This is an announcement for the paper "A new metric invariant for Banach spaces" by F. Baudier, N. J. Kalton, and G. Lancien. Abstract: We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into $X$. We show that the converse is true when $X$ is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20; 46T99 Remarks: 22 pages The source file(s), new_invariant_BKL.tex: 63462 bytes, is(are) stored in gzipped form as 0912.5113.gz with size 19kb. The corresponding postcript file has gzipped size 132kb. Submitted from: florent.baudier@univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.5113 or http://arXiv.org/abs/0912.5113 or by email in unzipped form by transmitting an empty message with subject line uget 0912.5113 or in gzipped form by using subject line get 0912.5113 to: math@arXiv.org.