We calculate the amplitude of the rare flavour-changing neutral-current decay $Bto piell^+ell^-$ at large recoil of the pion. The nonlocal contributions in which the weak effective operators are combined with the electromagnetic lepton-pair emission
are systematically taken into account. These amplitudes are calculated at off-shell values of the lepton-pair mass squared, $q^2<0$, employing the operator-product expansion, QCD factorization and light-cone sum rules. The results are fitted to hadronic dispersion relations in $q^2$, including the intermediate vector meson contributions. The dispersion relations are then used in the physical region $q^2>0$. Our main result is the process-dependent addition $Delta C^{(Bpi)}_9(q^2)$ to the Wilson coefficient $C_9$ obtained at $4m_ell^2<q^2lesssim m_{J/psi}^2$. Together with the $Bto pi$ form factors from light-cone sum rules, this quantity is used to predict the differential rate, direct CP-asymmetry and isospin asymmetry in $Bto piell^+ell^-$. We also estimate the total rate of the rare decay $Bto pi ubar{ u}$.
In these lectures, I present several important applications of QCD sum rules to the decay processes involving heavy-flavour hadrons. The first lecture is introductory. As a study case, the sum rules for decay constants of the heavy-light mesons are c
onsidered. They are relevant for the leptonic decays of $B$-mesons. In the second lecture I describe the method of QCD light-cone sum rules used to calculate the heavy-to-light form factors at large hadronic recoil, such as the $Bto pi ell u_ell$ form factors. In the third lecture, the nonlocal hadronic amplitudes in the flavour-changing neutral current decays $Bto K^{(*)}ellell$ are discussed. Light-cone sum rules provide important nonfactorizable contributions to these amplitudes.
I overview the hadronic input for the exclusive flavour-changing neutral-current $B$-decays with a vector ($V=K^*,rho$) or pseudoscalar ($P=K,pi$) meson in the final state. After presenting the current status of $Bto P,V$ form factors, I discuss the
estimate of the charm-loop effect in $Bto K^{(*)} ell^+ell^-$ and $Bto K^* gamma$.
The correlation function of two pseudoscalar charmed quark currents with a positive hadronic spectral density is employed to obtain upper bounds on the decay constants of $D$ and $D_s$ mesons. Including all known terms of the operator-product-expansi
on of this correlation function in QCD and taking into account the estimated uncertainties, we obtain $f_{D}<230 $ MeV and $f_{D_s}<270$ MeV. Comparison with the decay constants determined from $Dto l u_l$ and $D_sto l u_l$ measurements, reveals a tension between the bound and current experimental value of $f_{D_s}$.
