Neutrino physics Lecture 2: Theory of neutrino mass, and physics BSM? Herbstschule für Hochenergiephysik Maria Laach Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2 Contents  Measuring neutrino mass  The seesaw paradigm  Neutrino mass models at the TeV scale: What ingredients do “natural” models need?  Is it possible that new physics shows up in the neutrino sector only?  How does the large  13 affect our understanding of (lepton) flavor?  Summary and conclusions

Measuring neutrino mass

4 Tritium end point experiments (Guido Drexlin, NOW 2008)  Direct test of neutrino mass by decay kinematics  Current bound: 1/ x m e (2 eV) TINY!  Future experiment: KATRIN ( Karlsruhe Tritium Neutrino Experiment) 1/ x m e (0.2 eV) ~8800 km

5 n n  Two times simple beta decay:  Neutrinoless double beta decay: Neutrinoless double beta decay … if the neutrino is ist own antiparticle, a Majorana neutrino! p e-e- W-W- p n e-e- W-W- p e-e- W-W- 2 x 2 x e 0 x 2 x e n p e-e- W-W- = Caveat: discovering 0  does not mean that one has actually seen Majorana neutrinos!

6 Cosmological tests  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) … might finally be used rule to out that neutrino physics in charge of 0  !

The seesaw paradigm

8 Why is the neutrino mass so small?  Why are the neutrinos more than times lighter than the electron?  Cannot be described in simple extensions of the Standard Model  Is the neutrino mass the lowest order perturbation of physics BSM?  Seesaw mechanism: Neutrino mass suppressed by heavy partner, which only exists in the early universe (GUT seesaw)?  Decay of M R origin of matter-antimatter-asymmetry?  CP violation? Test in neutrino oscillations!  Requires Majorana nature of neutrino! Test in neutrinoless double beta decay (0  ) Other SM particles Heavy partner

9 Lepton flavor violation (LFV) BSM physics described by effective operators in the low-E limit (gauge invariant): Effective field theories  : Scale of new physics Neutrino mass (LNV) But these are no fundamental theories (non- renormalizable operators). Idea: Investigate fundamental theories (TeV completions) systematically!

10  Neutrino mass from d=5 (Weinberg) - Operator  Fundamental theories at tree level:  Neutrino mass ~ Y 2 v 2 /  (type I, III see-saw)  For Y = O(1), v ~ 100 GeV:  ~ GUT scale  For  ~ TeV scale: Y <<  Interactions difficult to observe at LHC  Couplings “unnaturally“ small? Seesaw mechanism Type I Type II Type IIISeesaw  LL  ?

Neutrino masses at the TeV scale? … and physics at the LHC …

12 Neutrino masses at the TeV scale  Goals:  New physics scale “naturally“ at TeV scale (i.e., TeV scale not put in by hand)  Testable at the LHC?!  Yukawa couplings of order one  Requires additional suppression mechanisms. The typical ones: 1)Radiative generation of neutrino mass (n loops) 2)Neutrino mass from higher than d=5 effective operator 3)Small lepton number violating contribution  (e.g. inverse see-saw, RPV SUSY models, …)

13 Example (suppression 3): Type-II, inverse seesaw (Florian Florence 2012)

14 Additional suppression (mechanisms 1+2): Loops versus dimension Tree1-loop2-loop d=5 d=7 d=8 d=11 Loop suppression, controlled by 1/(16  2 ) Suppression by d, controlled by 1/  2 Type I, II, II seesaw Depends on scale:  > 4  v ~ 3 TeV? Discrete symmetry to forbid d=5? How can I make sure that no lower order operators are generated? Depends on mediators/int. Zee, 1980; Ma, 1998; …

15 Example: Neutrino mass from higher dimensional operators  Approach: Use higher dimensional operators, e.g.  Leads to  Estimate: for  ~ 1 – 10 TeV and m linear in Yukawas (worst case):  d = 9 sufficient if no other suppression mechanism  d = 7 sufficient if Yukawas ~ m e /v ~ allowed

