# 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

## TL;DR

This paper investigates the significant tree-level long-distance contributions to certain rare B+ meson decays involving neutrinos, highlighting their impact on distinguishing short-distance physics signals from background effects.

## Contribution

It provides a detailed analysis of tree-level long-distance effects in B+ decays, quantifying their impact and comparing them to other similar processes, which was not thoroughly addressed before.

## Key findings

- Tree-level contributions account for 97% of B+ --> pi+ nu anti-nu decay rate.
- Long-distance effects contribute 12% and 14% to B+ --> K+ nu anti-nu and B+ --> K*+ nu anti-nu decays.
- These contributions can obscure the extraction of short-distance physics in B+ decays.

## Abstract

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.