CP violation in the neutrino sector

1. CP violation in theneutrinosector lepton Lecture 1: Introductiontoneutrinophysics Walter Winter Nikhef, Amsterdam, 06.03.2014 TexPoint fonts used in EMF: AAA

2. Contents (overall) • Lecture 1:Introduction to neutrino physics, sources of CP violation • Lecture 2:Neutrino oscillations in vacuum, measurement of dCP • Lecture 3:Matter effects in neutrino oscillations: “extrinsic CP violation” • Lecture 4:New sources of CP violation? References: • WW: “Lectures on neutrino phenomenology“, Nucl. Phys. Proc. Suppl. 203-204 (2010) 45-81 • Giunti, Kim: “Fundamentals of neutrino physics and astrophysics“, Oxford, 2007

3. Contents (lecture 1) • Introduction to neutrinos • Neutrinos and CP violation … some theory • Constraining neutrino mass • Summary

4. e- e- What are neutrinos? • Ordinary matter consists of protons, neutrons, and electrons • But that‘s not all. There are many other particles …For instance, for each of the above, there are about1.000.000.000 (1 billion) neutrinos in the universe= almost massless particles without electric charge

5. 10-4 10-3 103 104 105 106 107 108 109 1010 1011 1012 E [eV] keV MeV GeV TeV Where do the neutrinos come from? Natural sources Proton mass Electron mass LHC c.o.m. energy Man-madesources

6. n How many neutrinos are there? • So, why don‘t we care? • Neutrinos interact extremely weakly • Neutrinos escape even from very dense environments (e.g. Sun‘s interior, nuclear reactor, …) About 100.000.000.000.000 per second (100 trillions)

7. n Who “invented“ the neutrino? • From energy and momentum conservation, we have for the decay into N particles: • N=2: have particular, discrete energies • N>2: have continuous spectra Wolfgang Pauli

8. How to observe the neutrino? • Extremely difficult to catchthe neutrinos • Thus: Build huge detectors(O(1000 t)), often deepunder ground (background reduction!) (SNO) Flux: extremely large Cross section:extremely small Observation time:1-10 years Detector mass:matches the product

9. The mystery of the missing neutrinos • Raymond Davis Jr. (Nobel Prize 2002) found fewer solar neutrinos than predicted by theory (John Bahcall) • Do the neutrinos disappear?Or was the theory wrong?Discrepany over 30 years(1960s to 90s) pp-fusion chain Neutrino spectra

10. Neutrinos from the atmosphere • The rate of neutrinos should be the same from below and above • But: About 50% missing from below • Neutrino change their flavor on the path from production to detection: Neutrino oscillations • Neutrinos are massive!(Super-Kamiokande: “Evidence for oscillations of atmospheric neutrinos”, 1998)

11. Neutrinos and CP violation … some theory

12. What is CP violation? • C stands for “Charge conjugation“ • P stands for “Parity“ • “CP“ corresponds to particle – anti-particle interchange • Do particles and anti-particles behave the same? • Why is “C“ (charge conjugation) not sufficient? • Peculiarity of the Standard Model: couplings to left-handed particles and right-handed anti-particles (V-A interactions) • Need to flip parity as well to go from left-handed particle to right-handed anti-particle

13. Why would one care about CP violation? • Baryogenesis = dynamical mechanism to create the matter-anti-matter asymmetry in the early universe from a symmetric state • Three necessary conditions (Sakharov conditions): • B violation (need to violate baryon number)Need to create net baryon number • Out of equilibrium processesOtherwise any created asymmetry will be washed out again • CP violationParticles and anti-particles need to “behave“ differently Critical: the Standard Model does not have enough CP violation for that!Requires physics beyond the Standard Model (BSM) • There are many theories for baryogensis, e.g. electroweak baryogenesis, thermal leptogenesis, GUT baryogenesis etc • Addendum to 1): Can be also L violation, which is translated into a violation of baryon number by sphaleron processes before the electroweak phase transition

14. Related question: Why is the neutrino mass so small? Why are the neutrinos morethan 250.000 times lighter than the electron? Cannot be described in simple extensions of the Standard Model Seesaw mechanism: Neutrino mass suppressed by heavy partner, which only exists in the early universe (GUT seesaw)? Decay of (thermally produced) MR origin of matter-antimatter-asymmetry?Thermal leptogenesis CP violation? Test in neutrino oscillations! Requires Majorana nature of neutrino!Test in neutrinoless double beta decay (0nbb) Other SM particles Heavy partner

15. Where does the CP violation come from? • Example: Type I seesaw (heavy SM singlets Nc) Could also be type-II, III seesaw,radiative generation of neutrino mass, etc. Block-diag.  Flavor model(depends on UV completion) Charged leptonmass terms Eff. neutrinomass terms Sectorial origin ofCP violation? Observable CP violation(completely model-indep.) CC Depending on model, actual masses and mixings derived in non-trivial way!

