Neutrino Mixing Matrix with SU(2)4 Anyon Braids

We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to SU(2)2 Ising anyons. Remarkably, the braids of SU(2)4 anyons allow the neutrino mixing matrix to be generated with an accuracy close to measurements. This is an improvement over the model based on tribimaximal neutrino mixing, which predicts a vanishing solar neutrino angle θ13, which has now been ruled out. The discrete group of braids for SU(2)4 anyons is isomorphic to the small group (162,14), generated by a diagonal matrix σ1=R and a symmetric complex matrix σ2=FRF−1, where the (3×3) matrices F and R correspond to the fusion and exchange of anyons, respectively. We make use of the Takagi decomposition σ2=UTDU of σ2, where U is the expected PMNS unitary matrix and D is real and diagonal. We obtain agreement with the experimental results in about the 3σ range for the complex entries of the PMNS matrix with the angles θ13∼10°, θ12∼30°, θ23∼38°, and δCP∼240°. Potential physical consequences of our model are discussed.