Constrain the UT angle $γ$ by CP violation parameters in $B^0 \to π^+ π^-$

Abstract

We calculate the tree and penguin amplitudes in the $B^0\toπ^+π^-$ decay channel employing the perturbative QCD factorization approach. Using the amplitudes as input with the theoretical uncertainties sufficiently considered, we constrain the UT angle $γ$ to $53^\circ\leqγ\leq70^\circ$, from the measurements of the CP violation parameters $C_{π^+π^-}$ and $S_{π^+π^-}$ in $B^0\toπ^+π^-$. The U-spin breaking effect between $B^0\toπ^+π^-$ and $B_s^0\to K^+K^-$ is estimated to be around 30\%.

9 pages, 4 figures