Extraction of the CKM angle $γ$ from the new "mixed " system of $B^+ \to π^+ K^0$ and $B_d^0 \to π^0 K^0$ decays

Abstract

In this paper we try to extract the CKM angle $γ$ from the new "mixed" system of $B^+ \to π^+ K^0$ and $B_d^0 \to π^0 K^0$ decays. We also made an update for the constraints on the angle $γ$ from the observables $R$ and $A_0$. In the parametrization, the SU(2) isospin symmetry of strong interactions has been applied. We found the following results: (a) the measured value of $R$ is now very close to unit, the bound on the angle $γ$ from the measurement of $R$ is therefore not as promising as before, but some bounds on $γ$ can still be read off from $r-γ$ plane if $r$ could be fixed by using an additional input; (b) the measured $R_1$ implies a limit on the strong phase $Δ_1$; (c) due to the contribution from the color allowed electroweak penguin, the minimal value of $R_1$ can be larger than unit. For $ε_1=0.2$ and $R_1=1.2$, the range of $65^\circ \leq γ\leq 115^\circ$ will be excluded, such bounds on $γ$ are interesting and complimentary to the limits from global fit; (d) the dependences of extraction of $γ$ on the variation of parameters $ε_1$, $ρ$, $r_1$ and strong phases are also studied.