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

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Chen, Mu-Chun

Mahanthappa, K. T.

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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}/3 \sqrt{2}, the model gives rise to a sum rule,
\tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - {1/2}
\theta_{c} \cos\beta, which is a consequence of the Georgi-Jarlskog relations
in the quark sector. This deviation could account for the difference between
the experimental best fit value for the solar mixing angle and the value
predicted by the tri-bimaximal mixing matrix.

Comment: 11 pages; v2: additional references added; minor modifications made; conclusion unchanged; v3: version to appear in Phys. Lett. B

Comment: 11 pages; v2: additional references added; minor modifications made; conclusion unchanged; v3: version to appear in Phys. Lett. B

##### Keywords

High Energy Physics - Phenomenology