Exploring the construction of “reference” triangle through unitarity

Abstract

Motivated by the possibility of the low value of sin2β in the measurements of BABAR and BELLE collaborations, we have explored the possibilty 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 Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix give δ = 50 o ± 20 o , which translates to 130 o ± 20 o 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.

PROBING CKM PARAMETERS THROUGH UNITARITY, εK AND ΔMBd,s

“…A recently carried out unitarity based analysis [1,2] involving the evaluation of Jarlskog's rephasing invariant parameter J as well as the evaluation of the angles α, β and γ of the unitarity triangle is extended to include the effects of This range of sin2β is in agreement with the earlier result of BELLE, however has marginal overlap only with the lower limit of recent BELLE results. Interestingly, our results indicate that the lower limit of δ is mostly determined by unitarity, while the upper limit is governed by constraints from ∆m d .…”

“…The agreement between the equations 8, 9 and 10 strongly supports our evaluation of J through the triangle uc as detailed in [1,2]. To evaluate δ from J, we first consider the standard representation of CKM matrix [19], for example, …”

“…The present analysis attempts to evaluate CP violating phase δ, |V td | and the angles of the unitarity triangle α, β and γ by invoking the constraints imposed by unitarity, K o −K o and B o −B o mixings independently as well as collectively. As discussed in references [1,2], the unitarity constraints have been included via J evaluated through the triangle uc. Using the δ range, found from the constraints of unitarity only, we are able to reproduce the PDG CKM matrix rather well, also found from the considerations of unitarity.…”

“…The purpose of the present communication is to extend the analysis carried in references [1,2] by including independently the implications of K o −K o and B o −B o mixing, along with the unitarity on the CKM parameters. Besides comparing our results with one of the most recent analyses [6], we also intend to study the effect of the future refinements in the data.…”

“…To facilitate the discussion as well as to make the mss. readable, in section 2 we detail the essentials of the unitarity based analysis carried out in reference [2]. In the section 3, we determine the CKM phase δ from unitarity and the K o −K o mixing parameter ε K and then use it to evaluate CKM matrix elements and the angles α, β and γ of the CKM triangle.…”