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?
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 3
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 4
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 5
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: 6
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 7
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: ϕ and the 3 components of A We can combine these 4 quantities in a 4-vector Aμ, with μ = 0,1,2,3 A0 = ϕ, A1 = Ax, A2 = Ay, A3 = Az All of E&M can be written in terms of Aμ 8
Second Quantization Fundamental interactions of matter and fields Treat 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 9
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 photons The correct quantization method (e.g. Aμ) 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: 10
Spin: Bosons and Fermions All particles carry a quantum of angular momentum Bosons Integer spin Fermions Half integer spin Symmetric wavefunctions Force carrying particles Antisymmetric wavefunctions Obey Pauli exclusion principle Matter particles (take up space!) Spin states: Projection of angular momentum Mz integer from -s to s 2s+1 spin states Spin 0 (scalar) 1 spin state, mz = 0 Spin ½ 2 spin states, mz = -1/2, 1/2 Spin 1 (vector) 3 spin states, mz = -1, 0, 1 11
Units In quantum physics, we frequently encounter Planck's constant: Angular momentum In special relativity (and of course, E&M), we encounter the speed of light: Speed We can put them together for convenient, quick conversions: 12
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? 13
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) 14
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 15
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 16
The Feynman Path Integral Richard Feynman developed a method for computing interaction probabilities Path Integral (which adopted his name) Probability for photon to be emitted at point A and absorbed at point B Sum up amplitude from all possible paths 17
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 18
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 19
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 20
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 21
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 CONVERGE Other methods necessary, e.g. lattice QCD 22
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 + Lint free Use perturbation theory 23
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 antimatter This is a symmetry of nature They can be pair-produced or annihilate with one another 24
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 25
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 26
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 27
Using Feynman Diagrams in a Perturbation Series Feynman showed that a perturbation series can be described by a series of Feynman diagrams Order 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 interactions All we see is that two electrons scatter 28
Scattering A large class of particle interactions fall under the class of scattering Scattering is the collision of two particles Two incoming particles interact There is a probability for the interaction (characterized by the cross section) Rules for scattering: The center of mass energy can go into the final products As scattering energy increases, heavier final state particles are available Scattering experiments: Particle accelerators can collide particles with each other or fixed targets High energy particles (like in cosmic rays) can collide with other matter 29
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 30
Inelastic Scattering Incoming and Outgoing particles are different Center 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 ) 31
Decays Particles can decay into lighter particles Mass must always decrease In 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 32
The 4 Fundamental Forces Gravitation Electricity and Magnetism Weak nuclear force Strong nuclear force 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) 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 33
Leptons Charged leptons Electrically charged (-1) Electron (e) Mass = 511 kev Stable Muon (μ) Mass = 105.7 MeV Lifetime = 2.2 μs Tau (τ) Mass = 1.777 GeV Lifetime = 0.29 ps Uncharged leptons Empirical properties: Electron neutrino (νe) Muon neutrino (νμ) Tau neutrino (ντ) The total number of leptons is conserved l = #leptons #antileptons In the SM: neutrinos are massless neutrinos are stable We'll deal with the fact that this is wrong when we study neutrinos later in the course! The total number of each generation of leptons is conserved le = #e- + #νe - #e+ - #νe le = #μ- + #νμ - #μ+ - #νμ le = #τ- + #ντ - #τ+ - #ντ 34
Quarks Each quark carries a color charge Like electric charge (+,-) but three types Red, anti-red Green, anti-green Blue, anti-blue Up type Electric charge +2/3 Down type Electric charge -1/3 Up (u) Mass = 2.3 MeV Down (d) Mass = 4.8 MeV Charm (c) Mass = 1.27 GeV Strange (s) Mass = 95 MeV Top (t) Mass = 173.1 GeV 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 35
Bound States: Baryons Baryons are color neutral objects with 3 quarks (antibaryons have 3 antiquarks) Electric charge can be -1, 0, 1, 2 Examples: Proton (uud) Neutron (udd) Σ- (dds) Σc ++ (uuc) Only the lightest baryon (proton) is stable Free neutrons, for example, decay to protons The total number of baryons is conserved! This poses constraints on possible decays 36
Bound States: Mesons Mesons are composed of one quark and one antiquark The quark/antiquark pair contain the same color/anticolor (e.g. red-antired) color neutral No 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 37
