We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and OPP reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with non-trivial applications, the open-loop approach will permit to obtain precise predictions for a very wide range of collider processes.

5 pages, 3 figures; v2: Comment on ordering added after eq. (6); typos in eqs. (14,16,17) corrected; various cosmetic changes; reference added. Accepted for publication in PRL