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 (2008.09.19)

Motivation Experimental steps: CKM 12 23 13  unitarity MNS 12 23 13  (, ) 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:0804.4897[hep-ph] (PRD 2008)

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/0607020 (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, …….

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:0709.2220[hep-ph] (PLB 2008)

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 .

Neutrino oscillation For strict derivation: S. Antusch et al. hep-ph/0607020 (JHEP 2006)

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)

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:0804.4897[hep-ph] (PRD 2008)

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)

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

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

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

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.

Thanks !