TM_1 neutrino mixing with sinθ _13=1/√(3)sinπ/12

We construct a neutrino model using the flavour group S_4× C_4 × C_3× C_2 under the type 1 seesaw mechanism. The vacuum alignments of the flavons in the model lead to TM_1 mixing with sinθ _13=1/√(3)sinπ/12 . The mixing also exhibits μ-τ reflection symmetry. By fitting the eigenvalues of the effective seesaw mass matrix with the observed neutrino mass-squared differences, we predict the individual light neutrino masses. The vacuum alignment of the S_4 triplet appearing in the Majorana mass term plays a key role in obtaining the aforementioned TM_1 scenario. Since the symmetries of the flavour group are not sufficient to define this alignment, we apply the recently proposed framework of the auxiliary group in our model. Using this framework, the S_4 triplet is obtained by coupling together several irreducible multiplets that transform under an expanded flavour group consisting of the original flavour group as well as an auxiliary group. The vacuum alignment of each of these multiplets is uniquely defined in terms of its residual symmetries under the expanded flavour group. As a result, the S_4 triplet constructed from these multiplets also becomes uniquely defined.