Remainder of Course. 4/22 Standard Model; Strong Interaction 4/24 Standard Model; Weak Interaction 4/27 Course review 5/01 Final Exam, 3:30 5:30 PM
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1 Remainder of Course 4/22 Standard Model; Strong Interaction 4/24 Standard Model; Weak Interaction 4/27 Course review 5/01 Final Exam, 3:30 5:30 PM Practice Final on Course Web Page See HW #12 (not to be collected) on course web page, for quark diagram practice. This is testable.
2 Toy Model Decay Diagrams First order Next order
3 Toy Model Scattering Diagrams
4 The Real World: Quantum Electrodynamics Primitive Vertex
5 Space-time/Feynman Diagram Summary Diagrams should not be interpreted as the literal trajectories of particles Nevertheless, they convey information about the interactions of quantum fields Represent components of matrix elements Provide cartoon means of understanding fundamental interactions Calculation of matrix elements for all forces is beyond the scope of 5110 Being able to write down all the diagrams is not!
6 Deep Inelastic Scattering Confirmed Reality of Quarks Hadrons Mesons (qq) Baryons (qqq) More details needed on nature of force between quarks. Clue: Existence of ground states consisting of 3 identical quarks no orbital A.M... ground state!
7 Problem: u u u is three identical fermions in same quantum state! There has to be an additional internal quantum number Color ; red, green or blue Never observed before because all hadrons are color neutral (like atoms are charge neutral ). Two types of color neutrality: red + red = black red + blue + green = white
8 Quantum Chromodynamics Color is charge of strong interaction Gluon is exchange particle Primitive vertices Consequences Quarks cannot be free Glueballs possible (though not yet observed) QCD Feynman Rules, see e.g. Griffiths
9 Example: Draw a quark/gluon level Feynman diagram for the strong interaction process...
10 Standard Model: Quarks and the Weak Interaction
11 Weak Primitive Vertices
12 Try these... e + + e e e p + e n e
13
14 e- e ee+ Bremsstrahlung Pair Production e+
15 Additional Weak Primitive Vertices ( Neutral Current )
16 Note: There are no flavor changing neutral currents
17 Charged Current Neutral Current Weak Primitive Vertices
18 Strong Primitive Vertices
19 Electromagnetism Primitive Vertices
20 A last few topics...
21 The fourth ( charmed ) quark time Note space horizontal, time vertical Doesn't happen. No flavorchanging neutral currents
22 The fourth ( charmed ) quark What about... This process has two quark vertices, therefore reduced amplitude. But not enough for 10-8 suppression!
23 The fourth ( charmed ) quark What if there were four quarks? (G.I.M., 1970) Contributions from these two diagrams cancel. Explained KL + - suppression Charmed quark observed 1974
24 Quark Mixing Weak d, s quarks are mixtures of strong quarks: 2x2 matrix is known as Cabibbo or quark mixing matrix C. Conservation of probability requires that C be unitary, i.e. C C = 1
25 Quark Mixing Thus C can be written as a rotation matrix
26 Quark Mixing First evidence for 3rd quark generation... Cabibbo scheme generalizes to 3x3 matrix (Cabibbo-Kobayashi-Maskawa or CKM)
27 Quark Mixing In general, to be unitary a 3x3 matrix must have 4 independent parameters; three real angles and one complex phase. Cabibbo matrix
28 Quark Mixing In general, to be unitary a 3x3 matrix must have 4 independent parameters; three real angles and one complex phase.in general Complex phase is origin of CP violation is the reason we're here!
29 Unification of Forces EM and weak forces have been shown to be different aspects of the same force ( electroweak ). Their coupling constants can be related by... Assuming that the strong force can be unified with electroweak, EM and S will also be related.
30 Unification of Forces At high energies, ball in sombrero potential has no preferred orientation At low energies, symmetry of system is broken
31 Unification of Forces Normal modes of sombrero potential Motion along valley floor: requires no energy. Motion perpendicular to valley floor: requires energy
32 Unification of Forces Sombrero potential represents Higgs Field Sphere represents EW force carrier At low energies, force carrier has normal modes corresponding to massless (zero energy photon) massive (nonzero energy W±, Z0)
33 Standard Model Couplings
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