Constructing "Reference" Triangle through Unitarity of CKM Matrix

Abstract

Motivated by the possibility of the low value of sin2βin the measurements of BABAR and BELLE collaborations, a reference unitarity triangle is constructed using the unitarity of the CKM matrix 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 triangle are evaluated by finding the CP violating phase δthrough the Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix gives for δthe range 28^o to 152^o, which for sin2βtranslates to the range 0.21 to 0.88. This range is broadly in agreement with the recent BABAR and BELLE results. However, a value of sin2β\leq 0.2, advocated by Silva and Wolfenstein as a benchmark for new physics, would imply 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 sin2βstill higher.