16. ( ) ( ) ( ) = x x Three flavors: Mixings • Use same parameterization as for CKM matrix Pontecorvo-Maki-Nakagawa-Sakata matrix • Neutrinos  Anti-neutrinos: U  U* (neutrino oscillations) • If neutrinos are their own anti-particles (Majorana neutrinos): U  U diag(1,eia,eib) - do enter 0nbb, but not neutrino oscillations Potential CP violation ~ q13 (sij = sin qij cij = cos qij)

17. Three active flavors: Masses • Two independent mass squared splittings, typically (solar) (atmospheric)Will be relevant for neutrino oscillations! • The third is given by • The (atmospheric) mass ordering (hierarchy) is unknown (normal or inverted) • The absolute neutrino massscale is unknown (< eV) 8 8 Normal Inverted

18. The flavor problem Mixings? ~ (hep-ph/0111263) Masses? Degenerate neutrinos: m1 ~ m2 ~ m3 Hierarchical neutrinos: m1 << m2 << m3 How can one describe the differences amongthe generations and species?Where does the CPV come from?

19. The tri-bimaximal mixing (TBM) “prejudice“ • Tri-bimaximal mixings probably most discussed approach for neutrinos (Ul often diagonal, ) • Can be obtained in flavor symmetry models (e.g., A4, S4) • Consequence: no CPV since q13=0  Obviously not! (next lecture) • Ways out for large q13?

20. Impact of large q13 on theory of flavor? q13 ? very small very large Structure:A4, S4, TBM, … Anarchy:Random draw? vs. TBM Corrections?CL sector?RGR running? Some structure + randomness:Froggatt-Nielsen? e.g. q12 = 35 + q13cosd(Antusch, King, Masina, …) Quark-leptoncomplementarity:q13 ~ qC? Different flavor symmetry?

21. Anarchy? • Idea: perhaps the mixing parameters are a “random draw“? • Challenge: define measure which is independent of how random numbers generated • Result: large q13 “natural“, no magic needed • Consequence: CP violation from a random draw of phases? (Hall, Murayama, Weiner, 2000; de Gouvea, Murayama, 2003, 2012)

22. What is the origin of the CP violation, then, after all? • Fundamental parameters in Yukawas/couplings, i.e., interactions with the Higgs field? Example: • Are these mass matrices fundamental parameters? • Possible additions modifications aim to describe the masses and mixings, such as in this model, from more “fundamental“ models • Origin of CPV? • Through spontaneous symmetry breaking (e.g. flavon models)? • “Geometric“, such as by Clebsch-Gordan coefficients of a group? • Coincidence/random choice?

23. Constraining neutrino mass

24. Tritium end point experiments • Direct test of neutrino mass by decay kinematics • Current bound: 1/250.000 x me (2 eV) TINY! • Future experiment: KATRIN (Karlsruhe Tritium Neutrino Experiment)1/2.500.000 x me (0.2 eV) ~8800 km

25. e- W- n p 0nbb: Is the neutrino its own anti-particle? • Two times simple beta decay: • Neutrinoless double beta decay: e- e- 2 x n2 x e W- W- n n p p e- = 0 x n2 x e W- n p

26. Mixing matrix for Majorana neutrinos • Additional phases in mixing matrix without effect in neutrino oscillations • Cannot be rotated away by re-definition of lepton fields if neutrinos are their own anti-particles • Relevant vor neutrinoless double beta decay • Potential additional source of CP violation • These CP phases are potentially connected with the CP violation in the early universe

27. 0nbb phenomenology • Rate ~ |mee|2 x |nucl. matrix element| Majorana phases (Lindner, Merle, Rodejohann, 2005)

28. 0nbb phenomenology (2) • Normal ordering: Lightest mass is m1 • Inverted ordering: Lightest mass is m3 Very difficultto access(~ s132) Potentially small parameters: cancellation possible Always largest term, no cancellations Bands:Impact ofphases/currentknowledge (Lindner, Merle, Rodejohann, 2005) Lightest mass m1 or m3

29. Measurement of Majorana phase a? • Measurement of a difficult because of nuclear matrix element uncertainty • Come potential to exclude some values by combination of data(if external measurement of absolute mass scale) a/(2p) Minakata, Nunokawa, Quiroga, arXiv:1402.6014

30. Cosmological tests of neutrino mass • Example:Relativistic neutrinos damp the formation of structure • Essentially sensitive to sum of neutrino masses • Information from different cosmological datasets used in literature • Limit ~ eV (S. Hannestad)

31. Summary • CP violation is required to describe the matter-anti-matter asymmetry of the universe (baryogenesis) • A new source of CP violation beyond the Standard Model is needed • Massive neutrinos are a scientific fact from neutrino oscillations. Thus, neutrino masses need to be added to the Standard Model • This requires new fields and implies that there are potentially new sources of CP violation • Thermal leptogenesis with heavy Majorana neutrinos is a straightforward extension of the Standard Model, which describes • Massive neutrinos • Smallness of neutrino mass • Baryogenesis through leptogenesis • This is often believed to be the simplest possible extension of the Standard Model to solve these problems • Experimental evidence (indirect): 0nbb, CPV in neutrino oscillations