonsThe correct quantization method (e.g. A

μ) gives the correct classical limit

Forces are mediated by exchange particles (force carriers)

● Two electrons interact by exchanging a photon

● The photon carries momentum from one particle to the other

● Averaging over many interactions, F = dp/dt

● On average:


Spin: Bosons and Fermions

All particles carry a quantum of angular momentum

BosonsInteger spin

Symmetric wavefunctionsForce carrying particles

FermionsHalf integer spin

Antisymmetric wavefunctionsObey Pauli exclusion principleMatter particles (take up space!)

Spin 0 (scalar)1 spin state, m

z = 0

Spin ½2 spin states, m

z = -1/2, 1/2

Spin 1 (vector)3 spin states, m

z = -1, 0, 1

Spin states:Projection of angular momentumMz integer from -s to s2s+1 spin states


Units

In quantum physics, we frequently encounter Planck's constant:

In special relativity (and of course, E&M), we encounter the speed of light:

We can put them together for convenient, quick conversions:

Angular momentum

Speed


Nothing magical about these Universal Constants

Consider the speed of light in different units

It has different numerical values, but light ALWAYS travels at the same speed!

Why does this conversion constant exist?

Because we measure time and distance in different units[space] = m, cm, miles, …[time] = s, h, years, …

● Why don't we measure them in the same units so that c = 1 and is dimensionless?● Same arguments apply for Planck's constant (ratio of energy to frequency, or time)● Why don't we measure time and space in the same units as energy?


Natural Units

Let's choose units of energy, electron volts, as our basis of measurement

Since c = 1 and is dimensionless

Since ћ = 1 and is dimensionless

Again, since c = 1 and is dimensionless

● This greatly simplifies equations and computations● Dimensional analysis is simpler (fewer units to keep track of)


Warnings with Natural Units

Beware of reciprocal units

They work backwards with multipliers

● Converting a number in Natural Units to “Usable” units● You can Always convert back!● Only requires dimensional analysis

● There will be exceptions to using Natural Units● Example: cross sections

● Units of area, should be eV-2

● But we typically use cm2


How Particles Interact

The fundamental interaction: Boson exchange

● In particle physics, the fermions that make up matter transmit force by interacting with one another

● This interaction is mediated by a boson exchange● One fermion (say an electron) emits a boson (say a

photon) which is absorbed by another fermion (say another electron

● The boson carries momentum and energy from one particle to the other

● The affect of this can be attraction (like gravity or opposite electric charges) or repulsion (like same charges)

● It can also be more exotic● Change of particle type● Creation of new particles and antiparticles


The Feynman Path Integral

Probability for photon to be emitted at point A and absorbed at point BSum up amplitude from all possible paths

Richard Feynman developed a method for computing interaction probabilitiesPath Integral (which adopted his name)


Perturbation Theory

Recall from Quantum Mechanics:Assume you have a Hamiltonian with exact, known energy solutions:

But the true Hamiltonian has a perturbing term H1

Then the true eigenvalues are

The true eigenvalues and eigenfunctions can be expanded in a perturbation series


Bra-ket notation

Dirac introduced a shorthand notation for describing quantum states

Bra

Ket

Put the together to get a Braket

You can also use this for expectation values


More on bra-ket notation

You can operate directly on a ket

Or take expectation values of operators

You can use shorthand notation to describe the wavefunction in the bra and ket, and label any relevant quantum number inside the ket

Or you can use symbols to describe the state such as a neutrino or Schrödinger's cat


Calculating the Perturbation Series

What's important for us?

● A perturbing Hamiltonian can be expanded in a perturbation series

● The eigenvalues and eigenstates can be computed from expectation values of the perturbing Hamiltonian

● If the series for a system converges, we can describe that system by this series● Leading order● Next-to-leading order● Next-to-next-to leading order● etc

and so on


Perturbation Theory in Particle Physics

Can we use perturbation theory to describe fundamental particles and their interactions?

Sometimes

In many cases, the Hamiltonian can be described by a “free particle” term (H0) and

and “interaction” term (H1)

We describe interactions in leading order, next to leading order, and so on

This doesn't always work!

