1. Neutrino Physics - Lecture 3 Steve Elliott LANL Staff Member UNM Adjunct Professor 505-665-0068, elliotts@lanl.gov

2. Spring 2007Steve Elliott, UNM Seminar Series2 Lecture 3 Outline Matter enhanced oscillations 3 flavor oscillations Neutrinos from the Sun The neutrinos Past experiments What we know and what we want to learn

3. Spring 2007Steve Elliott, UNM Seminar Series3 What about MSW? The Sun is mostly electrons (not muons). e can forward scatter from electrons via the charged or neutral current.  can only forward scatter via the neutral current. The e picks up an effective mass term, which acts on the weak eigenstates.

4. Spring 2007Steve Elliott, UNM Seminar Series4 The MSW H term. This extra term results in an oscillation probability that can have a resonance. Thus even a small mixing angle, , can have a large oscillation probability.

5. Spring 2007Steve Elliott, UNM Seminar Series5 Similar algebra as before

6. Spring 2007Steve Elliott, UNM Seminar Series6 Constant Density Solutions Note similar form to vacuum Oscillations. Note that sin 2 2  m can be 1 even when sin 2 2  is small. That is when: L/L 0 = cos2 

7. Spring 2007Steve Elliott, UNM Seminar Series7 Variable Density Integrate over the changing density (such as in a star or supernova or Earth).

8. Spring 2007Steve Elliott, UNM Seminar Series8 Three Formulism

9. Spring 2007Steve Elliott, UNM Seminar Series9 Transition Probability

10. Spring 2007Steve Elliott, UNM Seminar Series10 Transition Probability Real U’s

11. Spring 2007Steve Elliott, UNM Seminar Series11 Complex U’s If U is complex, then we have the possibility

12. Spring 2007Steve Elliott, UNM Seminar Series12 Oscillation Experiments Appearance: look for  when none are expected Disappearance: look for decrease in flux of 

13. Spring 2007Steve Elliott, UNM Seminar Series13 SolarReactorAtmospheric Maki, Nakagawa, Sakata, Pontecorvo

14. Spring 2007Steve Elliott, UNM Seminar Series14 PDB parameterization

15. Spring 2007Steve Elliott, UNM Seminar Series15 Phases in the mixing matrix For nxn unitary matrix (U): 2n 2 parameters in a complex matrix -n 2 unitarity constraints -(2n-1) unphysical phases: that can be absorbed into the fields, and =(n-1) 2 parameters (1/2)(n-1)n of these are rotation angles Note however, that for Majorana fields, the phases of and are related. Hence there are only n unphysical phases.

16. Spring 2007Steve Elliott, UNM Seminar Series16 CP violation

17. Spring 2007Steve Elliott, UNM Seminar Series17 The Jarlskog Invariant Note the product of the sin of all the angles. If any angle is 0, CP violation is not observable. Note that I have seen different values of the leading constant. (taken to be 1 here)

18. Spring 2007Steve Elliott, UNM Seminar Series18 CP violation - Vacuum 1st term associated with atmos  m 2 2nd term associated with solar  m 2 The interference term changes signs for anti-neutrinos, because U is replaced by U*

19. Spring 2007Steve Elliott, UNM Seminar Series19 CP violation hep-ph/0306221

20. Spring 2007Steve Elliott, UNM Seminar Series20 There are only 2 independent  m 2 for 3 This will be important when we discuss LSND.

21. Spring 2007Steve Elliott, UNM Seminar Series21 Solar Neutrinos and Oscillations Solar neutrinos –Few MeV, L~10 11 m –Electron neutrinos –Most are disappearance expts. (Except SNO NC and SK’s slight NC sensitivity)

22. Spring 2007Steve Elliott, UNM Seminar Series22 Solar Model Assumptions Hydrostatic Equilibrium –radiative & particle pressures balance gravity Energy Transport –photon diffusion in deep interior Energy Generation –nuclear fusion Isotopic/Elemental Abundances –changes occur only by nuclear reactions –initially agrees with current surface observations

23. Spring 2007Steve Elliott, UNM Seminar Series23 The pp fusion reactions p + e - + p  2 H + e 2 H + p  3 He +  3 He + p  4 He + e + + e 3 He + 4 He  7 Be +  7 Be + e -  7 Li +  + e 7 Li + p   +  3 He + 3 He  4 He + 2p 99.75%0.25% 85%~15% 0.02%15.07% ~10 -5 % 7 Be + p  8 B +  8 B  8 Be* + e + + e p + p  2 H + e + + e

24. Spring 2007Steve Elliott, UNM Seminar Series24 The energy spectrum

25. Spring 2007Steve Elliott, UNM Seminar Series25 MSW at high energies, vacuum at low. Ratio of oscillation length in matter to vacuum

26. Spring 2007Steve Elliott, UNM Seminar Series26 Matter and Vacuum matter vacuum About 1 MeV For the Sun If  < cos2  12 ~0.4 then the oscillation probability is given by the vacuum averaged result. hep-ph/0305159

27. Spring 2007Steve Elliott, UNM Seminar Series27 The Cl Experiment Ray Davis and his tank of cleaning fluid

28. Spring 2007Steve Elliott, UNM Seminar Series28 Cl Operations 615 tons of C 2 Cl 4, 814-keV threshold Homestake Gold Mine Bubble He gas through to extract Ar Ar trapped in cold trap. PC filled with Ar gas (7% methane) 37 Cl is 24% abundant.

29. Spring 2007Steve Elliott, UNM Seminar Series29 The Homestake Mine

30. Spring 2007Steve Elliott, UNM Seminar Series30 The Cl Apparatus