Introduction to particle physics Part IV Physics 129, Fall 2010; Prof. D. Budker Introduction to particle physics Part IV

Bubble chamber Great topics for oral presenantion! The Gargamelle at CERN: discovered weak neutral currents in 1973 Professor Donald A. Glaser Great topics for oral presenantion! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

How particles decay Decay probability goes as dt : Particles do not age! Board work: Mean Lifetime = 1/ Branching Ratios Partial decay rates add Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Effective area Inclusive vs. exclusive Elastic vs. inelastic (different reactions are called channels) Resonances Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Effective area Differential cross section Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Some cross-sections diverge (e.g., for Rutherford scattering) Effective cut-off Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Mandelstam Variables Universally used! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Units of cross section Origin: Uranium nucleus 10-24 cm2 --- as "big as a barn" Unit Symbol m2 cm2 megabarn Mb 10−22 10−18 barn b 10−28 10−24 millibarn mb 10−31 10−27 microbarn (or "outhouse"[3]) μb 10−34 10−30 nanobarn nb 10−37 10−33 picobarn pb 10−40 10−36 femtobarn fb 10−43 10−39 attobarn ab 10−46 10−42 shed[4][5] (10−24 barn) [none] 10−52 10−48 Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Cross Sections Luminosity: number of particles in a beam per unit area per unit time Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Luminosity What about colliding beams? Luminosity = collision frequency  n1  n2 / beam area Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Luminosity Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

LHC luminosity: reality check Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Fermi Golden Rule mi – mass of ith particle pi – 4-momentum of ith particle S – statistical factor accounting for identical particles M – amplitude (p1, …. , pn) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Fermi Golden Rule Kinematic constraints: All outgoing particles are on the mass shell All outgoing particles have positive energy Energy & momentum conservation Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Fermi Golden Rule 2π rules: Every δ gets a 2π Every d gets a 1/(2π) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Fermi Golden Rule With the kinematic constraints, the G.R. simplifies to: For two-body decay: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Feynman-Diagram Rules Goal: figure out amplitude M Draw all possible diagrams for the process The amplitudes from different diagrams add Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Feynman-Diagram Rules For each diagram: Label external momenta pi , label internal momenta qi, draw arrows (arbitrary for internal lines) For each vertex, write coupling constant Each internal line  propagator: For each vertex: energy/momentum conservation: (minus for outgoing lines) Add for each internal line; integrate Erase the resulting ; multiply by The result is M ; examples in Ch. 6 of Griffiths Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Higher-order diagrams Problem: loop integrals (logarithmically) diverge at large q This is not because the diagrams are bad! Regularization: introduce a heavy particle  cut-off (p. 219) Renormalization; running coupling constants…. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Example/interlude: Diagrams in Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Example/interlude: Diagrams in Vanishes for Vanishes in the high-frequency limit Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Relativistic Equations Nonrelativistic Relativistic; spin zero Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The Dirac Equation (relativistic, spin ½) Introduce 44 Dirac Matrices: Relativistic; spin 1/2 Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Solving the Dirac Equation Assume wavefunction independent of position: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Solving the Dirac Equation Four independent solutions: The Dirac Sea Plane wave solutions (Sec. 7.2) Electron  Electron  Positron  Positron  Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Dirac Spinor Algebra Some useful facts about spinors: How do Dirac spinors transform under P? Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Dirac Spinor Algebra Introduce another matrix: What about 4 ? Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Bilinear Covariants Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Physics 129, Fall 2010, Prof. D. Budker; http://budker. berkeley