Low energy strong interactions DO NOT CONVERGEOther methods necessary, e.g. lattice QCD


Lagrangian Formulation

● In particle physics, we typically work with the Lagrangian rather than the Hamiltonian● More specifically, a Lagrangian Density

● H and L are related through:

● Like in Hamiltonian formulation, split L into free and interaction terms● L = L

free + L

int

● Use perturbation theory


Matter and Antimatter

● Dirac developed a relativistic treatment of electrons● For the relativistic Hamiltonian for a free particle, start with

special relativity

● Dirac essentially took the square root of a QM version of this equation

● Since both the positive and negative square roots are solutions, there are both positive and negative energy solutions

● The negative energy solutions are interpreted as antiparticles that have all quantum numbers identical except electric charge, which is equal and opposite

All fundamental fermions exist in pairs of matter and antimatterThis is a symmetry of natureThey can be pair-produced or annihilate with one another


Feynman Diagrams

● Richard Feynman developed pictures to represent particle interactions● The “Feynman Rules” associate different mathematical factors for each part

of a diagram● By writing a diagram, you can directly read off the QFT factors to compute

interaction probabilities


Parts of a Feynman Diagram

Fermions are drawn as a solid line with an arrow● The arrow shows the flow of matter● Matter flows forward in time● Antimatter flows backward in time

Photons are drawn as a squiggly line

W/Z/Higgs bosons are drawn as a dashed line

Gluons are drawn as loopy line

Labels:● Bosons do not have arrows (neither matter nor antimatter)● Fermions typically have a label to identify the particle● Sometimes the bosons do too, when it is not obvious what it is

- - - - - - - - - -


Axes

● One axis represents time, and the other space● But unfortunately, there are two conventions● And diagrams seldom have the axes labeled

● In this course, I will exclusively use time from left to right● But keep in mind that when you look up a Feynman diagram you

must know which axis is time


Using Feynman Diagrams in a Perturbation Series

Feynman showed that a perturbation series can be described by a series of Feynman diagramsOrder proportional to the number of loops

Zeroth order is described by “Tree Level” diagrams

First order is described by one loop diagrams

When two electrons scatter, is it a tree level, one loop, two loop process?

Answer: We don't know! (see QED by Feynman)

Remember the path integral formulation:Sum up ALL possible interactionsAll we see is that two electrons scatter


Scattering

A large class of particle interactions fall under the class of scattering

Scattering is the collision of two particlesTwo incoming particles interactThere is a probability for the interaction (characterized by the cross section)

Rules for scattering:The center of mass energy can go into the final productsAs scattering energy increases, heavier final state particles are available

Scattering experiments:Particle accelerators can collide particles with each other or fixed targetsHigh energy particles (like in cosmic rays) can collide with other matter


Elastic Scattering

Elastic scattering: Ingoing and Outgoing particles the same

Examples:

Electron electron scattering Electron neutrino scattering

● Very analogous to classical elastic scattering● No kinetic energy is lost, it is transfers from one

particle to another


Inelastic Scattering

Incoming and Outgoing particles are differentCenter of mass energy goes into new particles

Examples:

Neutrino neutron scattering Electron positron annihilation

● Analogous to classical inelastic scattering● There is a transfer of kinetic and mass energy (KE is “created” or

“destroyed”)


Decays

Particles can decay into lighter particlesMass must always decreaseIn particle's rest frame, only mass energy available

Particles decay with a lifetime given by

Most common example:● Radioactive decay of nuclei● A neutron inside a nucleus can decay into a proton and an

electron (if the nuclear binding energy of the final state is lower)

Other examples:● Muons decaying to electrons and neutrinos● Exotic quark states (mesons) decaying into lighter mesons


The 4 Fundamental Forces

GravitationElectricity and MagnetismWeak nuclear forceStrong nuclear force

● Everything except gravity can be described by quantum field theory● E&M + Weak interactions are unified by the electroweak theory● This predicted the Higgs boson, and also explains mass generation● Strong interactions describe the substructure of nucleons, as well as other

exotic particles● These combine to make up the Standard Model of particle physics

Separates particles into categories

Bosons (force carriers)● Photon, W, Z, gluon, Higgs

Fermions (matter particles)● 3 generations● Quarks (up and down type)● Leptons (charged and

uncharged)


Leptons

Charged leptonsElectrically charged (-1)

Electron (e)Mass = 511 keVStable

Muon (μ)Mass = 105.7 MeVLifetime = 2.2 μs

Tau (τ)Mass = 1.777 GeVLifetime = 0.29 ps

Uncharged leptons

Electron neutrino (νe)

Muon neutrino (νμ)

Tau neutrino (ντ)

In the SM: ● neutrinos are massless● neutrinos are stableWe'll deal with the fact that this is wrong when we study neutrinos later in the course!

