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We calculate tree-level contributions to the inclusive rare $\bar B \toX_{s(d)} \, \ell^+\ell^-$ decays. At the partonic level they stem from thefive-particle process $b \to s(d) \, q \bar q \, \ell^+\ell^-$, with $q \in\{u,d,s\}$. While for $b \to d$ transitions such five-body final statescontribute at the same order in the Wolfenstein expansion compared to thethree-body partonic decay, they are CKM suppressed in $b \to s$ decays. In theperturbative expansion, we include all leading-order contributions, as well aspartial next-to-leading order QCD and QED effects. In the case of thedifferential branching ratio, we present all results completely analytically interms of polylogarithmic functions of at most weight three. We also considerthe differential forward-backward asymmetry, where all except one interferencecould be obtained analytically. From a phenomenological point of view the newlycalculated contributions are at the percent level or below.

Five-particle contributions to the inclusive rare $\bar B \to X_{s(d)} \, \ell^+\ell^-$ decays