Tribimaximal mixing

Tribimaximal mixing is a specific postulated form for the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) lepton mixing matrix U. Tribimaximal mixing is defined by a particular choice of the matrix of moduli-squared of the elements of the PMNS matrix as follows: Tribimaximal mixing is a specific postulated form for the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) lepton mixing matrix U. Tribimaximal mixing is defined by a particular choice of the matrix of moduli-squared of the elements of the PMNS matrix as follows: This mixing is presently excluded by experiment at the level of 5σ. The tribimaximal mixing form was compatible with much older neutrino oscillation experiments and may be used as a zeroth-order approximation to more general forms for the PMNS matrix e.g. which are also consistent with the data. In the PDG convention for the PMNS matrix, tribimaximal mixing may be specified in terms of lepton mixing angles as follows: The above prediction has been falsified experimentally, because θ13 was found to be nontrivial, θ13 =8.5°. A non-negligible value of θ13 has been foreseen in certain theoretical schemes that were put forward before tribimaximal mixing and that supported a large solar mixing, before it was confirmed experimentally (these theoretical schemes do not have a special name, but for the reasons explained above, they could be called pre-tribimaximal or also non-tribimaximal). This situation is not new: also in the 1990s, the solar mixing angle was supposed to be small by most theorists, until KamLAND proved the contrary to be true. The name tribimaximal reflects the commonality of the tribimaximal mixing matrix with two previously proposed specific forms for the PMNS matrix, the trimaximal and bimaximal mixing schemes, both now ruled out by data. In tribimaximal mixing, the ν 2 {displaystyle u _{2}} neutrino mass eigenstate is said to be 'trimaximally mixed' in that it consists of a uniform admixture of ν e {displaystyle u _{e}} , ν μ {displaystyle u _{mu }} and ν τ {displaystyle u _{ au }} flavour eigenstates, i.e. maximal mixing among all three flavour states. The ν 3 {displaystyle u _{3}} neutrino mass eigenstate, on the other hand, is 'bimaximally mixed' in that it comprises a uniform admixture of only two flavour components, i.e. ν μ {displaystyle u _{mu }} and ν τ {displaystyle u _{ au }} maximal mixing, with effective decoupling of the ν e {displaystyle u _{e}} from the ν 3 {displaystyle u _{3}} , just as in the original bimaximal scheme. By virtue of the zero ( | U e 3 | 2 = 0 {displaystyle |U_{e3}|^{2}=0} ) in the tribimaximal mixing matrix, exact tribimaximal mixing would predict zero for all CP-violating asymmetries in the case of Dirac neutrinos (in the case of Majorana neutrinos, Majorana phases are still permitted, and could still lead to CP-violating effects). For solar neutrinos the large angle MSW effect in tribimaximal mixing accounts for the experimental data, predicting average suppressions ⟨ P e e ⟩ ≃ 1 / 3 {displaystyle langle P_{ee} angle simeq 1/3} in the Sudbury Neutrino Observatory (SNO) and ⟨ P e e ⟩ ≃ 5 / 9 {displaystyle langle P_{ee} angle simeq 5/9} in lower energy solar neutrino experiments (and in long baseline reactor neutrino experiments). The bimaximally mixed ν 3 {displaystyle u _{3}} in tribimaximal mixing accounts for the factor of two suppression ⟨ P μ μ ⟩ ≃ 1 / 2 {displaystyle langle P_{mu mu } angle simeq 1/2} observed for atmospheric muon-neutrinos (and confirmed in long-baseline accelerator experiments). Near-zero ν e {displaystyle u _{e}} appearance in a ν μ {displaystyle u _{mu }} beam is predicted in exact tribimaximal mixing ( | U e 3 | 2 = 0 {displaystyle |U_{e3}|^{2}=0} ), and future experiments may well rule this out. Further characteristic predictions of tribimaximal mixing, e.g. for very long baseline ν μ {displaystyle u _{mu }} and ν τ {displaystyle u _{ au }} (vacuum) survival probabilities ( P μ μ = P τ τ ≃ 7 / 18 ) {displaystyle (P_{mu mu }=P_{ au au }simeq 7/18)} , will be extremely hard to test experimentally. The L/E flatness of the electron-like event ratio at Super-Kamiokande severely restricts the neutrino mixing matricesto the form: