1. Probing Majorana Neutrinos in the LHC Era YongPyong2010 Seoul National University of Tech. Sin Kyu Kang

2. Outline  Introduction  Issues on neutrino masses  Probing Majorana neutrino via (1) 0nbb (2) rare meson decays (3) at the LHC  Concluding remarks

3.  Neutrinos are massless in the SM Prologue No right-handed ’s  Dirac mass term is not allowed. Conserves the SU(2)_L gauge symmetry, and only contains the Higgs doublet (the SM accidently possesses (B - L) symmetry);  Majorana mass term is forbidden.  Historic Era in Neutrino Physics Atmospheric  ’s are lost. (SK) (1998) converted most likely to  (2000) Solar e is converted to either  or  (SNO) (2002) Only the LMA solution left for solar neutrinos (Homestake+Gallium+ SK+SNO) (2002) Reactor anti- e disappear (2002) and reappear (KamLAND) (2004)

4. 4 What we learned Lepton Flavor is not conserved Neutrinos have tiny mass, not very hierarchical Neutrinos mix a lot Very different from quark sectors the first evidence for incompleteness of Minimal Standard Model

5. What we don’t know  absolute mass scale of neutrinos remains an open question.  m 1 and m 3, which is bigger?  normal or inverted hierarchy?  What is the value of  13 ? Is it small? how small?  Reactor & accelerator -oscillation experiments can answer, but possibly estimated from a global fit  Why  23 and  12 are large and close to special values?  Very strong hints at a certain (underlying) flavor symmetry.  Is CP violated in neutrino sector?  Neutrinos are Dirac or Majorana?

6. 6 Interest in Neutrino Mass  Window to high energy physics beyond the SM!  Why are physicists interested in neutrino mass ?  How exactly do we extend it?  Without knowing if neutrinos are Dirac or Majorana, any attempts to extend the Standard Model are not successful.

7. 7  2 possible types of neutrino masses  Dirac mass terms are invariant under a global symmetry, but Majorana mass terms are not so. Thus Dirac mass can be associated with a conserved quantum number, but Majorana mass violates L number conservation. chiral projection :

8. 8  A pure Dirac mass added into the SM is theoretically not favored: mainly because it is hard to naturally explain the smallness of m (violating ‘t Hooft’s naturalness criterion)  Challenging task is -- to look for experimental evidence to probe new physics  -- to distinguish the underlying theoretical models leading to the effective operator.  Within the context of the SM, gauge invariant operator rel evant to the neutrino Majorana mass :

9. If Neutrinos are Majorana The mass eigenstates are self-conjugate up to a phase. The relative phases between two ’s become observable U = U D X  The Majorana character is only observable for processes ΔL=2 through the mass term that connects interacting neutrinos with antineutrinos: A Z  A (Z+2) + 2e -, μ - + A Z  e + + A (Z-2), μ -  e + + 2e - ( in 2nd. order)

10.  Neutrino masses, if neutrinos are of Majorana nature, must have a different origin compared to the masses of charged leptons and quarks.  A natural theoretical way to understand why 3 -masses are very small : Seesaw mechanism Type-I : Right-handed Majorana neutrinos. Type-II : Higgs triplet. Type-III : Triplet fermions. ν :

11. Loop Models: Light neutrino masses are radiatively induced. Ma RPV: Sneutrino gets small VeVs inducing a mixing between & . Alternative mechanisms for majorana  mass

12. Fundamental physics and seesaw scale For k order of one, seesaw scale : 10 13-14 GeV. no hope of direct observation We may keep L free and look for theoretical predictions TeV scale seesaw For testability, low scale seesaw is desirable it may harms naturalness problem

13. Probing Majorana Neutrinos  Lepton number violation by 2 units plays a crucial role to probe the Majorana nature of ’s,  Provides a promising lab. method for determining the absolute neutrino mass scale that is complementary to other measurement techniques Black Box 0   The observation of 0 ,

14. Opening Black Box 0  exchange of a virtual light neutrino Helicity mismatch  mass mechanism Neutrino  Majorana particle L/R symmetric models Exchange of a massive neutrino Constraints on the model parameters: R R

15. 111 / ~ 0.06 for m SUSY ~ 1 TeV 0  decay Light M exchange ? Heavy particle exchange ?

