1. TeV Seesaws and Non-unitary -oscillations
Zhi-zhong Xing (邢志忠)
IHEP, Beijing
 H. Murayama (SUSY08)
Hi, I am a theorist …..

2. Elusive Neutrinos Supernovae Ourselves Galaxies Accelerators Sun
They are everywhere;
They are abundant;
They are almost massless;
They travel almost at the speed of light;
They are very very shy; ……
Ourselves
Galaxies
They are fundamentally important;
They might allow you to touch NP!
(NP = New Physics or Nobel Prize)
Accelerators
Sun
Reactors
Big Bang
Earth

3. SPIRES: find title NEUTRINOS and date XX
The Road Behind
SPIRES: find title NEUTRINOS and date XX
> Papers
Reines Cowan
Davis 68
Golden time (1)
Koshiba 87
Golden time (2) ??
EXAMPLES:
discovery of ’s
solar  anomaly
1987 supernova ’s
1998 atmospheric ’s

4. LHC
J-PARC
IceCube 

5. Why Seesaws? Origin of -mass
A natural theoretical way to understand why 3 -masses are very small.
Type-I: SM + 3 right-handed Majorana ’s (Minkowski 77; Yanagida 79; Glashow 79; Gell-Mann, Ramond, Slanski 79; Mohapatra, Senjanovic 79)
Type-II: SM + 1 Higgs triplet (Magg, Wetterich 80; Schechter, Valle 80; Lazarides et al 80; Mohapatra, Senjanovic 80; Gelmini, Roncadelli 80)
Type-III: SM + 3 triplet fermions (Foot, Lew, He, Joshi 89)
Other variations or combinations (e.g., type-I + type-II in SO(10) GUT)

6. Why TeV Seesaws? Planck GUT TeV Fermi
Is the seesaw mechanism of -mass generation testable or not?
Planck
Fermi
GUT
to unify strong, weak & electromagnetic forces?
TeV
to solve the unnatural gauge hierarchy problem?
Is the “seesaw scale” close to a fundamental physics scale?
Conventional (Type-one) Seesaw Picture: close to the GUT scale
TeV Seesaw Idea: driven by testability at LHC
Naturalness?
Testability?

7. What is the first step to test seesaws at the LHC?
ANSWER:
to discover the Higgs boson(s)
and
to verify the Yukawa interactions

8. TeV Neutrino Physics ???
LHC TeV 
Why
Not
Try

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

10. Natural or Unnatural? Part A
Natural case: no large cancellation in the leading seesaw term.
0.01 eV
100 GeV
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

11. Structural Cancellation
Part A
Structural Cancellation
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).
Tiny -masses can be generated from tiny corrections to this complete “structural cancellation”, by deforming M_D or M_R .
Simple example:

12. L = 2 like-sign dilepton events
Part A
Fast Lessons
Lesson 1: two necessary conditions to test a seesaw model with heavy right-handed Majorana neutrinos at the LHC:
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

13. collider analogue to 0 decay N can be produced on resonance
Part A
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

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

15. Part A
Type-II Seesaw
Type-II (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

16. Collider Signature Part A Signatures:
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; ……)

17. Type-(I+II) Seesaw Part A not small collider signature tiny mass
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
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.

18. Possible LHC Signature
Part A
Possible LHC Signature

19. Some Recent Works Part A Type-II Type-I Type-III Possible combinations
★ Han, Zhang, PRL (06)
★ Buckley, Murayama, PLB (06)
★ del Aguila et al, JPCS (06)
★ Bar-Shalon et al, PLB (06)
★ de Gouvea et al, PRD (07)
★ Atwood et al, PRD (07)
★ del Aguila et al, JHEP (07)
★ de Almeidaet al, PRD (07)
★ Chen, Mahanthappa, PRD (07)
★ Bajc et al, PRD (07)
★ Graesser, PRD (07)
★ Kersten, Smirnov, PRD (07)
★ Xing, PLB (08)
★ de Gouvea, Jenkins, PRD (08)
★ Chen et al, arXiv:
★ Bar-Shalon et al, arXiv:
★ Hirsch et al, arXiv:
★ del Aguila et al, arXiv:
★ Cogollo et al, arXiv:
★ Murayama, arXiv:
★ ……
★ Hektor et al, NPB (07)
★ Han et al, PRD (07)
★ Dorsner, Mocioiu, NPB (08)
★ Goravoa, Schwetz, JHEP (08)
★ Chao et al, PRD (08)
★ Akeroyd et al, PRD (08)
★ McDonald et al, JCAP (08)
★ Xing, PRD (08)
★ Ren, Xing, PLB (08)
★ Gogoladze et al, arXiv:
★ Chao et al, arXiv:
★ Fileviez Perez et al, arXiv:
★ Hirsch et al, arXiv:
★ ……
Type-I
Type-II
Type-III
How to experimentally distinguish one type from another?
Possible combinations
★ Barr, Dorsner, PLB (06)
★ Bajc, Senjanovic, JHEP (07)
★ Fileviez Perez, PLB (07)
★ Dorsner, Fileviez Perez, JHEP (07)
★ Abada et al, JHEP (07)
★ Abada et al, arXiv:
★ Franceschini et al, arXiv:
★ Gogoladze et al, arXiv:
★ Mohapatra et al, arXiv:
★ ……

20. Part A
Indistinguishable?
Type-(I+II)

21. Part A
Some 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.
 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?
 An uneasy feeling ---- the generation of tiny neutrino masses seems always to be decoupled from appreciable collider signals of TeV Majorana neutrinos. Unnatural? Unnatural? Unnatural?
 Non-unitary CP Violation is a straightforward consequence of TeV seesaws ---- it might manifest itself in both the oscillations of light neutrinos and the decays of heavy neutrinos.

