Implications of the Unitarity Triangle ‘uc ’ for J, δ and |VCKM | elements.

The Jarlskog rephasing invariant parameter |J | is evaluated using one of the six Unitarity Triangles involving well known CKM matrix elements |Vud|, |Vus|, | Vub Vcb |, |Vcd|, |Vcs| and |Vcb|. With PDG2000 values of |Vud| etc. as input, we obtain |J | = (2.71 ± 1.12) × 10 , which in the PDG representation of CKM matrix leads to the range 21 to 159 for the CP violating phase δ. The CKM matrix elements evaluated using this range of δ are in agreement with the PDG CKM matrix. The implications of refinements in the input on |J |, δ and CKM matrix elements have also been studied. Recent discovery of neutrino oscillations in atmospheric neutrinos by the SuperKamiokande Collaboration [1] has not only given the first clear cut signal for physics beyond the standard model (SM), but has also triggered great amount of activity in neutrino mixing phenomena as well as in the related issue of fermion mass matrices. This has also given an impetus to study more deeply the quark mixing phenomena which have been under investigation for the last two decades. In fact, there is a need to closely examine the quark mixing phenomena in the hope that one may decipher some signal, howsoever faint, for physics beyond the SM. In the context of quark mixing phenomena, over the last two decades, several analyses have been carried out [2], some of these in the last few years [3]. The basic purpose of these analyses has been the evaluation of Cabibbo, Kobayashi and Maskawa matrix (VCKM) elements defined as,