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We calculate the amplitude of the rare flavour-changing neutral-current decay$B\to \pi\ell^+\ell^-$ at large recoil of the pion. The nonlocal contributionsin which the weak effective operators are combined with the electromagneticlepton-pair emission are systematically taken into account. These amplitudesare calculated at off-shell values of the lepton-pair mass squared, $q^2<0$,employing the operator-product expansion, QCD factorization and light-cone sumrules. The results are fitted to hadronic dispersion relations in $q^2$,including the intermediate vector meson contributions. The dispersion relationsare then used in the physical region $q^2>0$. Our main result is theprocess-dependent addition $\Delta C^{(B\pi)}_9(q^2)$ to the Wilson coefficient$C_9$ obtained at $4m_\ell^2<q^2\lesssim m_{J/\psi}^2$. Together with the $B\to\pi$ form factors from light-cone sum rules, this quantity is used to predictthe differential rate, direct CP-asymmetry and isospin asymmetry in $B\to\pi\ell^+\ell^-$. We also estimate the total rate of the rare decay $B\to\pi\nu\bar{\nu}$.

Hadronic effects and observables in $B\to \pi\ell^+\ell^-$ decay at large recoil