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PHYS 3446 – Lecture #22

PHYS 3446 – Lecture #22. Wednesday, Nov. 29, 2006 Dr. Jae Yu. 1. The Standard Model Symmetry Breaking and the Higgs particle Higgs Search Strategy Neutrino Oscillations Issues in the Standard Model 2. Feynmann Diagrams. Spontaneous Symmetry Breaking.

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PHYS 3446 – Lecture #22

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  1. PHYS 3446 – Lecture #22 Wednesday, Nov. 29, 2006 Dr. JaeYu • 1. The Standard Model • Symmetry Breaking and the Higgs particle • Higgs Search Strategy • Neutrino Oscillations • Issues in the Standard Model • 2. Feynmann Diagrams PHYS 3446, Fall 2006 Jae Yu

  2. Spontaneous Symmetry Breaking While the collection of ground states does preserve the symmetry in L, the Feynman formalism allows to work with only one of the ground states through the local gauge symmetry  Causes the symmetry to break. This is called “spontaneous” symmetry breaking, because symmetry breaking is not externally caused. The true symmetry of the system is hidden by an arbitrary choice of a particular ground state. This is the case of discrete symmetry w/ 2 ground states. PHYS 3446, Fall 2006 Jae Yu

  3. EW Potential and Symmetry Breaking Not symmetric about this axis Symmetric about this axis PHYS 3446, Fall 2006 Jae Yu

  4. The Higgs Mechanism • Recovery from a spontaneously broken electroweak symmetry gives masses to gauge fields (W and Z) and produce a massive scalar boson • The gauge vector bosons become massive (W and Z) • The massive scalar boson produced through this spontaneous EW symmetry breaking is the Higgs particle • In SM, the Higgs boson is a ramification of the mechanism that gives masses to weak vector bosons, leptons and quarks The Higgs Mechanism PHYS 3446, Fall 2006 Jae Yu

  5. Higgs Production Processes at Hadron Colliders Gluon fusion: WW, ZZ Fusion: Higgs-strahlung off W,Z: Higgs Bremsstrahlung off top: PHYS 3446, Fall 2006 Jae Yu

  6. Hadron Collider SM Higgs Production s LHC We use WHen+b`b channel for search for Higgs at Tevatron Tevatron PHYS 3446, Fall 2006 Jae Yu

  7. 140GeV/c2 SM Higgs Branching Ratio We use WHen+b`b channel for search for Higgs PHYS 3446, Fall 2006 Jae Yu

  8. Silicon Detectors 1” b   vertex Beampipe How do we find the Higgs particle? • Look for WHl+n+b b-bar • Use the finite lifetime of mesons containing b-quarks within a particle jets. PHYS 3446, Fall 2006 Jae Yu

  9. What do we know as of Winter 06? LEP EWWG: http://www.cern.ch/LEPEWWG PHYS 3446, Fall 2006 Jae Yu 114.4<MH<199GeV

  10. Good beam focusing Good target Sufficient dump p Long decay region How do we make a Neutrino Beam? • Use large number of protons on target to produce many secondary hadrons (p, K, D, etc) and focus as many of them as possible • Let p and K decay in-flight for nm beam in the decay pipe • pm+nm (99.99%), Km+nm (63.5%) • Let the beam go through shield and dirt to filter out m and the remaining hadrons, except for n • Dominated by nm PHYS 3446, Fall 2006 Jae Yu

  11. di-poles How can we select sign of neutrinos? • Neutrinos are electrically neutral • Need to select the charge of the secondary hadrons from the proton interaction on target • Sets of Dipoles are used to select desired charges of the secondary hadrons PHYS 3446, Fall 2006 Jae Yu

  12. How can there be wrong sign of neutrinos in a sign selected beam? • Interaction of correct sign secondary hadrons with beamline elements, including dump and shields • Act as if a fixed target is hit by hadron beam • Back-scatter of unused protons into the beamline • CP violating neutrino oscillations PHYS 3446, Fall 2006 Jae Yu

