Exploring the Unitarity Triangle through CP violation observables in $B_s\to K^{+}{K}^{-}$

Abstract

We discuss the determination of the CKM parameters from the forthcoming $CP$ violation observables in $B_s\to K^{+}{K}^{-}$ decays. Combining the information on mixing induced CP violation in $B_s\to K^{+}{K}^{-}$, with the $B_d\to J/\psi K_s$ precision observable $\sin 2\beta$ and the $B_s^0$--$\overline{B_s^0}$ mixing phase ${\varphi }_s$, we propose a determination of the unitarity triangle $(\bar{\rho },\bar{\eta })$. Computing the penguin parameters $(r,\theta )$ within QCD factorization yield precise determination of $(\bar{\rho },\bar{\eta })$, reflected by a weak dependence on the $\theta$ which is shown as a second order effect. The impact of the direct CP violation observable $C_{KK}$ on the penguin parameters are investigated and a lower bound on $C_{KK}$ is extracted. We also discuss the effect of the $B_s^0$--$\overline{B_s^0}$ new physics mixing phase on the penguin parameters $(r,\theta )$ and $S_{KK}$. Using the SU(3)-flavour symmetry argument and the current $B$-factories data provided by the $B_d\to {\pi }^{+}{\pi }^{-}$ modes, we complement the $B_s\to K^{+}{K}^{-}$ CP-violating observables in a variety of ways, in particular we find that $S_{KK}>0$. Finally we analyze systematically the SU(3)-symmetry breaking factor within QCD factorization.

Comments: 22 pages, 6 figures, typos corrected, reference and some remarks added