1. TeV scale see-saws from higher than d=5 effective operators Neutrino masses and Lepton flavor violation at the LHC Würzburg, Germany November 25, 2009 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2. 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. 3 Lepton flavor violation (LFV) BSM physics described by effective operators in the low-E limit (gauge invariant): Effective theory  : Scale of new physics Neutrino mass (LNV) 0  decay! But these are no fundamental theories (non- renormalizable operators). Idea: Investigate fundamental theories (TeV completions) systematically! LNV scale ~ LFV scale ???

4. 4 See-saw mechanism  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 << 10 -5  Interactions difficult to observe at LHC  Couplings „unnaturally“ small?  ~ H, L ~ l Type I Type II Type IIISeesaw  LL  ?

5. 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. 6 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 ~ 10 -6 allowed

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

8. 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. 9 Higher dim. operators in THDM  Simplest possibility (d=7): Z 5 with e.g. (SUSY: Z 3 ) d=7 operator which is allowed in SUSY and for which d=5 can be independently forbidden Same for d=9

10. 10 TeV completions for d=7 op.  Example: two extra fermions, one scalar Z 5 charges Leads 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. 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  -term

12. 12 Systematic study of d=7  Systematically decompose d=7 operator in all possible ways  Notation for mediators: SU(2) Lorentz Y=Q-I 3

13. 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. 14 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  < TeV Example 1: d=9 at tree level Example 2: d=7 at two loop

15. 15 Example 1: d=9 tree level  Inverse see-saw-like, with even higher suppression of LNV term  Requires Z 7 symmetry

16. 16 … and with higher representations  Add fermion left- + right-handed 5-plet  plus scalar 4-plets  1,  2  Leads to dim. 9 operator and neutrino mass (Picek, Radovcic, arXiv:0911.1374)

17. 17 Example 2: two-loop d=7  Neutrino masses emerge from breaking of the new symmetry  Charges (Z 5 ) Without scalar potential: Respects U(1) Y, U(1) L, and a new U(1); no mass Violates all cont. symmetries except from U(1) Y, while respecting Z 5 If S is integrated out: Term ~  5 (respects Z 5, violates U(1) )

18. 18 Neutrino mass in example 2  Neutral fermion fields (integrate out scalars): Contributions to neutrino mass: Leading contribution for  > TeV

19. 19 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

20. 20 Summary and outlook  „Natural“ TeV see-saw requires additional suppression mechanisms beyond three standard see-saws  Framework of additional Higgs doublet (THDM) used   ~ 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   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.

21. BACKUP

22. 22 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)