Empirical properties:

The total number of leptons is conservedl = #leptons – #antileptons

The total number of each generation of leptons is conservedle = #e- + #ν

e - #e+ - #ν

e

le = #μ- + #ν

μ - #μ+ - #ν

μ

le = #τ- + #ν

τ - #τ+ - #ν

τ


Quarks

Up typeElectric charge +2/3

Up (u)Mass = 2.3 MeV

Charm (c)Mass = 1.27 GeV

Top (t)Mass = 173.1 GeV

Each quark carries a color chargeLike electric charge (+,-) but three typesRed, anti-redGreen, anti-greenBlue, anti-blue

Down typeElectric charge -1/3

Down (d)Mass = 4.8 MeV

Strange (s)Mass = 95 MeV

Bottom (t)Mass = 4.2 GeV

Empirical properties:● No bare color charge has ever been observed● Quarks (and gluons) are contained in composite objects that are color neutral● Mesons: 1 quark plus 1 anti-quark● Baryons: 3 quarks


Bound States: Baryons

Baryons are color neutral objects with 3 quarks(antibaryons have 3 antiquarks)Electric charge can be -1, 0, 1, 2Examples:Proton (uud)Neutron (udd)Σ- (dds)Σc

++ (uuc)

Only the lightest baryon (proton) is stableFree neutrons, for example, decay to protonsThe total number of baryons is conserved!

This poses constraints on possible decays


Bound States: Mesons

Mesons are composed of one quark and oneantiquarkThe quark/antiquark pair contain the samecolor/anticolor (e.g. red-antired) → colorneutralNo conservation law for mesons→ All mesons decay

● Hadrons (both mesons and baryons) are found in patters● Derivable from group theory● This was used to predict many, many bound states of quarks● What we call the particle zoo


The Photon

● Massless boson● Transmits electromagnetic force● Couples to electric charge but does not carry

charge● Spin 1 particle

● Naively, there should be 3 spin projection states● mz = -1,0,1● It turns out, mz = 0 is not allowed because of● special relativity (transverse nature of E&M

waves)● 2 spin states → 2 polarizations

Long range force:Because the photon ismassless, it can propagateindefinitelyTwo charged particles cancommunicate from across theuniverse

Coupling strength (or strength offorce) is electric charge

EM interaction always possiblebetween charged particles, never forneutral particles


Gluons

● The gluon (g) transmit the strong interaction● The spin is 1● But only two polarization states (like the● photon)● Unlike the photon, the gluon carries color● charge● Quarks carry color, antiquarks carry anticolor● Gluons carry both color and anticolor● 8 color-anticolor states

The strong interaction gets stronger asthe range increasesIf you try to pull a quark free, moreenergy is pumped into the gluonsNew quark-antiquark pair is produced

● The timescale for the strong interaction is very short ~ 10-22 s● Thus, lifetimes of strongly interacting particles are short● However, the strong interaction preserves quark generations!● Example: # of t + b quarks is unchanged in strong interactions● We need the weak interaction to break this rule


Example: Rho Decay


Example: J/Psi Decay


Example: Pion Exchange

● The force that holds the nucleus together is a special case of strong interactions● Protons and neutrons interact by exchanging pi mesons (pions)


Weak Interaction

The W and Z bosons that transmit the weakinteraction need careful discussionThey are massivem

W = 80.4 GeV

mZ

= 91.2 GeVSpin 1 particles, but also each with only 2 spinprojection states (same as photon)Slower interaction than Strong 10-8 – 10-13 s

The W carries electric charge● W+, W-

● W interactions change particle type● Underlying processes like radioactive decay● Only the W changes quark/lepton flavor

Massive bosons = short range forceThese heavy bosons are not long livedThey do not propagate freelyInteractions can only happen over a distance ~10-16 m or lessThis makes the force effectively very weak

The Z is electrically neutralCoupling / timescale same as W

Two important features of the weak interaction


Why is the weak force weak?

