TeV scale see-saws from higher than d=5 effective operators

1. TeV scale see-saws from higher than d=5 effective operators CTP International Conference on Neutrino Physics in the LHC Era Luxor, Egypt November 15, 2009Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAAAAA

2. Contents • Introduction • Neutrino mass from eff. operators higher than d=5 • TeV completions for effective operators • Summary and outlook Based on F. Bonnet, D. Hernandez, T. Ota, W. Winter, arXiv:0907.3143, JHEP 10 (2009) 076. Special thanks to Belen Gavela.

3. Effective theory BSM physics described by effective operators in the low-E limit (gauge invariant): L: Scaleof new physics Neutrinomass(LNV)0nbb decay! Leptonflavorviolation (LFV) But these are no fundamental theories (non-renormalizable operators). Idea: Investigate fundamental theories (TeV completions) systematically!

4. See-saw mechanism • Neutrino mass from d=5 (Weinberg) - Operator • Fundamental theories at tree level: • Neutrino mass ~ Y2 v2/L (type I, III see-saw) • For Y = O(1), v ~ 100 GeV: L ~ GUT scale • For L ~ TeV scale: Y << 10-5 • Interactions difficult to observe at LHC • Couplings „unnaturally“ small? H H ? f ~ H, L ~ l Type II Type III Seesaw Type I L L

5. Typical ways out • Goals: • New physics scale „naturally“ at TeV scale(i.e., TeV scale not put in by hand) • Yukawa couplings of order one • Requires additional suppression mechanisms. The typical ones: • Radiative generation of neutrino mass • Small lepton number violating contribution (e.g. inverse see-saw, RPV SUSY models, …) • Neutrino mass from higher than d=5 effective operator (d=5 forbidden)

6. Neutrino mass from higher dimensional operators • Approach: Use higher dimensional operators, e.g. • Leads to • Estimate: for L ~ 1 – 10 TeV and mn linear in Yukawas (worst case): • d = 9 sufficient if no other suppression mechanism • d = 7 sufficient if Yukawas ~ me/v ~ 10-6 allowed

7. The loop issue H H • Loop d=5 contribution dominates for or L >~ 3 TeV • Conclusion: If assumed that d=7 leading, one effectively has to put L << 3 TeV by hand(see e.g. Babu, Nandi, Tavartkiladze, arXiv:0905.2710) • But this is only a subclass of LHC-testable models!? H H H H Close loop L L L L H+ d=5 operator d=7 operator

8. 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/0612017; Godoladze, Okada, Shafi, arXiv:0809.0703)(e.g. Babu, Nandi, hep-ph/9907213; Giudice, Lebedec, arXiv:0804.1753)

9. Higher dim. operators in THDM d=7 operatorwhich is allowed inSUSY and for whichd=5 can beindependentlyforbidden • Simplest possibility (d=7): Z5 with e.g.(SUSY: Z3) Same for d=9

10. TeV completions for d=7 op. • Example: two extra fermions, one scalarZ5 chargesLeads to neutrino mass via effective d=7 operator: • Issue: also new U(1) Need enhanced scalar sector (explicit breaking) or a soft breaking term (a la MSSM)

11. … and the inverse see-saw • Similar to inverse see-saw • Mass matrix for neutral fermion fields:with LNV term suppressed by new physics scale! • That also works for the e-term

12. Systematic study of d=7 • Systematically decompose d=7 operator in all possible ways • Notation for mediators: Lorentz SU(2) Y=Q-I3

13. Generalizations of see-saws • Generalizations of orginial 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!

14. Even higher suppression? Loop suppression, controlled by 1/(16 p2) Tree 1-loop 2-loop Switched off bydiscrete symmetry Switched off by discrete symmetry d=5 To beavoided d=7 Suppression by d, controlled by 1/L2 d=8 for L < 3 TeV d=11 Example 1: d=9 at tree level Example 2: d=7 at two loop

15. Example 1: d=9 tree level • Inverse see-saw-like,with even higher suppression of LNV term • Requires Z7 symmetry

16. Example 2: two-loop d=7 • Neutrino masses emerge from breaking of the new symmetry • Charges (Z5) Without scalar potential: Respects U(1)Y, U(1)L, and a new U(1); no n mass Violates all cont. symmetries except from U(1)Y, while respecting Z5If S is integrated out: Term ~ f5 (respects Z5, violates U(1) )

17. Neutrino mass in example 2 • Neutral fermion fields (integrate out scalars):Contributions to neutrino mass: Leading contribution for L > 3 TeV

18. Features of example 2 • Incorporates all three suppression mechanisms: • Radiative generation of neutrino mass • Small lepton number violating contribution (optional: LNV couplings can be chosen small) • Neutrino mass from higher than d=5 effective operator (d=5 forbidden) • Neutrino mass related to breaking of new U(1) to discrete symmetry • TeV scale naturally coming out, with large Yukawa couplings possible

19. Summary and outlook • „Natural“ TeV see-saw requires additional suppression mechanisms beyond three standard see-saws • Framework of additional Higgs doublet (THDM) used • L ~ 3 TeV is the splitting point between tree level and loop contributions dominating neutrino mass • Generic models should be „stable“ with whole LHC-testable range  requires symmetries to control leading contribution to neutrino mass • TeV completions of higher than d=5 effective operators often lead to inverse see-saw-like structures with the LNV term suppressed by L-(d-6) • LHC phenomenology of such models still needs to be worked out (partly work in progress) • Some of the generic results can be translated to other extensions of the SM (such as different Higgs sector) Reference: F. Bonnet, D. Hernandez, T. Ota, W. Winter, arXiv:0907.3143, JHEP 10 (2009) 076.

20. BACKUP

21. On the U(1) problem • Lagrangian invariant under new U(1) symmetry (aka Peccei-Quinn symmetry wrt Higgs potential) • Unwanted Goldstone bosons? • Typical ways out (example d=7 tree level): • Enhanced scalar sector with eff. term • Soft-breaking term (a la MSSM)Contribution ~ (<< tree level d=7)