  13. nm,(`nm) m-, (m+) k k’ pm, qm W+(W-) q=k-k’ q, (`q) } xP EHad Partonic hard scatter P Non-perturbative, infra-red part 4. QCD Factorization Theorem Factor the whole interaction into two independent parts!! s=f*sp Allow QCD perturbation theory to work and physical observables calculable. sp f PHYS 3446, Fall 2006 Jae Yu

  14. How is sin2qW measured? • Cross section ratios between NC and CC proportional to sin2qW • Llewellyn Smith Formula: • Define experimental variable to distinguish NC and CC • Compare the measured ratio with MC prediction PHYS 3446, Fall 2006 Jae Yu

  15. Event Length y-view Charged Current Events Nothing is coming in!!! m x-view m y-view Neutral Current Events Nothing is coming in!!! Nothing is going out!!! x-view How Can Events be Separated? PHYS 3446, Fall 2006 Jae Yu

  16. Neutrino Oscillation • First suggestion of neutrino mixing by B. Pontecorvo at the K0, K0-bar mixing in 1957 • Solar neutrino deficit in 1969 by Ray Davis in Homestake Mine in SD.  Called MSW effect • Caused by the two different eigenstates for mass and weak • Neutrinos change their flavor as they travel  Neutrino flavor mixing • SM based on massless neutrinos • SM inconsistent • Oscillation probability depends on • Distance between the source and the observation point • Energy of the neutrinos • Difference in square of the masses PHYS 3446, Fall 2006 Jae Yu

  17. where and are weak eigenstates, while and are mass eigenstates, and q is the mixing angle that give the extent of mass eigenstate mixture, analogous to Cabbio angle Neutrino Oscillation Formalism • Two neutrino mixing case: OR PHYS 3446, Fall 2006 Jae Yu

  18. where and . Oscillation Probability • Substituting the energies in the wave functions: • Since the n’s move at the speed of light, t=x/c, where x is the distance to the source of nm. • The probability for nm with energy En oscillates to ne at the distance L from the source becomes PHYS 3446, Fall 2006 Jae Yu

  19. n Sources for Oscillation Experiments • Natural Sources • Solar neutrinos • Atmospheric neutrinos • Manmade Sources • Nuclear Reactor • Accelerator PHYS 3446, Fall 2006 Jae Yu

  20. Oscillation Detectors • The most important factor is the energy of neutrinos and its products from interactions • Good particle ID is crucial • Detectors using natural sources • Deep under ground to minimize cosmic ray background • Use Cerenkov light from secondary interactions of neutrinos • ne + e  e+X: electron gives out Čerenkov light • nm CC interactions, resulting in muons with Čerenkov light • Detectors using accelerator made neutrinos • Look very much like normal neutrino detectors • Need to increase statistics PHYS 3446, Fall 2006 Jae Yu

  21. Atmospheric Neutrinos & Their Flux • Neutrinos resulting from the atmospheric interactions of cosmic ray particles • He, p, etc + N  p,K, etc • p m+nm • m e+ne+nm • This reaction gives 2 nm and 1 ne • Expected flux ratio between nm and ne is 2 to 1 • Give a predicted ratio of PHYS 3446, Fall 2006 Jae Yu

  22. 0.35 SNO Experiment Results PHYS 3446, Fall 2006 Jae Yu

  23. Importance of the Zenith Angle • The Zenith angle represents the different distance the neutrinos traveled through the earth • The dependence to the angle is a direct proof of the oscillation probability PHYS 3446, Fall 2006 Jae Yu

  24. Super-K Atmospheric Neutrino Results PHYS 3446, Fall 2006 Jae Yu

  25. Accelerator Based Experiments • Mostly nm from accelerators • Far better control for the beam than natural or reactor sources • Long and Short baseline experiments • Long baseline: Detectors located far away from the source, assisted by a similar detector at a very short distance (eg. MINOS: 370km, K2K: 250km, etc) • Compare kinematic quantities measured at the near detector with the far detector, taking into account angular dispersion • Short baseline: Detectors located at a close distance to the source • Need to know flux well PHYS 3446, Fall 2006 Jae Yu

