2 00 8 Constructing the Leptonic Unitarity Triangle

Following analogy of the ‘db’ triangle in the quark mixing case, we have explored the construction of the ‘ν2.ν3’ leptonic unitarity triangle using the MNS matrix obtained by Bjorken et al. through generalization of the tribimaximal scenario. In particular, for the Ue3 range 0.05− 0.15, the existence of leptonic unitarity triangle indicates a fairly good possibility of having non zero CP violation. In the last few years, apart from establishing the hypothesis of neutrino oscillations, impressive advances have been made in understanding the phenomenology of neutrino oscillations through solar neutrino experiments [1], atmospheric neutrino experiments [2], reactor based experiments [3] and accelerator based experiments [4] enabling the determination of the basic form of the Maki-Nakagawa-Sakata (MNS) leptonic mixing matrix [5]. At present, one of the key issues in the context of neutrino oscillation phenomenology is the existence of CP violation in the leptonic sector. Taking clues from the existence of the unitarity triangle and consequently CP violation in the quark sector [6], several attempts [7]-[9] have been made to explore such a possibility in the leptonic sector. In particular, Farzan and Smirnov [8] have discussed the desirability of exploring the construction of leptonic unitarity triangle for finding possible clues to the existence of CP violation in the leptonic sector. Considering the ‘e-μ’ triangle, for Ue3 values in the range 0.09− 0.22, they have examined the detailed implications of different values of CP violating phase δ on the possible accuracy required in the measurement of various oscillation probabilities. Very recently, Bjorken et al. [9], have constructed a generalization of the tribimaximal scenario and have not only presented a very useful form of the MNS matrix but have also proposed a unitarity triangle, referred to as ‘ν2.ν3’ which could be leptonic analogue of the much talked about ‘db’ triangle in the quark sector. This immediately suggests a need for deeper study of the ‘ν2.ν3’ triangle using clues from the ‘db’ triangle in the quark sector. In particular, it would be very much desirable, as a complimentary approach to the scenario investigated by Farzan and Smirnov [8], to