Prospects for reconstruction of leptonic unitarity quadrangle and neutrino oscillation experiments

After the observation of non-zero θ13θ13 the goal has shifted to observe CP violation in the leptonic sector. Neutrino oscillation experiments can, directly, probe the Dirac CP phases. Alternatively, one can measure CP violation in the leptonic sector using Leptonic Unitarity Quadrangle (LUQ). The existence of Standard Model (SM) gauge singlets – sterile neutrinos – will provide additional sources of CP   violation. We investigate the connection between neutrino survival probability and rephasing invariants of the 4×44×4 neutrino mixing matrix. In general, LUQ contain eight geometrical parameters out of which five are independent. We obtain CP   asymmetry (Pνf→νf′−Pν¯f→ν¯f′) in terms of these independent parameters of the LUQ and search for the possibilities of extracting information on these independent geometrical parameters in short baseline (SBL) and long baseline (LBL) experiments, thus, looking for constructing LUQ and possible measurement of CP violation. We find that it is not possible to construct LUQ using data from LBL experiments because CP asymmetry is sensitive to only three of the five independent parameters of LUQ. However, for SBL experiments, CP asymmetry is found to be sensitive to all five independent parameters making it possible to construct LUQ and measure CP violation.