1. Neutrino Physics - Lecture 2 Steve Elliott LANL Staff Member UNM Adjunct Professor 505-665-0068, elliotts@lanl.gov

2. Spring 2007Steve Elliott, UNM Seminar Series2 Lecture 2 Outline Neutrino detection Sources of neutrinos Neutrino Mixing Discussion

3. Spring 2007Steve Elliott, UNM Seminar Series3 Neutrino detection Targets H 2 O D 2 O Scintillator Ga Cl Emulsion Ice Iron Rock ES on e - : x + e - -> x + e - CC on Nucleus: l + A-> A ’ + l NC on Nucleus: x + A-> A ’ + x

4. Spring 2007Steve Elliott, UNM Seminar Series4 Cross sections 10,000 light years of Pb to stop half of solar neutrinos (few MeV e ) Beta decay provides estimate of strength Neutron beta decay Anti-neutrino absorption

5. Spring 2007Steve Elliott, UNM Seminar Series5 Cross Sections The small size of these cross sections is what led early researchers to believe they had postulated an undetectable particle.

6. Spring 2007Steve Elliott, UNM Seminar Series6 Hard experiments Rates are very low –Big detectors Background difficulties –Signal may not be very distinct –Other more common processes can mimic signal –Rare variations of common phenomena…

7. Spring 2007Steve Elliott, UNM Seminar Series7 Sources of neutrinos Big Bang Radioactive decays Stars Supernovas Cosmic rays Reactors Accelerators

8. Spring 2007Steve Elliott, UNM Seminar Series8 Big Bang Relic neutrinos contribute at least as much mass to the Universe as all the stars. There are as many leftover neutrinos as photons. –N  ~420/cc Photon energy: 2.728 K Neutrino energy: 2 K –There are no viable ideas for detecting such low energy neutrinos. –But they might have detectable effects for large scale structure –Note that neutrinos are studied via their particle nature –The microwave background was discovered by the wave nature of photons.

9. Spring 2007Steve Elliott, UNM Seminar Series9 Radioactive Decays MCi sources have been made Mostly for use by solar neutrino radiochemical experiments for efficiency measurements. Proposals for other neutrino property measurements Electron capture isotopes provide a monoenergetic neutrino. 51 Cr 37 Ar

10. Spring 2007Steve Elliott, UNM Seminar Series10 Stars (our Sun) Features Produce only e through fusion reactions Very long baseline, e disappearance, x appearance Low energy, spectral shape well known L/E is large so sensitive to small  m 2 Large Flux Matter enhancement Data Rates from several experiments Energy dependence Day vs. Night Seasonal

11. Spring 2007Steve Elliott, UNM Seminar Series11 Supernovas Features ~ Very long baseline ~  's and  's ~ Complicated and poorly understood source ~ Target cross sections not all well understood Data ~ Not a common phenomenon once ~30 years in our galaxy ~ SN1987A provided little physics data ~ SN1987A did give hope for the future My personal prediction is that neutrinos will teach us a lot about supernovae, but the inverse will be much harder.

12. Spring 2007Steve Elliott, UNM Seminar Series12 Supernovas By using various targets with different energy- and flavor-dependent cross sections, one may be able to de-convolute the various fluxes. Its difficult to get a dedicated supernova neutrino experiment funded.

13. Spring 2007Steve Elliott, UNM Seminar Series13 Cosmic Rays

14. Spring 2007Steve Elliott, UNM Seminar Series14 Reactors Features Complicated but well-understood source. Low energy Short, medium, long baselines Disappearance experiments Data Several at short baselines; 10-250 m CHOOZ/Palo Verde at ~1 km KamLAND at ~250 km

15. Spring 2007Steve Elliott, UNM Seminar Series15 Accelerators Features Usually appearance Various baselines and wide energy range Controlled experimental conditions Data Oscillation limits for many species Lots of experimental results

16. Spring 2007Steve Elliott, UNM Seminar Series16 A reminder of the questions Are neutrinos Majorana or Dirac? What is the absolute mass scale? How small is  13 ? How maximal is  23 ? Is there CP violation in the neutrino sector? Is the mass hierarchy inverted or normal? Is the LSND evidence for oscillation true? Are there sterile neutrinos?

17. Spring 2007Steve Elliott, UNM Seminar Series17 Present Values (from oscillation expts.) hep-ph/0606054

18. Neutrino Oscillations Or how we know most of what we know

19. Spring 2007Steve Elliott, UNM Seminar Series19 Outline Two-flavor vacuum oscillations Two-flavor matter oscillations Three-flavor oscillations –The general formalism –The “rotation” matrices

20. Spring 2007Steve Elliott, UNM Seminar Series20 Consider Two Mass States  1 corresponding to m 1  2 corresponding to m 2 Think of  as a Vector

21. Spring 2007Steve Elliott, UNM Seminar Series21  is a solution of H

22. Spring 2007Steve Elliott, UNM Seminar Series22 The Neutrinos Consider the weak eigenstates e, . These are not the mass eigenstates, 1, . The mass eigenstates are propagated via H. The Mixing Matrix: U

23. Spring 2007Steve Elliott, UNM Seminar Series23 Mixing Weak eigenstates are a linear superposition of mass eigenstates.

24. Spring 2007Steve Elliott, UNM Seminar Series24 In Vacuum, no potential in H Denote c = cos  s = sin 

25. Spring 2007Steve Elliott, UNM Seminar Series25 U H U -1

26. Spring 2007Steve Elliott, UNM Seminar Series26 The energy difference (and Trig.)

27. Spring 2007Steve Elliott, UNM Seminar Series27 U H U -1 becomes The algebra is going to get involved, so lets define A, B, and D such that:

28. Spring 2007Steve Elliott, UNM Seminar Series28 The Diff Eq A solution to this equation should have the form:

29. Spring 2007Steve Elliott, UNM Seminar Series29 Insert proposed solution

30. Spring 2007Steve Elliott, UNM Seminar Series30 Two Equations

31. Spring 2007Steve Elliott, UNM Seminar Series31 r + solution r - solution

32. Spring 2007Steve Elliott, UNM Seminar Series32  is a superposition of these 2 solutions (D+2A) is a constant so we sweep it into a redefinition of the C’s.

33. Spring 2007Steve Elliott, UNM Seminar Series33 The solutions To determine the C’s, use =1 and assume that at t=0, we have all e.

34. Spring 2007Steve Elliott, UNM Seminar Series34 The time dependent solution What is the probability of finding all   at time t?

35. Spring 2007Steve Elliott, UNM Seminar Series35 Transition probability

36. Spring 2007Steve Elliott, UNM Seminar Series36 The Answer Complete mixing: large sin2  and long R/L would result in an “average”: that is P=1/2.