  26. Long Baseline Experiment Concept (K2K) Compare kinematic distributions between near and far detectors PHYS 3446, Fall 2006 Jae Yu

  27. Different Neutrino Oscillation Strategies PHYS 3446, Fall 2006 Jae Yu

  28. Exclusion Plots nm disappearance `ne appearance ne appearance PHYS 3446, Fall 2006 Jae Yu

  29. Future: Neutrino Factory • Spin-off of a muon collider research • One a hot, summer day at BNL, the idea of neutrino storage ring popped up • Future facility using muon storage ring, providing well understood neutrino beam (nm and ne) at about 106 times higher intensity PHYS 3446, Fall 2006 Jae Yu

  30. What do we know now? • We clearly know neutrinos oscillate  Neutrinos have masses • It seems that there are three allowed regions of parameters (sin22q and Dm2) that the current data seem to point • LSND ~1eV2; Super-K ~ 10-3 eV2, Solar (LMA) ~ 10-5 eV2 • There are at least three flavors participating in oscillation • Sin22q23 ~ 1 at 90% confidence level • |Dm322| ~ 2x10-3 eV2 • Dm212 ~ 2x10-3 eV2 (If LMA confirmed) • Sin22q12 ~ 0.87 at 90% confidence level (if LMA confirmed) • Sin22q13 < O(0.1) PHYS 3446, Fall 2006 Jae Yu

  31. What do we not know? • Does 3-flavor mixing provide the right framework? • For CP–violating oscillation, additional neutrino flavors, neutrino decay, etc? • How many flavors of neutrinos do we have? • Is sin22q13 0 or small? • What is the sign of Dm32? • What are the configuration of neutrino masses? • What are the actual masses of neutrinos mass eigenstates? • What are the matter effects? • Is sin22q23 = 1? PHYS 3446, Fall 2006 Jae Yu

  32. Issues in SM • Why are the masses of quarks, leptons and vector bosons the way they are? • Why are there three families of fundamental particles? • What gives the particle their masses? • Do the neutrinos have mass? • Why is the universe dominated by particles? • What happened to anti-particles? • What are the dark matter and dark energy? • Are quarks and leptons the “real” fundamental particles? • Other there other particles that we don’t know of? • Why are there only four forces? • How is the universe created? • Where are we from? PHYS 3446, Fall 2006 Jae Yu

  33. Feynman Rules • The rules for any process are: • Draw all possible diagrams • Different time-orderings of a given process are represented by the same diagram. • Given the initial momentum and energy, define how momentum and energy flow for each line in the diagram. • Where each diagram has a closed loop, there is an arbitrary momentum and energy flow around the loop and we must integrate over all possible choices for these quantities. • Each intermediate line in the diagram contributes a factor to the amplitude of  1/(E2-p2c2-m2c4) where m is the appropriate mass for the particle type represented by the line. Note that this says that the more "virtual" the particle represented by a line is, the smaller the contribution of the diagram. • Add the amplitude factors from all possible diagrams to get the total amplitude for the process. PHYS 3446, Fall 2006 Jae Yu

  34. Feynman Diagram Components PHYS 3446, Fall 2006 Jae Yu

  35. Feynman Diagram Rules PHYS 3446, Fall 2006 Jae Yu

  36. A Few Example Feynman Diagrams PHYS 3446, Fall 2006 Jae Yu

  37. A Few Feynman Diagram Exercises • Leptonic decays of W+, W- and Z0 • Leptonic decay of p-, p+ and p0 • Top quark decay (tbW) possibilities • P and `P collisions • WH production and final states from P and `P collisions PHYS 3446, Fall 2006 Jae Yu

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