Constrain the UT angle $\gamma$ by CP violation parameters in $B^0\to {\pi }^{+}{\pi }^{-}$

Abstract

We calculate the tree and penguin amplitudes in the $B^0\to {\pi }^{+}{\pi }^{-}$ decay channel employing the perturbative QCD factorization approach. Using the amplitudes as input with the theoretical uncertainties sufficiently considered, we constrain the UT angle $\gamma$ to $53^{\circ }\le \gamma \le 70^{\circ }$, from the measurements of the CP violation parameters $C_{{\pi }^{+}{\pi }^{-}}$ and $S_{{\pi }^{+}{\pi }^{-}}$ in $B^0\to {\pi }^{+}{\pi }^{-}$. The U-spin breaking effect between $B^0\to {\pi }^{+}{\pi }^{-}$ and $B_s^0\to K^{+}{K}^{-}$ is estimated to be around 30\%.

Comments: 9 pages, 4 figures