CP-Violation in B_{q} Decays and Final State Strong Phases

TL;DR

This paper derives bounds on final state phases in B_q decays using symmetry principles, showing their compatibility with experimental CP asymmetries and exploring implications for weak phases and form factors within the Standard Model.

Contribution

It provides new bounds on final state phases based on unitarity and symmetry, and links these to CP asymmetries and heavy quark effective theory predictions.

Findings

Final state phases are consistent with experimental CP asymmetries.

Bound on + is a69.

Predicted (rac{S_{+}+S_{-}}{2})_{D^{ ext{*}}\u03c0} ext{ } ext{ is } ext{ } }

Abstract

Using the unitarity, SU(2) and $C$-invariance of hadronic interactions, the bounds on final state phases are derived. It is shown that values obtained for the final state phases relevant for the direct CP-asymmetries $A_{CP}(B^{0}\to K^{+}\pi ^{-},K^{0}\pi ^{0})$ are compatiable with experimental values for these asymmetries. For the decays $B^{0}\to D^{(\ast)-}\pi ^{+}$ $(D^{(\ast)+}\pi ^{-})$ described by two independent single amplitudes $A_{f}$ and $A_{\bar{f}}^{\prime}$ with differnt weak phases (0 and $\gamma $) it is argued that the $C$-invariance of hadronic interactions implies the equality of the final state phase $\delta_{f}$ and $\delta_{\bar{f}}^{\prime}$. This in turn implies, the CP-asymmetry $% \frac{S_{+}+S_{-}}{2}$ is determined by weak phase ($2\beta +\gamma)$ only whereas $\frac{S_{+}-S_{-}}{2}=0.$ Assuming factorization for tree graphs, it is shown that the $B\to D^{(\ast)}$ form factors are in excellent agreement with heavy quark effective theory. From the experimental value for $(\frac{S_{+}+S_{-}}{2})_{D^{\ast}\pi},$ the bound $% \sin (2\beta +\gamma)\geq 0.69$ is obtained and $(\frac{S_{+}+S_{-}}{2%}) _{D_{S}^{\ast -}K^{+}}\approx -(0.41\pm 0.08)\sin \gamma $ is predicted. For the decays described by the amplitudes $A_{f}\neq A_{\bar{f}}$ such as $B^{0}\longrightarrow \rho ^{+}\pi ^{-}:$ $A_{\bar{f}}$ and $% B^{0}\longrightarrow \rho ^{-}\pi ^{+}:A_{f}$ where these amplitudes are given by tree and penguin diagrams with differnt weak phases, it is shown that in the limit $\delta_{f,\bar{f}}^{T}\to 0,r_{f,\bar{f}}\cos \delta_{f,\bar{f}}=\cos \alpha $ and $\frac{S_{\bar{f}}}{S_{f}}=\frac{% S+\Delta S}{S-\Delta S}=-\frac{\sqrt{1-C_{\bar{f}}^{2}}}{\sqrt{1-C_{f}^{2}}}% . $