Tree-level contributions to the rare decays B+→π+νν¯, B+→K+νν¯, and B+→K*+νν¯ in the Standard Model

The tree-level contributions to the rare decays B+→π+νν¯, B+→K+νν¯, and B+→K*+νν¯ are analyzed and compared to those occurring in K+→π+νν¯, D+→π+νν¯, and Ds+→π+νν¯. It is shown that these purely long-distance contributions, arising from the exchange of a charged lepton, can be significant in B+ decays for an intermediate τ, potentially blurring the distinction between the modes used to extract B+→τ+ντ and those used to probe the genuine short-distance b→dνν¯ and b→sνν¯ FCNC transitions. Numerically, the tree-level contributions are found to account for 98%, 12% and 14% of the total B+→π+νν¯, B+→K+νν¯, and B+→K*+νν¯ rates, respectively.