Speaker
Prof.
Mu-Chun Chen
(University of California at Irvine)
Description
We propose a model based on $SU(5) \times { }^{(d)}T$ 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 $Z_{12} \times Z_{12}^{\prime}$ 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, $\tan^{2}
\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - e^{i\beta} \theta_{c}/2$, 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.
Authors
Prof.
K.T. Mahanthappa
(University of Colorado at Boulder)
Prof.
Mu-Chun Chen
(University of California at Irvine)