1. Non-unitary deviation from the tri-bimaximal mixing and neutrino oscillations
Shu Luo (IHEP) @
The Summer Topical Seminar on Frontier of Particle Physics 2008: Neutrino Physics and Astrophysics, Beijing ( )

2. Motivation Experimental steps: CKM 12 23 13  unitarity
MNS     (, ) non-unitarity
Current data leave little room for the unitarity violation of the CKM matrix.
The smallest mixing angle 13 is a crucial turning-point in doing precision measurements, detecting CP violation and probing New Physics.
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.
Unitarity violation is a typical low-energy signal of new physics.
Content:
Non-unitarity & neutrino oscillation (matter effects)
Address on the effects of additional CP-violating phases
Luo, arXiv: [hep-ph] (PRD 2008)

3. Is the MNS matrix unitary ?
If three light neutrinos mix with other degrees of freedom
light sterile neutrinos —— no good th/ex motivation today
heavy Majorana neutrinos —— popular seesaw mechanisms
whole tower of KK states —— models with extra dimensions
The Scheme of Minimal Unitarity Violation (MUV)
S. Antusch et al. hep-ph/ (JHEP 2006)
Only 3 light neutrino species are considered.
Sources of non-unitary are allowed only in those terms of the SM Lagrangian which involve neutrinos.
Combine the experimental data on neutrino oscillations, W and Z decays, rare LFV modes and lepton universality tests, …….

4. Parametrize a non-unitary mixing matrix
Degree of freedom
3 £ 3 unitary matrix: 9 (including unphysical phases)
3 £ 3 general matrix (non-unitary): 2 £ 32 = 18
additional 9 parameters: 6 modules, 3 phases
another way of parametrization: V=AV0 (A: triangle matrix)
(A and H can be related by a unitary transformation)
Z. Z. Xing, arXiv: [hep-ph] (PLB 2008)

5. Non-unitary deviation from TB mixing
An intriguing point of view V = H V0
Bounds on those newly introduced parameters
“the resulting 13 measured in e ! e oscillation”
additional CP-violating phases from

6. Neutrino oscillation
For strict derivation: S. Antusch et al. hep-ph/ (JHEP 2006)

7. Neutrino oscillation Oscillation probability in vacuum
Jarlskog invariants of CP violation
unitary: universal Jarlskog invariant = 2 area of the unitarity triangle.
non-unitary: 9 different Jarlskog invariants, unitarity triangles deformed.
“zero-distance”
effect (L=0)

8. Neutrino oscillation in matter
In the mass eigenbasis in vacuum
Oscillation probability in matter of constant density
X can be regarded as the effective neutrino mixing matrix in matter (non-unitary)
U can be solved by using the perturbation theory
( and are regarded as the small parameters of the same order)
For complete process and results: Luo, arXiv: [hep-ph] (PRD 2008)

9. Neutrino oscillation in matter
The effective mass squared differences in matter
—— solid lines: tri-bimaximal mixing + non-unitary perturbation
dashed lines: unitary mixing with nonzero 13
Corrections from non-unitary perturbations can reach 10-2 Ev VNC.
In the non-unitary case (zero 13), can also reach zero. (NH)

10. Neutrino oscillation in matter
Oscillation probabilities to the first order of ……
Neutral current interaction
New CP-violating term
Fake CP-violating effects
Conventional CP-violating term

11. Non-unitarity vs. nonzero 13
I: tri-bimaximal mixing + non-unitary perturbation
II: tri-bimaximal mixing + nonzero 13
III: exact tri-bimaximal mixing
III II I

12. Phase of 23 vs.  ẑ Mass squared differences Oscillation
probabilities
I: tri-bimaximal mixing
+ non-unitary perturbation
II: tri-bimaximal mixing
+ nonzero 13 II I I II

13. Concluding remarks To see the non-unitarity
If the MNS mixing matrix is non-unitary
“zero-distance” effects
oscillation probabilities rely on VNC
additional CP-violating phases
To see the non-unitarity
relatively long baseline, high neutrino energy
u !  is most sensitive to the non-unitary effects
more precise solar, atmospheric and reactor data.

14. Thanks !