1. Zhi-zhong Xing 【 IHEP, Beijing 】 Naturalness & Testability of Seesaw Models at the LHC Workshop on Neutrino Oscillations in Venice, April 15-18, 2008 LHC TeV (1) Brief Overview of TeV Seesaws: Natural or Unnatural? (2) Correlation between the Charged Current Interactions of Light & Heavy Majorana Neutrinos (3) Possible Collider Signatures: type-II Seesaw Example (4) Non-unitary CP Violation in Neutrino Oscillations (5) Concluding Remarks: (Un)naturalness and Testability

2. Overview of TeV Seesaws Part A

3. 3 At least 2 ’s are Massive Particles! Strong evidence for neutrino oscillations: solar, atmospheric, reactor & accelerator experiments --- all have seen anomalies ( disappearance). One stone ( oscillation) can kill all the birds (anomalies): at least 2 neutrinos are massive and 3 lepton flavors are mixed. It is the only new physics established on solid experimental ground! No need of exotic new physics changing SSM new particles fine-tuning parameters Convincing? Different neutrino sources neutrino types neutrino beam energies neutrino travel distances

4. 4 Are ’s Massive Majorana Particles? A natural theoretical expectation that has little experimental evidence. Type-one Seesaw (Minkowski 77, Yanagida 79, Glashow 79, Gell-Mann, Ramond, Slanski 79, Mohapatra, Senjanovic 80) Triplet Seesaw (Magg, Wetterich 80, Schechter, Valle 80, Lazarides, Shafi, Wetterich 81, Mohapatra, Senjanovic 81, Gelmini, Roncadelli 81) Type-II Seesaw (a few right-handed Majorana neutrinos and one Higgs triplet are both added into the SM) Fer mi scal e

5. 5 Where is the Seesaw Scale? Planck Fermi Is the seesaw scale very close to a fundamental physics scale? (e.g., Feruglio & Shaposhnikov’s talks) How heavy are the heavy Majorana neutrinos or the Higgs triplet? Conventional (Type-one) Seesaw Picture: close to the GUT scale TeV Seesaw Idea: driven by testability at LHC Naturalness ? Testability ? GUT to unify strong, weak & electromagnetic forces? TeV to solve the unnatural gauge hierarchy problem?

6. 6 Example (1): Type-I Seesaw Seesaw: Strength of Unitarity Violation Hence V is not unitary Diagonalization (flavor basis  mass basis): Type-I Seesaw: add 3 right-handed Majorana neutrinos into the SM. or

7. 7 Natural or Unnatural? TeV-scale (right-handed) Majorana neutrinos: small masses of light Majorana neutrinos come from sub-leading perturbations. Unnatural case: large cancellation in the leading seesaw term. 0.01 eV 100 GeV Natural case: no large cancellation in the leading seesaw term. 0.01 eV 100 GeV

8. 8 Structural Cancellation Small -masses can be generated from slight deviation from this complete “structural cancellation”, by deforming M_D or M_R. The relevant perturbation parameters are mainly responsible for those neutrino masses and contribute little to possible collider signatures –-- decoupling between collider physics and the neutrino mass generation. Given diagonal M_R with 3 eigenvalues M_1, M_2 and M_3, the leading (i.e., type-I seesaw) term of the light neutrino mass matrix vanishes, if and only if M_D has rank 1, and if (Buchmueller, Greub 91; Ingelman, Rathsman 93; Heusch, Minkowski 94; ……; Kersten, Smirnov 07).

9. 9 Lessons Lesson 1: two necessary conditions to test a seesaw model with heavy right-handed Majorana neutrinos at the LHC: (A) Masses of heavy Majorana neutrinos must be of O (1) TeV or below; (B) Light-heavy neutrino mixing (i.e., M_D/M_R) must be large enough. Lesson 2: LHC-collider signatures of heavy Majorana ’s are essentially decoupled from masses and mixing parameters of light Majorana ’s. Lesson 3: non-unitarity of the light neutrino flavor mixing matrix might lead to observable effects in neutrino oscillations and rare processes. Lesson 4: nontrivial limits on heavy Majorana neutrinos can be derived at the LHC, if the SM backgrounds are small for a specific final state.  L = 2 like-sign dilepton events

10. 10 Collider Signature Lepton number violation: like-sign dilepton events at hadron colliders, such as Tevatron (~2 TeV) and LHC (~14 TeV). collider analogue to 0  decay N can be produced on resonance dominant channel

