Constraining the Unitarity Triangle with B -> V gamma

We discuss the exclusive radiative decays $B\to K^{*}\gamma$, $B \to\rho\gamma$, and $B\to\omega\gamma$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\to\rho l\nu$ decay spectrum to the branching fraction of $B\to\rho\gamma$. The method is based on the cancellation of soft hadronic form factors in the large energy limit, which occurs in a suitable region of phase space. The ratio of the $B\to\rho\gamma$ and $B\to K^{*}\gamma$ branching fractions determines the side $R_{t}$ of the standard unitarity triangle with reduced hadronic uncertainties. The recent Babar bound on $B(B^0\to\rho^0\gamma)$ implies $R_t < 0.81 (\xi/1.3)$, with the limiting uncertainty coming only from the SU(3) breaking form factor ratio $\xi$. This constraint is already getting competitive with the constraint from $B_{s}$-$\bar B_{s}$ mixing. Phenomenological implications from isospin-breaking effects are briefly discussed.Comment: 23 pages, 8 figure

Exploring the Unitarity Triangle through CP violation observables in Bs→K+K−B_s \to K^+ K^-

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

Direct CP Violation, Branching Ratios and Form Factors B→πB \to \pi, B→KB \to K in BB Decays

The $B \to \pi$ and $B \to K$ transitions involved in hadronic B decays are investigated in a phenomenological way through the framework of QCD factorization. By comparing our results with experimental branching ratios from the BELLE, BABAR and CLEO Collaborations for all the B decays including either a pion or a kaon, we propose boundaries for the transition form factors $B \to \pi$ and $B \to K$ depending on the CKM matrix element parameters $\rho$ and $\eta$. From this analysis, the form factors required to reproduce the experimental data for branching ratios are $F^{B \to \pi}= 0.31 \pm 0.12$ and $F^{B \to K}= 0.37\pm 0.13$. We calculate the direct CP violating asymmetry parameter, $a_{CP}$, for $B \to \pi^{+} \pi^{-} \pi$ and $B \to \pi^{+} \pi^{-} K$ decays, in the case where $\rho-\omega$ mixing effects are taken into account. Based on these results, we find that the direct CP asymmetry for $B^{-} \to \pi^{+} \pi^{-} \pi^{-}$, $\bar{B}^{0} \to \pi^{+} \pi^{-} \pi^{0}$, $B^{-} \to \pi^{+} \pi^{-} K^{-}$, and $\bar{B}^{0} \to \pi^{+} \pi^{-} \bar{K}^{0}$, reaches its maximum when the invariant mass $\pi^{+} \pi^{-}$ is in the vicinity of the $\omega$ meson mass. The inclusion of $\rho-\omega$ mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod$(\pi)$ in the determination of the CKM angles $\alpha$ in case of $b\to u$ and $\gamma$ in case of $b \to s$.Comment: 74 pages, 15 figures, 8 tables. A few misprints corrected, two references adde