Nearly tri-bimaximal mixing in the S_3 flavour symmetry
We present an analysis of the theoretical neutrino mixing matrix, V_{PMNS}^{th}, previously derived in the framework of the minimal S_3-invariant extension of the Standard Model. All entries in the neutrino mixing matrix, V_{PMNS}^{th}, the mixing angles and the Majorana phases are given as exact, explicit analytical functions of the mass ratios of the charged leptons and neutrinos, and one Dirac phase, in excellent agreement with the the latest experimental data. Here, it will be shown that all entries in V_{PMNS}^{th} are numerically very close to the tri-bimaximal form of the neutrino mixing matrix, so that V_{PMNS}^{th} may be written as V^{tri}+\Delta V_{PMNS}^{tri}. The small correction \Delta V_{PMNS}^{tri} is expressed as a sum of two terms: first, a small correction term proportional to m_{e}/m_{\mu} depending only on the charged lepton mass ratios and, second, a Cabbibo-like, small term, \delta t_{12}, which is a function of both the charged lepton and the neutrino mass ratios.