Tri-bimaximal mixing and the neutrino oscillation data
Section snippets
Motivation
The first data from the Sudbury solar neutrino experiment (SNO) [1] have dramatically confirmed the long-standing HOMESTAKE [2] solar neutrino result with regard to the high-energy charged-current νe-rate (SNO/BP2001 =0.347±0.029, HOMESTAKE/BP2001=0.337±0.030). At the same time, the comparison with the existing rather precise SUPER-K (SK) result for solar-neutrino electron elastic scattering (SK/BP2001 =0.459±0.007 [3]) (which includes a neutral-current contribution) has provided a significant
The trend of the data
The atmospheric neutrino results are known to point strongly to twofold maximal νμ–ντ mixing (or at least to effective twofold maximal νμ–ντ mixing at the atmospheric scale). In particular the SUPER-K zenith angle distribution for multi-GeV ‘μ-like’ events (Fig. 2(a)) clearly indicates a suppression of upward νμ with respect to downward νμ by a factor of ∼1/2 (from Fig. 2 the up-to-down ratio for multi-GeV muons is (U/D)μ≃0.53±0.05 for zenith angles |cosθ|>0.20). By contrast, the corresponding
‘Tri-bimaximal’ mixing
In this section we simply take the above ‘default’ values Ue3=0, |Uμ3|2=1/2 and |Ue2|2=1/3 as given, and use them to evaluate the resulting lepton mixing matrix.
The lepton mixing matrix is defined with the rows labelled by the charged-lepton mass-eigenstates (e, μ, τ) and the columns labelled by the neutrino mass-eigenstates (ν1, ν2, ν3). Focussing on the last column (the ν3 column), we note that with Ue3=0 and |Uμ3|2=1/2, we have |Uτ3|2=1/2 from unitarity, so that the last column is just as in
Simple mass matrices
Our mass-matrices will be taken to be hermitian (i.e., we will throughout be implicitly referring to hermitian-squares of mass-matrices linking left- handed fields, ). Fermion mass-matrices are most naturally considered in a ‘weak’ basis (i.e., a basis which leaves the charged-current weak-interaction diagonal and universal).
Maximal mixing (whether trimaximal or bimaximal) undeniably suggests permutation symmetries [28]. We postulate that, in a particular weak basis, the mass-matrices
Perspective
Tri-bimaximal mixing is a specific mixing matrix (Eq. (1)/Eq. (6)) which encapsulates the trends of a broad range of experimental data (the LSND oscillation signal [32] was not considered on the grounds that it still awaits confirmation). Tri-bimaximal mixing is closely related to a number of previously suggested lepton mixing schemes, notably trimaximal mixing [9], bimaximal mixing [23], the Fritzsch–Xing democratic ansatz [21] and the Altarelli–Feruglio scheme [25] (of which tri-bimaximal
Acknowledgements
It is a pleasure to thank A. Astbury for a helpful suggestion. This work was supported by the UK Particle Physics and Astronomy Research Council (PPARC).
References (35)
- et al.
Phys. Rev. D
(2001)- et al.
Phys. Lett. B
(1999) Nucl. Phys. B (Proc. Suppl.)
(2000)- et al.
Phys. Rev. D
(2001)- A. Suzuki, in: 8th Int. Workshop Neutrino Telescopes,...
Phys. Rev. Lett.
(2001)Astropart. Phys.
(1998)
Phys. Rev. Lett.
Phys. Rev. Lett.
Astrophys. J.
Phys. Rev. D
Phys. Rev. C
Phys. Lett. B
Phys. Lett. B
Phys. Lett. B
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