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 $B^0_s$--$\bar{B^0_s}$ mixing phase $\phi_s$, 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 $B^0_s$--$\bar{B^0_s}$ 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.Comment: 22 pages, 6 figures, typos corrected, reference and some remarks adde