1. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 1 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

2. Wednesday, Nov. 29, 2006PHYS 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.

3. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 3 EW Potential and Symmetry Breaking Symmetric about this axis Not symmetric about this axis

4. Wednesday, Nov. 29, 2006PHYS 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

5. Wednesday, Nov. 29, 2006PHYS 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:

6. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 6 Hadron Collider SM Higgs Production  LHC Tevatron We use WH  e +b  b channel for search for Higgs at Tevatron

7. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 7 SM Higgs Branching Ratio 140GeV/c 2 We use WH  e +b  b channel for search for Higgs

8. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 8 How do we find the Higgs particle? Look for WH  l+ +b b-bar Use the finite lifetime of mesons containing b-quarks within a particle jets. b   vertex Silicon Detectors Beampipe 1”

9. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 9 LEP EWWG: http://www.cern.ch/LEPEWWGhttp://www.cern.ch/LEPEWWG 114.4<M H <199GeV What do we know as of Winter 06?

10. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 10 How do we make a Neutrino Beam? Use large number of protons on target to produce many secondary hadrons ( , K, D, etc) and focus as many of them as possible Let  and K decay in-flight for  beam in the decay pipe –    +   K     Let the beam go through shield and dirt to filter out  and the remaining hadrons, except for –Dominated by  p Good target Good beam focusing Long decay region Sufficient dump

11. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 11 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 di-poles

12. Wednesday, Nov. 29, 2006PHYS 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

13. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 13 4. QCD Factorization Theorem Non-perturbative, infra-red part     kk’      W + (W - ) p ,   } E Had P q= k-k’ q, (  q) xPxP Partonic hard scatter  =f*  p f pp Factor the whole interaction into two independent parts!! Allow QCD perturbation theory to work and physical observables calculable.

14. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 14 How is sin 2  W measured? Cross section ratios between NC and CC proportional to sin 2  W Llewellyn Smith Formula: Define experimental variable to distinguish NC and CC Compare the measured ratio with MC prediction

15. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 15 Charged Current Events Neutral Current Events How Can Events be Separated? x-view y-view x-view y-view Nothing is coming in!!!   Nothing is going out!!! Event Length

16. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 16 Neutrino Oscillation First suggestion of neutrino mixing by B. Pontecorvo at the K 0, K 0 -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

17. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 17 Neutrino Oscillation Formalism Two neutrino mixing case: where and are weak eigenstates, while and are mass eigenstates, and  is the mixing angle that give the extent of mass eigenstate mixture, analogous to Cabbio angle OR

18. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 18 Oscillation Probability Substituting the energies in the wave functions: where and. Since the ’s move at the speed of light, t=x/c, where x is the distance to the source of . The probability for  with energy E oscillates to e at the distance L from the source becomes

19. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 19 Sources for Oscillation Experiments Natural Sources –Solar neutrinos –Atmospheric neutrinos Manmade Sources –Nuclear Reactor –Accelerator

20. Wednesday, Nov. 29, 2006PHYS 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 e + e  e+X: electron gives out Čerenkov light  CC interactions, resulting in muons with Čerenkov light Detectors using accelerator made neutrinos –Look very much like normal neutrino detectors Need to increase statistics

21. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 21 Atmospheric Neutrinos & Their Flux Neutrinos resulting from the atmospheric interactions of cosmic ray particles –He, p, etc + N  ,K, etc       e+ e +  –This reaction gives 2  and 1 e Expected flux ratio between  and e is 2 to 1 Give a predicted ratio of

22. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 22 SNO Experiment Results 0.35

23. Wednesday, Nov. 29, 2006PHYS 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

24. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 24 Super-K Atmospheric Neutrino Results

25. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 25 Accelerator Based Experiments Mostly  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

26. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 26 Long Baseline Experiment Concept (K2K) Compare kinematic distributions between near and far detectors

27. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 27 Different Neutrino Oscillation Strategies

28. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 28 Exclusion Plots  e appearance e appearance  disappearance

29. Wednesday, Nov. 29, 2006PHYS 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 (  and e ) at about 10 6 times higher intensity

30. Wednesday, Nov. 29, 2006PHYS 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 (sin 2 2  and  m 2 ) that the current data seem to point –LSND ~1eV 2 ; Super-K ~ 10 -3 eV 2, Solar (LMA) ~ 10 -5 eV 2 –There are at least three flavors participating in oscillation –Sin 2 2  23 ~ 1 at 90% confidence level –|  m 32 2 | ~ 2x10 -3 eV 2 –  m 21 2 ~ 2x10-3 eV 2 (If LMA confirmed) –Sin 2 2  12 ~ 0.87 at 90% confidence level (if LMA confirmed) –Sin 2 2  13 < O(0.1)

31. Wednesday, Nov. 29, 2006PHYS 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 sin 2 2  13 0 or small? What is the sign of  m 32 ? –What are the configuration of neutrino masses? –What are the actual masses of neutrinos mass eigenstates? What are the matter effects? Is sin 2 2  23 = 1?

32. Wednesday, Nov. 29, 2006PHYS 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?

33. Wednesday, Nov. 29, 2006PHYS 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/( E 2- p 2 c 2- m 2 c 4) 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.

34. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 34 Feynman Diagram Components ImageDescriptionParticle Represented straight line, arrow to the right electron straight line, arrow to the left positron wavy linephoton

35. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 35 Feynman Diagram Rules

36. Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 36 A Few Example Feynman Diagrams

37. Wednesday, Nov. 29, 2006PHYS 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