Gravitons could permeate extra space dimensions inaccessible to all other p
articles, which would be confined to "branes". We point out that these bran
es could be "fat" and have a non-vanishing width in the dimensions reserved
for gravitons. In this case the other particles, confined within a finite
width, should have "branon" excitations. Chiral fermions behave differently
from bosons under dimensional reduction, and they may - or may not - be mo
re localized than bosons. All these possibilities are in principle testable
and distinguishable, they could yield spectacular signatures at colliders,
such as the production of the first branon excitation of gamma's or Z's, d
ecaying into their ground state plus a quasi-continuum of graviton recurren
ces. We explore these ideas in the realm of a future lepton collider and we
individuate a dimensiometer: an observable that would cleanly diagnose the
number of large "extra" dimensions. (C) 2000 Elsevier Science B.V. All rig
hts reserved.