16 The loop issue  Loop d=5 contribution dominates for or  > 3 TeV  Conclusion: If assumed that d=7 leading, one effectively has to put  << 3 TeV by hand (see e.g. Babu, Nandi, Tavartkiladze, 2009)  Can one avoid this?  LL     LL   Close loop d=7 operator d=5 operator

17 Forbid lower dim. operators  Define genuine d=D operator as leading contribution to neutrino mass with all operators d<D forbidden  Use new U(1) or discrete symmetry (“matter parity“)  Problem: H + H can never be charged under the new symmetry!  Need new fields!  The simplest possibilities are probably (e.g. Chen, de Gouvea, Dobrescu, hep-ph/ ; Godoladze, Okada, Shafi, arXiv: ) (e.g. Babu, Nandi, hep-ph/ ; Giudice, Lebedec, arXiv: )

18 Higher dim. operators in THDM  Simplest possibility (d=7): Z 5 with e.g. (SUSY: Z 3 ) SUSY: only this one (but: there can be operators with the scalar singlet in the NMSSM) Same for d=9 Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

19 Systematic study of d=7  Systematically decompose d=7 operator in all possible ways  Notation for mediators: SU(2) Lorentz Y=Q-I 3 Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

20 Generalizations of see-saws  Generalizations of originial see-saws: Duplication of the original see-saws plus scalars  Type I (fermionic singlet)  Type II (scalar triplet)  Type III (fermionic triplet) Characteristics: Similar phenomenology! Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

21 A SUSY example  Neutral fermion mass matrix after EWSB in basis Krauss, Ota, Porod, Winter, Phys. Rev. D84 (2011) Fermionic doublets #17 from list Compare to “inverse see-saw“ (suppression mechanism 3) if heavy doublets integrated out Flavor struct. byMass states: n i

22 Test at the LHC? (example) Krauss, Ota, Porod, Winter, Phys. Rev. D84 (2011)  Test mediators  Test LFV  Test LNV compare

23 Even higher suppression? Tree1-loop2-loop d=5 d=7 d=8 d=11 Loop suppression, controlled by 1/(16  2 ) Suppression by d, controlled by 1/  2 Switched off by discrete symmetry To beavoided for  < 3 TeV Example 1: d=9 at tree level Example 2: d=7 at two loop  Suppression mechanisms 1), 2), and 3) Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076 Physics at TeV scale with O(1) couplings Strategies for higher loops: Farzan, Pascoli, Schmidt, arXiv:

New physics in neutrino sector only? Most discussed options in literature:  Light sterile neutrinos (aka: light SM singlets)  Heavy SM singlets (  non-unitary mixings)  Non-standard interactions (aka: flavor changing neutral currents)

25 Evidence for sterile neutrinos?  LSND/MiniBooNE  Reactor+gallium anomalies  Global fits Neutrino 2012) (B. Fleming, TAUP 2011) (Kopp, Maltoni, Schwetz, )

26 Example: 3+1 framework (with addl.  m 2 ~ 1 eV 2 )  Well known tension between appearance and disapp. data (appearance  disappearance in both channels)  Need one or more new experiments which can test  e disappearance (Gallium, reactor anomalies)   disappearance (overconstrains 3+N frameworks)  e -  oscillations (LSND, MiniBooNE)  Neutrinos and antineutrinos separately (CP violation? Gallium vs reactor?)  Example: nuSTORM - Neutrinos from STORed Muons (LOI: arXiv: ) Summary of options: Appendix of white paper arXiv:

27 Non-unitarity of mixing matrix?  Integrating out heavy fermion fields (such as in a type-I TeV see-saw), one obtains neutrino mass and the d=6 operator (here: fermion singlets)  Re-diagonalizing and re-normalizing the kinetic terms of the neutrinos, one has  This can be described by an effective (non-unitary) mixing matrix  with N=(1+  ) U  Relatively stroung bounds already, perhaps not so good candidate for future measurements (see e. g. Antusch, Baumann, Fernandez-Martinez, arXiv: ) also: “MUV“

28 Non-standard interactions  Typically described by effective four fermion interactions (here with leptons)  May lead to matter NSI (for  =  =e)  May also lead to source/detector NSI How plausible is a model leading to such NSI (and showing up in neutrino sector only)?