In E&M, the photon didn't require any mass energyBut in weak interactions, the W and Z do requiremass energyHow does that happen for low energy particles?

The uncertainty principle!

I can borrow an elephant if I give it back on time

If two particles are close enough, they can “borrow” energy tocreate a Z or W just long enough to transmit the force


Example: Beta+ Decay

A proton (udd) changes to a neutron (uud) by emitting a W+, whichdecays into a positron and a neutrino


Example: neutrino – electron scattering


Example: B meson decays


Unification of Forces


Electroweak Unification

● E&M and Weak interaction are unified at high energy

● This means that they behave the same, or are indistinguishable, at that energy

● How does this work, if the W, Z are massive but the photon is massless?

● At high enough energy, E > 100 GeV there is no need to “borrow” energy for these bosons

Challenges of unification:The QFT treatment of A

μ for E&M does

not work for massive bosonsNo way to satisfy special relativity with massive bosonsBut special relativity is observed!

Answer:Solve the problem with massless particlesIntroduce a new mechanism that gives mass as a side effectThis is the Higgs mechanism

What are the boundary conditions?● Massless photon● Massive W, ZA valid theory must satisfy these!


Electroweak Symmetry

● Gauge symmetry ↔ Special Relativity● Treats the four gauge bosons (photon, W+, W-, Z) the

same● Masseless bosons obeying special relativity ● Symmetric under gauge transformations (Lorentz

Transformations)● A single coupling → can't distinguish E&M and Weak

● Charge at rest in one frame● No B field

● Moving in another frame● Does have B field

● Maxwell's equations are consistent with this


The Higgs Mechanism

Write the rest of the SM in as massless particles

● This includes both the bosons and the fermions

● Recall, the photon was massless, so we already know how to solve this problem

● Quantize Aμ

● This means the W and Z would be massless, and behave like the photon (hint hint, unification)

Add a quartic potential to the SM

A QFT treatment of this lets us define a scalar (spin 0) field Φ to quantize this potential (via second quantization)

Consequences of Φ● Any particles associated with this

field would be spin 0● Remember we only had spin ½ and 1

so far● The quartic potential gives 4 degrees

of freedom● Quantization yields 4 states

● Higgs doublet● (2 pairs, charged and neutral)


Vacuum Expectation Value (vev)

A vev is the expectation value of a field (QFT version of a potential) at its minimum value, e.g. the bottom of the potential

For the potential we introduced, the vev is zeroSpontaneous symmetry breaking breaks the degenerecy of the potential:

This has a non-zero vevIf vev is negative (only if x is complex) then vev is lower after symmetry breaking


Mexican Hat Potential

Since the Higgs field is complex, the quartic potential makes a “Mexican Hat”

False vacuum (at origin) is not the minimum in potential

A “ring” at potential minimum

● Azimuthal symmetry● Infinite positions around circle

at minimum● Nature has to select one

→ Breaks symmetry


Spontaneous Symmetry Breaking

● The fact that the Higgs “spontaneously” chooses some value for the minimum “breaks” gauge symmetry

● E&M and Weak interaction are no longer the same

● Happens below electroweak unification scale

● Couplings become distinct


The Higgs Doublet Revisited

What are the consequences of spontaneous symmetry breaking?

Three of the Higgs doublet states become mass terms for the Weak bosons:

But the fourth state is leftover (called a Goldstone boson)

Interactions of fermions with the Higgs field (not the boson, the field) give mass terms to the fermions● Mass is a property, not a force● The coupling to the Higgs field is mass● Heavier particles couple more strongly to the field


What does the Higgs do?

● The mass of fermions and W/Z bosons comes from interactions with Higgs field

● The coupling is the particle's mass ● No longer the same for every particle (like α in E&M)● Gives effective drag to particles as they propagate● Heavier particles couple more strongly than lighter particles

The origin of mass


Predictions of the Higgs Mechanism

Predicted a very precise relationship between W and Z mass

● The Weinberg angle is a calculated quantity in the Higgs mechanism

● After discovering and measuring the W mass, the Z mass was precisely predicted

● The Z was discovered exactly where it should be at 91.2 GeV

Higgs Boson● Massive spin zero particle● It's a boson, so it transmits a

force● Not a new force, a 5th component

of the electroweak force (unified E&M with Weak)

● It HAD to exist for the mechanism to work

● Discovered in 2013● Higgs and Englert awarded 2013

Nobel Prize

● Introduced to particle physics in 1962 following work done in superconductivity

● Before the discovery of W, Z, H

Exceptionally successful mechanism!


