1. Open questions in  physics  : mechanism & EFT III. Neutrinos

2. New “ Periodic Table ” Courtesy: R.D. McKeown Not physical states

3. Missing Solar Neutrinos … Courtesy: R.D. McKeown

4. Neutrino Oscillations: What We’ve Learned & What’s Unknown The status of the present knowledge of the neutrino oscillation phenomena is schematically depicted in this slide. Three quantities are unknown at present: a)The mass m 1 b)The angle  13 c)Whether the normal or inverted hierarchy is realized. Courtesy: P. Vogel

5. Neutrino Masses and Mixing: Scales Courtesy: R.D. McKeown

6. Maki – Nakagawa – Sakata Matrix CP violation Future Reactor Experiment! Courtesy: R.D. McKeown

7. “Seesaw mechanism” M The Mass Puzzle Courtesy: R.D. McKeown Very heavy neutrino } Familiar light neutrino {

8. The Mixing Angle Puzzle Why so different??? Courtesy: R.D. McKeown

9. What is the absolute value of m ? Why is m so tiny ? What is the mass hierarchy ? Is the neutrino its own antiparticle? What is  13 ? Do neutrinos violate CP? How do neutrinos affect/reflect astrophysical phenomena ? Open Questions

10.  -Decay: LNV? Mass Term? Dirac Majorana  -decay Long baseline ? ? Theory Challenge: matrix elements+ mechanism m EFF & neutrino spectrum NormalInverted See-saw mechanism Leptogenesis L L R HH Lepton Asym -> Baryon Asym GERDACUORE EXOMajorana

11. Majorana or Dirac Or equivalently, is the total lepton number conserved? Courtesy: P. Vogel

12.  & Lepton Number Violation 0  e–e– e–e– uddu ( ) R L WW Whatever processes cause , its observation would imply the existence of a Majorana mass term: Schechter and Valle,82 By adding only Standard model interactions we obtain (  ) R  ( ) L Majorana mass term Courtesy: P. Vogel

13.  Decay vs.  Decay virtual state of the intermediate nucleus Courtesy: P. Vogel

14.  Decay vs.  Decay assumed 2% resolution   ratio 1:100 ratio 1:10 6 Courtesy: P. Vogel

15.  -Decay: Theoretical Challenges Dirac Majorana Theory Challenge: matrix elements+ mechanism Light M exchange: can we determine m Shell Model vs. QRPA Configs near Fermi surface Levels above Fermi surface Vogel et al: reduce QRPA spread by calibrating g PP to T 2

16.  Decay Matrix Elements Why it is difficult to calculate the matrix elements accurately? Contributions of different angular momenta J of the neutron pair that is transformed in the decay into the proton pair with the same J. Note the opposite signs, and thus tendency to cancel, between the J = 0 (pairing) and the J  0 (ground state correlations) parts. The same restricted s.p. space is used for QRPA and NSM. There is a reasonable agreement between the two methods Courtesy: P. Vogel

17.  Decay Matrix Elements Full estimated range of M  within QRPA framework and comparison with NSM (higher order currents now included in NSM) Courtesy: P. Vogel

18.  -Decay: Theoretical Challenges Dirac Majorana Theory Challenge: matrix elements+ mechanism Mechanism: does light M exchange dominate ? How to calc effects reliably ? How to disentangle H & L ? O(1) for  ~ TeV

19.  -Decay: Mechanism & m  signal equivalent to degenerate hierarchy Loop contribution to m of inverted hierarchy scale

20.  -Decay: Theoretical Challenges Dirac Majorana Theory Challenge: matrix elements+ mechanism Mechanism: does light M exchange dominate ? How to calc effects reliably ? How to disentangle H & L ? O(1) for  ~ TeV Prezeau, R-M, Vogel: EFT Does operator power counting suffice?

21.  - decay Mechanism: EFT 4 quark operator: low energy EFT How do we compute & separate heavy particle exchange effects?

