Evidence for the charmless annihilation decay mode $B^0_s \to \pi^+\pi^-$

We search for annihilation decay modes of neutral $b$ mesons into pairs of charmless charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron. Using a data sample corresponding to 6 fb$^{-1}$ of integrated luminosity, we obtain the first evidence for the $B^0_s \to \pi^+\pi^-$ decay, with a significance of $3.7\sigma$, and a measured branching ratio $\mathcal{B}(B^0_s \to \pi^+\pi^-)= (0.57 \pm 0.15 (stat) \pm 0.10 (syst))\times 10^{-6}$. A search for the $B^0 \to K^+K^-$ mode in the same sample yields a significance of $2.0\sigma$, and a central value estimate $\mathcal{B}(B^0 \to K^+K^-)= (0.23 \pm 0.10 (stat) \pm 0.10 (syst))\times 10^{-6}$.