Discovery of the Higgs

Large Hadron Collider (LHC)● Located at Cern in the Swiss/French

Alps● 4 Experiments on the LHC● ALICE: Discovered and studies quark

gluon plasma● LHCb: Studies b-meson physics● ATLAS and CMS: Higgs and new particle

searches

● 14 TeV center of mass energy● Proton – proton collisions● Composite objects, so only part of the

14 TeV is available in collisions● High luminosity → high statistics● Hadronic interactions → lots of top

quarks● Since Higgs couples to mass, look for

rare production of Higgs boson through heavy intermediate states (e.g. top)


Symmetry in the SM

Symmetry is at the core of the SMNoether's theorem:For every symmetry, there is a corresponding conserved quantityTranslational symmetry → conservation of momentumRotational symmetry → conservation of angular momentumGauge symmetry (special relativity) → conservation of electric chargeSU(2) symmetry of QCD → conservation of color chargeAnd so on...

Emmy Noether:Referred to as “the most important woman in the history of mathematics”


Fundamental Rule of Particle Physics

Anything not expressly forbidden is possible!

Conserved quantities in the SM:Globally conserved● Energy, momentum, angular momentum● Electric charge● Color charge● Lepton number (and lepton flavor number)● Baryon numberConserved by strong interaction● Quark generation number

● For each of these quantities, there is a symmetry in the SM to describe it● Other quantities were naively expected to be conserved● Parity (mirror symmetry), Charge conjugation times parity● There is no symmetry in the SM to conserve them, so they are found to NOT be

conserved● Exception: CP violation in strong interactions IS conserved, but there is no

symmetry to protect it


Helicity (handedness)

Recall particle spin:● Fermions (spin ½)● Two spin states● Can be aligned or antialigned with momentum● Right or Left handed helicity● Sometimes called handedness or chirality

The same can be said for the spin 1 bosons (e.g. right, left polarized light)


Handedness in Weak Interactions

Observational curiosity:The weak interaction only couples to left handed fermions and right handed antifermionsEvery Weak decay observed obeys this rule!

No good explanation for this

Always left handed!


Helicity and Special Relativity

Consider a weak decay of a particle at rest in the laboratory● The fermions in the decay products will always

be left handed.● But Special Relativity says I can boost (Lorentz

Transformation) into a frame where the momentum changes sign (spin stays the same)

● How does this decay take place in that frame?● This is an open question

● Helicity is not a Lorentz invariant quantity!● Not a good quantum number for special

relativity● Yet it is a conserved quantity in the Weak

Interaction


SM Neutrinos and Helicity

● In the standard model, neutrinos have zero mass● They move at the speed of light● Then, helicity is a good quantum number● This solves at least part of the mystery of the

handedness of the weak interaction● Neutrinos are always left handed and antineutrinos are

always right handed in every frame


Where the SM Works

● Excellent description of 3 of the 4 fundamental forces● Explains nuclear structure, quark confinement, quark gluon

plasma● Explains weak interactions, radioactive decay● Explains EM interactions● Unifies EM and Weak● Describes all known constituents of matter

● Precisely predicted Z mass● Predicted existence of Higgs boson● Describes mass generation of W/Z and fermions

● Agrees with empirical constraints● Lepton and lepton flavor number conservation● Electric / color charge conservation● Left-handed weak interactions


What it Doesn't Include

Empirical problems● Neutrino masses● Handedness of Weak Interactions and neutrinos● Lepton generation number violation

Theoretical problems● Naturalness of Higgs mass (Hierarchy Problem)● Grand Unification Theory (GUT)

● Couplings don't meet at one point● Strong CP problem

● No symmetry protecting it

Missing physics● Dark Matter● Dark Energy

Extensions to the SM● Satisfy the tight experimental constraints of the SM● QCD, Electroweak symmetry breaking (Higgs), etc● Leave known SM physics unchanged


Neutrinos

Neutrino oscillations (2015 Nobel Prize)● Neutrinos change flavor

● Violation of lepton flavor number● Only possible for finite neutrino mass● If m ≠ 0, helicity not good quantum number● Can boost to frame moving faster than neutrino

Neutrino properties● Can the neutrino be its own antiparticle?