11. 11 Numerical Illustration Han, Zhang (hep-ph/0604064, PRL): cross sections are generally smaller for larger masses of heavy Majorana neutrinos. TevatronLHC Del Aguila et al (hep-ph/0606198): signal & background cross sections (in fb) as a function of the heavy Majorana neutrino mass (in GeV). A single heavy N (minimal Type-II)

12. 12 Example (2): Triplet Seesaw Triplet Seesaw: add 1 SU(2)_L Higgs triplet into the SM. or Potential: L and B–L violation Naturalness? (t’ Hooft 79, …, Giudice 08) (1) M_  is O(1) TeV or close to the scale of gauge symmetry breaking. (2) _  must be tiny, and _  =0 enhances the symmetry of the model. 0.01 eV

13. 13 Collider Signature From the viewpoint of direct tests, the triplet seesaw has an advantage: The SU(2)_L Higgs triplet contains a doubly-charged scalar that can be produced at colliders, depending only on its mass and independently of the Yukawa coupling. Signatures: Rough number of events for pair (N_4l) and single (N_2l) production of doubly-charged Higgs at the LHC (See, e.g., Han et al 07; Akeroyd et al 08; Perez et al 08; ……)

14. 14 Example (3): Type-II Seesaw Incomplete cancellation between two leading terms of the light neutrino mass matrix in type-II seesaw scenarios. The residue of this incomplete cancellation generates the neutrino masses: (Chao, Luo, Z.Z.X., Zhou 08) not small not small collider signature tiny mass generation Collider signatures: both heavy Majorana neutrinos and doubly-charged scalars are possible to be produced at the LHC (e.g., Azuleos et al 06; del Aguila et al 07; Han et al 07; ….). But decoupling between collider physics & the mechanism of neutrino mass generation is very possible. Discrete flavor symmetries may be used to arrange the textures of two mass terms, but fine-tuning seems unavoidable in the (Big – Big) case.

15. 15 In the Following ★ to parametrize the V –R correlation in terms of 9 rotation angles and 9 phase angles ---- a bridge between neutrino and collider physics. ★ to discuss correlative signatures of a heavy Majorana neutrino and a doubly-charged Higgs in the minimal Type-II seesaw model at the LHC. ★ to calculate new CP-violating effects induced by non-unitarity of V in short- or medium-baseline ( _  to _  ) neutrino oscillations. Z.Z.X.: Correlation between the charged-current interactions of light and heavy Majorana neutrinos, Phys. Lett. B 660 (2008) 515 Chao, Luo, Z.Z.X., Zhou: Compromise between neutrino masses and collider signatures in the type-II seesaw model, Phys. Rev. D 77 (2008) 016001 Chao, Si, Z.Z.X., Zhou: Correlative signatures of heavy Majorana neutrinos and doubly-charged Higgs bosons at the LHC, arXiv:0804.1265 [hep-ph]

16. V-R Correlation Part B

17. 17 Charged Current Interactions The standard charged current interactions in the lepton flavor basis In the presence of heavy right-handed Majorana neutrinos, the overall 6×6 neutrino mass matrix can be diagonalized by a unitary matrix: either Type-I or Type-II seesaw. Neutrino flavor states in terms of light/heavy neutrino mass states: Correlated CC-interactions:

18. 18 Correlation between V and R R : production & detection of heavy Majorana neutrinos at LHC; V : oscillations & other phenomena of light Majorana neutrinos. They are two 3 × 3 sub-matrices of the 6×6 unitary matrix, hence they must be correlated with each other. This correlation characterizes the relationship between neutrino physics and collider physics. Strategy: parametrizing the 6 × 6 unitary matrix in terms of 15 rotation angles and 15 phase angles. The common parameters shared by R and V measure their correlation --- a general and useful approach. 2-dimensional rotation matrices in 6-dimensional complex space

19. 19 Standard Parametrization Parametrization: V_0 is the standard form of the 3 × 3 unitary neutrino mixing matrix: V = A V_0 Unitarity Violation

20. 20 Exact Results of A and R They share 9 rotation angles & 9 phase angles: V—R correlation.

21. 21 Model-independent Bounds In the SM, unitarity is the only constraint imposed on the CKM matrix. But the origin of neutrino masses must be beyond the SM. In this case, whether the MNS matrix is unitary or not relies on the model or theory. Extra CP-violating phases exist in a non-unitary neutrino mixing matrix and might lead to observable effects (Fernandez-Martinez et al 07). Effects of a few percent! In the scheme of Minimal Unitarity Violation, the 3×3 neutrino mixing matrix V gets constrained as follows (Antusch et al 07): accuracy of a few percent! 9 new mixing angles can maximally be of O(0.1).