29 Lepton flavor violation (d=6)  Charged lepton flavor violation  Strong bounds ee e  NSI ee e  CLFV e  4 -NSI Ex.: e e  Non-standard neutrino interact.  Effects in neutrino oscillations in matter  Non-standard int. with 4  Effects in environments with high neutrino densities (supernovae) BUT: These phenomena are not independent (SU(2) gauge invariance!) Is it possible that new physics is present in the neutrino sector only?

30 Idea: d=8 operator?  Decouple CLFV and NSI by SU(2) symmetry breaking with operator  Works at effective operator level, but are there theories allowing that? [at tree level] Davidson, Pena-Garay, Rius, Santamaria, 2003 Project out neutrino field

31 Systematic analysis for d=8  Decompose all d=8 leptonic operators systematically  The bounds on individual operators from non- unitarity, EWPT, … are very strong! (Antusch, Baumann, Fernandez-Martinez, arXiv: )  Need at least two mediator fields plus a number of cancellation conditions (Gavela, Hernandez, Ota, Winter, Phys. Rev. D79 (2009) ) Basis (Berezhiani, Rossi, 2001) Combine different basis elements C 1 LEH, C 3 LEH Cancel d=8 CLFV But these mediators cause d=6 effects  Additional cancellation condition (Buchmüller/Wyler – basis) Avoid CLFV at d=8: C 1 LEH =C 3 LEH Feynman diagrams

Implications of large  13 : flavor

33 Short seesaw-I mixing primer Charged lepton mass terms Eff. neutrino mass terms cf., charged current Rotates left- handed fields Block diag.

34 The TBM “prejudice“  Tri-bimaximal mixings probably most discussed approach for neutrinos (U l often diagonal)  Can be obtained in flavor symmetry models (e.g., A 4, S 4 )  Consequence:  13 =0  Obviously not!  Ways out for large  13 ?

35 Impact on theory of flavor? Structure: A 4, S 4, TBM, … Anarchy: Random draw?  13  very smallvery large Different flavor symmetry? Corrections? CL sector? RGR running? Some structure + randomness: Froggatt-Nielsen? vs. Quark-lepton compementarity:  13 ~  C ? e.g.  12 = 35  +  13 cos  (Antusch, King)

36 Anarchy?  Idea: perhaps the mixing parameters are a “random draw“?  Challenge: define parameterization- independent measure  Result: large  13 “natural“, no magic needed (Hall, Murayama, Weiner, 2000; de Gouvea, Murayama, 2003, 2012)

37 “Structure+randomness“: Froggatt Nielsen mechanism?   L/R are SM fermions  After integrating out the heavy fermions:  Integer power n is controlled by the (generation/flavor- dependent) quantum numbers of the fermions under the flavor symmetry  K: (complex) generation dependent (random) order one coefficients  Well-suited to describe hierarchies (F. Plentinger) Ml ~Ml ~ Example:

38 Hybrid alternatives? Charged leptons: Strong hierarchy, masses through SM Yukawas  Quarks: Strong hierarchies Small mixings Neutrinos: Mild (no?) hierarchy, large mixings, Majorana masses?  Origin: physics BSM? LNV operator? Flavor symmetry, structure? Tri-bimaximal mixing “paradigm“? Ansatz suitable for hierarchies, such as Froggatt-Nielsen? Meloni, Plentinger, Winter, PLB 699 (2011) 244   13 =0

39 Consequences  Can control the size of  13 by suitable U(1) charges/mass texture for the charged lepton sector:  Challenge:  Deviations from TBM  12 typically accompanied by large  13  Re-think zeroth order paradigm (TBM)??? Meloni, Plentinger, Winter, PLB 699 (2011) 244

40 Summary and outlook  Are neutrinos masses evidence for physics BSM?  Neutrinoless double beta decay  Tests at the LHC  0  signal + CPV in lepton sector + no evidence for mass at the LHC  GUT seesaw, leptogenesis?  Natural TeV neutrino mass model requires additional suppression mechanism; then, however, plausible to discover it at the LHC  Most likely case for new physics in neutrino sector: fourth generation (light sterile neutrino)?  Theory of flavor has to be re-thought after  13 discovery