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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

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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.

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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 ???

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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 ?

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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)

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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

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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

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8 Forbid lower dim. operators Define genuine d=D operator as leading contribution to neutrino mass with all operators d

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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

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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)

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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

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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

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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!

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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

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

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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)

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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) )

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

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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

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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.

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BACKUP

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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)

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