22.  - decay in EFT I We have a clear separation of scales L-violating new physics Non-perturbative QCD Nuclear dynamics

23. Effective Field Theory Systematically and effectively organizing our ignorance Weak: M W Hadronic:   Nuclear: k F Scale separation “Low-energy constants” parameterizing non- perturbative QCD Nuclear operators reflecting symmetries of short distance physics Power counting

24.  - decay in EFT II Tractable nuclear operatorsSystematic operator classification

25.  - decay in EFT III K  , K  NN, K NNNN can be O ( p 0 ), O ( p 1 ), etc.

26.  - decay in EFT IV Operator classification Spacetime & chiral transformation properties L (q,e) L ,N,e 

27.  - decay in EFT V Operator classification L (q,e) = e.g.  - decay: a = b = +

28.  - decay in EFT VI Operator classification Chiral transformations: SU(2) L x SU(2) R Parity transformations: q L q R  - decay: a = b = +

29.  - decay in EFT VI Hadronic basis,, Chiral transformations No derivatives K  ~ O (p 0 )

30.  - decay in EFT VIII Hadronic basis Chiral transformations Two derivatives K  ~ O (p 2 )

31.  - decay in EFT: Implications Prezeau, R-M, & Vogel L (q,e) = Chiral properties of O j ++ determine p-dependence of K   K  NN, K NNNN K  ~ O (p 0 ) K  ~ O (p 2 ) No W R - W L mixing W R - W L mix RPV SUSY

32. An open question Is the power counting of operators sufficient to understand weak matrix elements in nuclei ? 76 Ge 76 Se

33. An open question Is the power counting of operators sufficient to understand weak matrix elements in nuclei ? e.g. etc.

34.  -Decay: Interpretation Dirac Majorana Theory Challenge: matrix elements+ mechanism If the existence of the decay is established: What mechanism? Which additional isotopes ?

35.  -Decay: Mechanism & m - SM extensions with low (  TeV) scale LNV  ** ** In absence of fine-tuning or hierarchies in flavor couplings. Important caveat! See: V. Cirigliano et al., PRL93,231802(2004) Left-right symmetric model, R-parity violating SUSY, etc. possibly   unrelated to  m  2 R ~ O(     R = B  e /B  e  » 10 -2 B  e  =  (  e  )/  (  e  e )    (Z,A)  e - + (Z,A))    (Z,A)   + (Z,A)) B  e =

36. Lepton Flavor & Number Violation Present universeEarly universe Weak scalePlanck scale MEG: B  ->e  ~ 5 x 10 -14 Mu2e: B  ->e ~ 5 x 10 -17 ?? R = B  ->e B  ->e  Also PRIME

37. Lepton Flavor & Number Violation MEG: B  !e  ~ 5 x 10 -14 Mu2e: B  !e ~ 5 x 10 -17 Logarithmic enhancements of R Low scale LFV: R ~ O(1) GUT scale LFV: R ~ O  0  decay Light M exchange ? Heavy particle exchange ? Raidal, Santamaria; Cirigliano, Kurylov, R- M, Vogel k11 / ~ 0.09 for m SUSY ~ 1 TeV  ->e  LFV Probes of RPV: k11 / ~ 0.008 for m SUSY ~ 1 TeV  ->e LFV Probes of RPV:

38. What is the absolute value of m ? Why is m so tiny ? What is the mass hierarchy ? Is the neutrino its own antiparticle? What is  13 ? Do neutrinos violate CP? How do neutrinos affect/reflect astrophysical phenomena ? Open Questions

39. Precision Neutrino Property Studies Neutrino Mass: Terrestrial vs Cosmological WMAP & Beyond KATRIN, Mare Energy DensityPower Spectrum Beacom, Bell, Dodelson New interactions

40. Precision Neutrino Property Studies Mixing, hierarchy, & CPV Mini Boone Long baseline oscillation studies: CPV? Normal or Inverted ? Daya Bay Double Chooz T2K

41. Precision Neutrino Property Studies Solar Neutrinos KamLANDBorexinoSNO+LENS Ice Cube High energy solar s DM + EWB EM vs.  luminosity: MNSP unitarity? Solar model?