ar X iv : h ep - p h / 07 02 12 9 v 1 1 3 Fe b 20 07 Constructing the Leptonic Unitarity Triangle

Following analogy of the ‘db’ triangle in the quark mixing case, we have constructed the ‘ν2.ν3’ leptonic unitarity triangle using the MNS matrix formulated in the tribimaximal scenario by Bjorken et al. . In particular, for the Ue3 range 0.05 − 0.15, we find Dirac-like CP violating phase δ to be around 40, indicating a 2.5σ CP violation effect in the leptonic sector. 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 MNS leptonic mixing matrix [5]. At present, one of the key issues in the context of neutrino oscillation phenomenology is to investigate the existence of CP violation in the leptonic sector. Taking clue from the construction of the unitarity triangle in the quark sector [6], several attempts [7, 8, 9] have been made to construct the corresponding unitarity triangle in the leptonic sector. Farzan and Smirnov [8] have discussed, in detail, the desirability of investigating the construction of leptonic unitarity triangle for finding possible clues to the existence of CP violation in the leptonic sector. In particular, considering the ‘e-μ’ triangle, corresponding to the first two rows of leptonic mixing matrix, they have examined in detail the 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], by considering tribimaximal scenario, have not only constructed a 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. In view of the importance of the tribimaximal mixing scenario [10, 11], it would be interesting to investigate, in detail, the structure of the leptonic unitarity triangle suggested by this scenario. In particular, it would be very much desirable, as a complimentary approach to the scenario investigated by Farzan and Smirnov [8], to find the possible values of CP violating phase δ suggested by tribimaximal scenario of Bjorken et al. [9].