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 is massless, it can propagate indefinitely Two charged particles can communicate from across the universe Coupling strength (or strength of force) is electric charge EM interaction always possible between charged particles, never for neutral particles 38
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 as the range increases If you try to pull a quark free, more energy is pumped into the gluons New 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 39
Example: Rho Decay 40
Example: J/Psi Decay 41
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) 42
Weak Interaction The W and Z bosons that transmit the weak interaction need careful discussion They are massive mw = 80.4 GeV mz = 91.2 GeV Spin 1 particles, but also each with only 2 spin projection states (same as photon) Slower interaction than Strong 10-8 10-13 s Two important features of the weak interaction 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 force These heavy bosons are not long lived They do not propagate freely Interactions can only happen over a distance ~10-16 m or less This makes the force effectively very weak The Z is electrically neutral Coupling / timescale same as W 43
Why is the weak force weak? In E&M, the photon didn't require any mass energy But in weak interactions, the W and Z do require mass energy How 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 to create a Z or W just long enough to transmit the force 44
Example: Beta+ Decay A proton (udd) changes to a neutron (uud) by emitting a W+, which decays into a positron and a neutrino 45
Example: neutrino electron scattering 46
Example: B meson decays 47
Unification of Forces 48
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 Aμ for E&M does not work for massive bosons No way to satisfy special relativity with massive bosons But special relativity is observed! Answer: Solve the problem with massless particles Introduce a new mechanism that gives mass as a side effect This is the Higgs mechanism What are the boundary conditions? Massless photon Massive W, Z A valid theory must satisfy these! 49
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 50
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 A μ This means the W and Z would be massless, and behave like the photon (hint hint, unification) 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) 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) 51
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 zero Spontaneous symmetry breaking breaks the degenerecy of the potential: This has a non-zero vev If vev is negative (only if x is complex) then vev is lower after symmetry breaking 52
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 53
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 54
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 55
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 56
Predictions of the Higgs Mechanism Introduced to particle physics in 1962 following work done in superconductivity Before the discovery of W, Z, H 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 Exceptionally successful mechanism! 57
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) 58
Symmetry in the SM Symmetry is at the core of the SM Noether's theorem: For every symmetry, there is a corresponding conserved quantity Translational symmetry conservation of momentum Rotational symmetry conservation of angular momentum Gauge symmetry (special relativity) conservation of electric charge SU(2) symmetry of QCD conservation of color charge And so on... Emmy Noether: Referred to as the most important woman in the history of mathematics 59
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 number Conserved 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 60
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) 61
Handedness in Weak Interactions Observational curiosity: The weak interaction only couples to left handed fermions and right handed antifermions Every Weak decay observed obeys this rule! No good explanation for this Always left handed! 62
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 63
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 64
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 Agrees with empirical constraints Lepton and lepton flavor number conservation Electric / color charge conservation Left-handed weak interactions Precisely predicted Z mass Predicted existence of Higgs boson Describes mass generation of W/Z and fermions 65
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 66
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! 67
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 68
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 69
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 name Wino, gluino, etc SUSY bosons prepend s to particle name Selectron, squark, etc 70
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 71
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 72
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 mass Includes diagrams with e.g. top loops These loops give contributions This extreme cancelation of 34 orders of magnitude requires a lot of fine tuning 73
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 74
SUSY and GUT Without SUSY, running of couplings do not meet With SUSY, they meet at one point This implies that SUSY allow for unification of strong, weak, and EM forces in single force 75
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... 76
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! 77
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