We measure the branching fraction and time-dependent $CP$-violating asymmetry for $B^0to J/psipi^0$ decays using a data sample of 711 ${rm fb^{-1}}$ collected on the $Upsilon(4S)$ resonance by the Belle experiment running at the KEKB $e^+e^-$ collider. The branching fraction is measured to be $mathcal{B}(B^0to J/psipi^0) = [1.62,pm 0.11~({rm stat}) pm0.07~({rm syst})]times 10^{-5}$, which is the most precise measurement to date. The measured $CP$ asymmetry parameters are $mathcal{S} = -0.59,pm 0.19~({rm stat}) pm 0.03~({rm syst})$ and $mathcal{A} = -0.15,pm 0.14~({rm stat}),^{+0.04}_{-0.03}~({rm syst})$. The mixing-induced $CP$ asymmetry ($mathcal{S}$) differs from the case of no $CP$ violation by 3.0 standard deviations, and the direct $CP$ asymmetry ($mathcal{A}$) is consistent with zero.
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