Implications of unitarity and precision measurements on CKM matrix elements

Abstract

Unitarity along with precision measurements of sin 2β, V us and V cb allows one to find a lower bound V ub ≥ 0.0035 which, on using the recently measured angle α of the unitarity triangle, translates to V ub = 0.0035 ± 0.0002. This precise value, stable for a good deal of changes in α, along with CP violating phase δ found from unitarity allows the construction of a 'precise' CKM matrix. The above unitarity based value of V ub is in agreement with the latest exclusive value used as input by UTfit, CKMfitter, HFAG, however underlines the so called 'tension' faced by the latest inclusive V ub = 0.00449 ± 0.00033. Further, using this inclusive value of V ub along with the latest sin 2β, one finds δ = 23 o − 39 o , again in conflict with δ measured in B-decays. The calculated ranges of the elements of the CKM matrix are in excellent agreement with those obtained recently by UTfit, CKMfitter and HFAG. Also, the ratio Vts V td is in agreement with its latest measured value, whereas there is some disagreement between the 'measured' and the calculated V td values.

Implications of CP asymmetry parameter sin2beta on structural features of texture specific mass matrices

“…To this end, along with the latest experimental value of sin 2β, we have imposed the following PDG 2008 [2] constraints given by |V us | = 0.2255 ± 0.0019, |V cb | = (41.2 ± 1.1)10 −3 , |V ub | = 0.0035 ± 0.0002. (20) As mentioned earlier, we have considered the value of |V ub | obtained recently [6] using only the unitarity of the elements of the CKM matrix and current sin 2β value. Keeping in mind the above mentioned constraints and using the current values of quark masses given in equation ( 18), we have evaluated the entire CKM matrix at 1σ C.L.…”

“…Based on these precise values, several phenomenological analyses [2]- [5] have allowed us to conclude that the single CKM phase looks to be a viable solution of CP violation not only in the case of K-decays but also in the context of B-decays, at least to the leading order. Interestingly, it has also been shown [6] that the present value of sin 2β along with unitarity and other well measured CKM parameters leads to an almost precise value of V ub and CP violating phase δ, two important parameters yet to be measured precisely. Keeping in mind that the parameter sin 2β also provides vital clues to the structural features of texture specific mass matrices, comprising of hierarchy and phases of the elements of the mass matrices, several authors [7]- [14] have explored its implications for these.…”

Implications of Precision Measurements on Texture Specific Fermion Mass Matrices

“…In the case of quarks, the parameter sin 2β and the Cabibbo-Kobayashi-Maskawa (CKM) [3] matrix elements V us , V cb , V ud are known precisely [4], however, V ub is not that precisely known. In this context, our recent study [5] indicates that sin 2β plays a crucial role in fixing V ub . Similar to the case of quarks, in the case of neutrinos angles s 12 , s 23 as well as the mass square differences ∆m 2 12 , ∆m 2 23 are now rather well known [4,6], whereas only an upper limit is known regarding the third mixing angle s 13 .…”

“…Before we examine the compatibility of texture 4 zero mass matrices with the latest data, we would first like to briefly discuss the implications of sin 2β, along with the unitarity of the CKM matrix, on the CKM element V ub . Considering the usual 'db' unitarity triangle and definitions of the angles of the unitarity triangle, one arrives at a relation [5] involving CP violating phase δ, the mixing angles s 12 , s 23 , s 13 as well as the angle β of the unitarity triangle, e.g.,…”

“…Furthermore, we have used the constraints imposed by the following well known CKM parameters [4], |V us | = 0.2255 ± 0.0019, |V cb | = (41.2 ± 1.1)10 −3 , |V ub | = 0.0035 ± 0.0002, sin 2β = 0.681 ± 0.025. (11)As mentioned earlier, we have considered the value of |V ub | obtained recently[5] using only the unitarity of the elements of the CKM matrix and current sin 2β value. As a first step of our analysis, using these inputs we have obtained the CKM matrix at 1σ C.L.…”