● Dirac vs Majorana● Which neutrino is heaviest?

● Mass hierarchy● Why are neutrinos so much lighter than other fermions?

● e.g. Seasaw mechanism● Are there other kinds of neutrinos?

● Sterile neutrinos● Right handed neutrinos

So far, neutrinos are the only particles whose measured properties cannot be explained by the SM!


The Dark Universe

● The SM only explains ~ 5% of the stuff that makes up the universe

● The remaining 95% is Dark, e.g. we don't see it

● This description comes from many, many measurements!

● But no model of how the Dark sector behaves

● Dark Matter is likely a new particle● Not included in the SM● Need to add something to describe it and

its interactions

● Dark Energy is even more bizarre● Explains expansion of the universe● We know it's there, but don't know much

more about it


Axions

The Strong CP problem● CP → mirror reflection and charge conjugation

● Look at experiment in a mirror and change sign of electric charge● Are experimental results unchanged?

● Recall Noether's theorem:● Relationship between symmetry and conserved charge● For CP to be conserved, there must be a symmetry protecting it

● CP is conserved in strong interactions● All experiments tell us this● No symmetry protecting it in SM

The Axion● Add a new symmetry to strong interaction● Special type of field● This would give CP as conserved charge● Satisfy Noether's theorem● Explain the strong CP problem● The axion is the particle associated with this field● So far not observed


Supersymmetry (SUSY)

● Symmetry between bosons and fermions

● Every SM boson has a SUSY fermion partner

● Every SM fermion has a SUSY boson partner

● SUSY particles are called sparticles

● Doubles number of elementary particles

SUSY fermions are append -ino to particle nameWino, gluino, etc

SUSY bosons prepend s to particle nameSelectron, squark, etc


SUSY Breaking

● SUSY predicts particles and sparticles with same mass

● But we don't see 511 keV selectrons● SUSY must be broken (like Higgs does to

electroweak gauge symmetry)

● Same mechanism breaks SUSY and Electroweak symmetry

● Particles and sparticles no longer have same mass● Naturally gives sparticle masses at TeV scale

● Peculiarity of SUSY● Requires more than one Higgs doublet● Maybe we see signs of this at the LHC?● Time will tell


R-Parity

● SUSY allows for exotic processes like proton decay

● Proton decay has never been observed

● t1/2

> 1032 years

● R-Parity requires even number of sparticles in interactions● Sparticles produced in pairs● Keeps proton stable● Consequence:● Lightest SUSY particle would be stable● Possible DM candidate


The Hierarchy Problem

Radiative Corrections to Mass● Virtual interaction with own field● Example: Lamb shift● Electron emits and absorbs a photon● Shows up as shift in electron mass

Radiative corrections to the Higgs massIncludes diagrams with e.g. top loopsThese loops give contributions

This extreme cancelation of 34 orders of magnitude requires a lot of fine tuning


SUSY and the Hierarchy Problem

● SUSY adds a boson loop for every fermion loop

● Bosons give + sign, fermions give – sign● These cancel one another

● If SUSY were unbroken, they would cancel perfectly

● Since SUSY is broken, the cancelation isn't perfect

● Naturally gives ~100 GeV Higgs mass


SUSY and GUT

Without SUSY, running of couplings do not meetWith SUSY, they meet at one pointThis implies that SUSY allow for unification of strong, weak, and EM forces in single force


Characteristics of SUSY

● Full SUSY contains 105 free parameters● I can fit an elephant with 105 parameters!

● Usually work in minimal versions of SUSY● Minimal Supersymmetric Standard Model (MSSM)

● Only 4 ½ free parameters● 4 parameters and one sign● Still TONS of freedom● Countless models for new physics

● Next to MSSM (NMSSM)● Relax conditions and add another free parameter

● And so on...


Other Extensions to the SM

● Other symmetric extensions to the Lagrangian● Conserved charge is a good source for stable

particles (Noether’s theorem)● Dark Matter candidates● Dark Energy models● Other exotic particles to explain

● Neutrino mass and oscillations● CP violation and strong interactions● Hierarchy problem● Lepton / Baryon asymmetries in the universe

We’ll discuss many of these in this course!

Lecture 01 Elementary Particle Physics - Prof. E....

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