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 to generate the neutrino mixing matrix 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 $\theta_{13}$ which is now 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 $\sigma_1=R$ and a symmetric complex matrix $\sigma_2=FRF^{-1}$, where the $(3 \times 3)$ matrices $F$ and $R$ correspond to the fusion and exchange of anyons, respectively. We make use of the Takagi decomposition $\sigma_2=U^T D U$ of $\sigma_2$, where $U$ is the expected PMNS unitary matrix and $D$ is real and diagonal. We get agreement with the experimental results in about the $3\sigma$ range for the complex entries of the PMNS matrix with the angles $\theta_{13}\sim 10^o$, $\theta_{12}\sim30^o$, $\theta_{23}\sim 38^o$ and $\delta_{CP}\sim260^o$. Potential physical consequences of our model are discussed.