CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model

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Abstract
We propose a model based on SU(5) x {}^(d)T which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. Due to the (d)T transformation property of the matter fields, the b-quark mass can be generated only when the (d)T symmetry is broken, giving a dynamical origin for the hierarchy between m_b and m_t. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional Z_{12} x Z'_{12} symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for \theta_{13} \simeq \theta_{c}/2\sqrt{2}, the model gives rise to a sum rule, \tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - \theta_{c}/3, which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation accounts for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.

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