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 $3.7sigma$, 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 $2.0sigma$, and a central value estimate $mathcal{B}(B^0 to K^+K^-)= (0.23 pm 0.10 (stat) pm 0.10 (syst))times 10^{-6}$.
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