Neutrino mixing anarchy: Alive and kicking
Physics Letters B
Neutrino mixing anarchy is the hypothesis that the leptonic mixing matrix can be described as the result of a random draw from an unbiased distribution of unitary three-by-three matrices. In light of the very strong evidence for a nonzero sin 2 2θ 13 , we show that the anarchy hypothesis is consistent with the choice made by the Nature -the probability of a more unusual choice is 41%. We revisit anarchy's ability to make predictions, concentrating on correlations -or lack thereof -among the
... erent neutrino mixing parameters, especially sin 2 θ 13 and sin 2 θ 23 . We also comment on anarchical expectations regarding the magnitude of CP-violation in the lepton sector, and potential connections to underlying flavor models or the landscape. The flavor puzzle has befuddled generations of particle physicists. Since the first years of the quark model and the first successful description of flavor-violating weak processes, the pattern of fermion masses and mixing parameters seems to hint at the existence of some yet-to-be-uncovered organizing principle. The main idea is that new hidden symmetries -global or local, spontaneously or explicitly broken -"explain" the fact that the chargedfermion masses are very hierarchical and that the quark mixing matrix is very close to the identity matrix. The discovery of nonzero neutrino masses and lepton mixing in the end of the last century added new pieces to the flavor puzzle. In particular, the structure of U , the leptonic mixing matrix, 1 seems to be providing qualitatively different information. Unlike the quark mixing matrix, U cannot be understood as an identity matrix "perturbed" by small, hierarchical, off-diagonal matrices. Qualitatively speaking, all elements of the leptonic mixing matrix are large: |U αi | = O(1). The flavor literature is densely populated with ingenious attempts to identify the organizing principle behind U . The simplest (H. Murayama). 1 Here we assume no new physics beyond masses for the three active neutrinos and mixing among the lepton generations. The neutrino mass eigenstates, with masses m 1,2,3 are referred to as ν 1,2,3 , while the neutrino flavor eigenstates are ν e,μ,τ . U can be identified as the matrix that relates these two neutrino bases: ν α = U αi ν i , where α = e, μ, τ , i = 1, 2, 3.