16. the half-life time,,of the 0  decay can be factorized as : : phase space factor : Nuclear matrix element  depends on neutrino mass hierarchy  In the limit of small neutrino masses : : effective neutrino mass

17. Estimate by using the best fit values of parameters including uncertainties in Majorana phases Long Baseline

18.  Large uncertianties in NME About factor of 100 in NME  affect order 2-3 in | | Uncertianties (O.Cremonesi, 05)

19.  Best present bound : Heidel-Moscow Half-life consistent with cosmological bound

20. Probe of Majorana neutrinos via Rare meson decays  Taking mesons in the initial and final state to be pseudoscalar (M : K, D, Ds, B, Bc)  Not involve the uncertainties from nuclear matrix elements in 0  (G.Cvetic, C. Dib, SK, C.S.Kim in progress)

21.  transition rates are proportional to

22. Light neutrino case  The decay width :  Too small to be measured in future experiments  In the limit of S-type dominance, the amplitude can be expressed in a model independent way in terms of the measured decay constants of the pseudoscalar mesons in the initial and final state, f M and f M ’

23.  But, we can get bounds on | | (ex) for | | < 0.11 TeV

24. Intermediate mass scale neutrino case  the most dominant contribution to the process is from the “s-type” diagram because the neutrino propagator is kinematically entirely on-shell

25.  the neutrino propagator approximately becomes  For this mass range, the branching ratio can be substantially enhanced Intermediate mass scale neutrino case  the most dominant contribution to the process is from the “s-type” diagram because the neutrino propagator is kinematically entirely on-shell

26. 

27. When a certain number of initial M + is produced and the process is still not detected, the branching ratios allow us to deduce upper bounds on

28. For

30. Heavy neutrino case  In this case, both contributions of “s-type” and “t-type” diagrams are rather comparable.  neutrino propagators reduce to -1/(m N ) 2

31.  Present bounds on for heavy Majorana neutrino (m N > 100 GeV) are

33. It is hard to avoid the TeV-scale physics to contribute to flavor-changing effects in general whatever it is, –SUSY, extra dimensions, TeV seesaw, technicolor, Higgsless, little Higgs Probing Majorana Neutrinos at LHC In accelerator-based experiments, neutrinos in the final state are undetectable by the detectors, leading to the “missing energy”. So it is desirable to look for charged leptons in the final state.

34.  transition rates are proportional to Basic process we consider

35. Testability at the LHC  Two necessary conditions to test at the LHC: -- Masses of heavy Majorana ’s must be less than TeV -- Light-heavy neutrino mixing (i.e., M D /M R ) must be large enough.  LHC signatures of heavy Majorana ’s are essentially decoupled from masses and mixing parameters of light Majorana ’s.  Non-unitarity of the light neutrino flavor mixing matrix might lead to observable effects.

36.  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

37. Collider Signature Lepton number violation: like-sign d ilepton events at hadron colliders, su ch as Tevatron (~2 TeV) and LHC (~1 4 TeV). collider analogue to 0  decay N can be produced on resonance dominant channel

38. Some Results  Cross sections are generally smaller for larger masses of heavy Majorana neutrinos. [ Han, Zhang (hep-ph/0604064) ] TevatronLHC  Signal & background cross sections (in fb) as a function of the heavy Majorana neutrino mass (in GeV) : [ Del Aguila et al (hep-ph/0606198) ]

39. Concluding Remarks  Knowing if neutrinos are Dirac or Majorana is important.  We have discussed three possible ways to probe Majorana neutrinos.  Hoping that probing Majorana neutrinos via rare meson decays and collider signature would become more and more important.