22. Charged Current Interactions
Part B
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:

23. Part B
A Language

24. Correlation between V and R
Part B
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

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

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

27. Effects of a few percent! accuracy of a few percent!
Part B
Experimental 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).

28. Approximations of A and R
Part B
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.

29. UV-induced CP Violation
Part B
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%)

30. Neutrino Oscillations
Part B
Neutrino Oscillations
Production and detection of a neutrino beam via CC weak interactions: + _
Like the case of the non-standard interactions in initial & final states.

31. Part B
New Effects
Oscillation probability in vacuum (e.g., Antusch et al 06, Z.Z.X. 08):
Unitary: universal Jarlskog invariant = 2 area of each unitarity triangle.
Non-unitary: 9 different Jarlskog invariants, and triangles  polygons.
Jarlskog invariants of CP violation:
“Zero-distance” (near-detector) effect at L = 0 :

32. Part B
An Example
A non-unitary deviation from the tri-bimaximal mixing pattern:
Z.Z.X. 08, Luo 08 (matter effects), Z.Z.X., Zhou 08 (neutrino telescopes)
UV-induced CPV at 1% level?
Short- or medium-baseline experiments in the neglect of matter effects (Fernandez-Martinez et al 07). In particular (Z.Z.X. 08),
≈ 1

33. Numerical Illustration
Part B
Numerical Illustration
Example: an experiment with E  a few GeV & L ~ a few 100 km.
Sensitivity ≤ 1% ?
Neutrino
Factory?

34. MSW Matter Effects Part B
Illustration: one heavy Majorana neutrino and constant matter density.
(Goswami, Ota 08; Luo 08)
Genuine CPV
Matter effect
The same matter-effect term appears in _  _ oscillations (Luo 08).

35. Weak Interactions of N Part B In the mass basis
The standard weak interactions of 3 ’s with W, Z and H in the flavor basis:
where
In the mass basis

36. Part B
CP Violation
CP violation: interference between tree and one-loop amplitudes of N.
Resonant enhancement with 4 heavy Majorana neutrinos. (Bray, Lee, Pilaftsis 07)
Xing, Zhou (in progress) ~

37. Why 3 known ’s have tiny masses Why we can exist in a matter world
Part B
More on CP Violation
The KM mechanism of CP violation is not the whole story to interpret the matter-antimatter asymmetry of our universe.
Two reasons for this in the SM:
■ CP violation from the KM mechanism is highly suppressed;
■ The electroweak phase transition is not strongly first order.
New sources of CP violation are necessarily required.
heavy
Majorana
’s + CPV
Why 3 known ’s have tiny masses
Why we can exist in a matter world
seesaw
leptogenesis

38. Leptogenesis Part B Canonical idea (Fukugita, Yanagida 86):
● Lepton number violation at the tree level of Majorana neutrino decays;
● Direct CP violation at the one-loop level of Majorana neutrino decays;
● At least 2 heavy Majorana neutrinos are required.
CP violation
L-number asymmetry
B-number asymmetry
Developments and variations (Davidson, Nardi, Nir, Phys. Rept. 08):
● Recent developments: spectator processes; finite temperature effects; flavor effects; N_2 leptogenesis; resonant (TeV) leptogenesis; ……
● Some variations: soft (SUSY) leptogenesis; type-II leptogenesis; Dirac leptogenesis; type-III leptogenesis; electromagnetic leptogenesis; …….

39. A Grand Picture? Part B L  B so we
something occurred
over there
one billion years ago
today so we
are
here
Part B
A Grand Picture?
Cosmological matter-antimatter asymmetry
Seesaw +
Leptogenesis
CP violation in neutrino oscillations
CP violation
at colliders?
Origin of
-mass

40. Concluding Remarks The Road Ahead Concluding Remarks
Theory of ’s
In his autobiographic book The Road Ahead, Bill Gates admits that “people often overestimate what will happen in the next two years and underestimate what will happen in ten ”.
Concluding Remarks
Concluding Remarks
★ We have known a lot about the properties of 3 known ’s, but we have not seen a convincing (quantitative and predictive) theory of -mass.
★ We need new theoretical guiding principles, so as to solve the uniqueness problem of model building.
energy
frontier
intensity
cosmic 
★ We hope that the LHC will tell us much more behind 3 known ’s (new particles; symmetries; …….)