IMPLICATIONS OF THE UNITARITY TRIANGLE "uc" FOR J, δ AND |V_CKM| ELEMENTS

Abstract

The Jarlskog rephasing invariant parameter |J| is evaluated using one of the six Unitarity Triangles involving well known CKM matrixWith PDG2000 values of |V ud | etc. as input, we obtain |J| = (2.71 ± 1.12) × 10 −5 , which in the PDG representation of CKM matrix leads to the range 21 o to 159 o 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.

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.…”

Implications of unitarity and precision measurements on CKM matrix elements

“…Because of the strong hierarchical nature of the CKM matrix elements as well as the limitations imposed by the present level of measurements, it is difficult to study the implications of normalization relations, therefore, the six non-diagonal relations are used to study the implications of unitarity on CKM phenomenology. Out of the six, four triangles implied by these relations are highly skewed and it is difficult to study their implications [16,17] with the present knowledge of the CKM matrix elements. The implications of the other two are usually studied through the triangle expressed by the relation…”