Exploring the construction of “reference” triangle through unitarity

Motivated by the possibility of the low value of sin2β in the measurements of BABAR and BELLE Collaborations, we have explored the possibility of construction of reference unitarity triangle using the unitarity of the CKM matrix, the existence of nonzero CP violating phase δ and the experimental values of the well known CKM elements, without involving any inputs from the processes which might include the new physics effects. The angles of the reference triangle are evaluated by finding δ through the Jarlskogʹs rephasing invariant parameter J. The present data and the unitarity of the CKM matrix give δ=50°± 20°, which translates to 130°±20° in the second quadrant. The corresponding range for sin2β is 0.21 to 0.88. This range is broadly in agreement with the recently updated BABAR and BELLE results. However, a value of sin2β⩽0.2, advocated by Silva and Wolfenstein as a benchmark for new physics, would suggest a violation in the three generation unitarity and would hint towards the existence of a fourth generation. Further, the future refinements in the CKM elements will push the lower limit on sin2β still higher.