Tree-level contributions to the rare decays B+ --> pi+ nu anti-nu, B+ --> K+ nu anti-nu, and B+ --> K*+ nu anti-nu in the Standard Model

The tree-level contributions to the rare decays B+ --> pi+ nu anti-nu, B+ --> K+ nu anti-nu, and B+ --> K*+ nu anti-nu are analyzed and compared to those occurring in K+ --> pi+ nu anti-nu, D+ --> pi+ nu anti-nu, and Ds+ --> pi+ nu anti-nu. 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 tau, potentially blurring the distinction between the modes used to extract B --> tau nu and those used to probe the genuine short-distance b --> (s,d) nu anti-nu FCNC transitions. Numerically, the tree-level contributions are found to account for 97%, 12% and 14% of the total B+ --> pi+ nu anti-nu, B+ --> K+ nu anti-nu, and B+ --> K*+ nu anti-nu rates, respectively.