22. 22 Approximations of A and R All 9 rotation angles are expected to be small, but 9 phase angles may be large to generate new CP-violating effects. Observations: If the unitarity violation of V is close to the percent level, then elements of R can reach order of 0.1, leading to appreciable collider signatures for TeV-scale Majorana neutrinos. New CP-violating effects, induced by the non-unitarity of V, may show up in (short-baseline) neutrino oscillations. Such a parametrization turns out to be very useful in –phenomenology.

23. 23 Some Trivial Consequences The smallest matrix element of V is governed by the smallness of theta(13) : This ratio is completely irrelevant to those parameters appearing in A or R. Slight violation of the normalization condition in the first row of V : ≤ 1% Neutrinoless double-beta decay: Tritium beta decay:

24. Part C Collider Signatures

25. 25 Type-II Seesaw Type-II seesaw: 1/2/3 heavy Majorana neutrinos and 1 Higgs triplet in the model, and their masses are at the TeV scale. Key conjecture: not small not small collider signature tiny mass generation The production of H^++ & H^-- at the LHC mainly through the channles: 7 physical Higgs bosons: H^++, H^--, H^+, H^-, A^0, H^0 & h^0. The heavy Majorana neutrino N_i can be on-shell produced at the LHC: Signature: lepton-number-violating like-sign dilepton events

26. 26 Correlation The conjecture means a good approximation (Chao, Si, Z.Z.X., Zhou 08): This relation establishes an interesting correlation between the doubly- charged Higgs boson and heavy Majorana neutrinos in type-II seesaws. Remark 1: Only after both signatures of H^++/ H^-- and N_i are seen, one may claim a test of the type-II seesaw mechanism. Remark 2: The matrix R is also a measure of non-unitarity of the light neutrino mixing matrix. It bridges a gap between neutrino physics at low energies and collider physics at high energies. X

27. 27 Minimal Case “Minimal” type-II seesaw: 1 heavy Majorana neutrino + 1 Higgs triplet (Gu, Zhang, Zhou 06; Chan, Fritzsch, Luo, Z.Z.X., 07). LHC signatures: the total cross section of each process is factorized as: The reduced cross sections  _N,  _H,  _W &  _pair are independent of R.

28. 28 Reduced Cross Sections

29. 29 Correlative Signatures Parametrization of R : We find that each ratio is universal for ,  and  modes in the case under discussion. Correlation between H^++ and N_1. We consider the ratios:

30. 30 Numerical Illustration

31. Non-unitary CP Violation Part D

32. 32 To Deform Unitarity Triangles Leptonic Unitarity Triangles (Fritzsch, Z.Z.X. 00): Common Jarlskog = 2  area of a UT A measure of CPV in -oscillations. Triangles  Polygons due to unitarity violation ×

33. 33 UV-induced CP Violation Example: V_0 takes the tri-bimaximal mixing pattern which has Non-unitary V takes the simple form CP violation (9 Jarlskog invariants): New CPV O(≤1%)

34. 34 Neutrino Oscillations Oscillation probability in vacuum ( e.g., Antusch et al 06, Z.Z.X. 07 ): Short- or medium-baseline experiments in the neglect of matter effects ( Fernandez-Martinez et al 07 ). In particular ( Z.Z.X. 07 ), UV-induced CPV at the percent level?

35. 35 Numerical Illustration Example: an experiment with E  a few GeV & L ~ a few 100 km. Sensitivity ≤ 1% ? Neutrino Factory? Matter Effects (Goswami, Ota 08; Luo 08)

36. Concluding Remarks Part E

37. 37 Concluding Remarks  Naturalness of the SM implies that there should exist a kind of new physics at the TeV scale. We wonder whether it is also responsible for the neutrino mass generation ---- TeV seesaws.  Type-II Seesaw looks rather natural, if its scale is extremely high ---- theoretically natural but experimentally unverifiable.  TeV-scale type-II Seesaw can be more or less natural: Y/ N?  Triplet Seesaw seems to be natural at the TeV scale and also testable at the LHC ---- signal of doubly-charged Higgs boson.  Type-I Seesaw looks natural if its scale is extremely high ---- theoretically natural but experimentally unverifiable.  TeV-scale type-I Seesaw is structurally unnatural, but it can be tested at the LHC by detecting TeV Majorana neutrinos.

38. 38 Concluding Remarks  It seems that people are struggling for a convincing reason to consider TeV seesaws ---- a balance between TH naturalness and EX testability as the guiding principle.  But we want a bridge between -physics and collider physics.  Much more unnaturalness (fine-tuning) may show up on TeV seesaws, if we intend to link them to leptogenesis/dark matter. LHC scal e Naturalness Testability