  We re-examine unitarity bounds on the annihilation cross section of
thermal-WIMP dark matter. For high-mass pointlike dark matter, it is generic to
form WIMP bound states, which, together with Sommerfeld enhancement, affects
the relic abundance. We show that these effects lower the unitarity bound from
139 TeV to below 100 TeV for non-self-conjugate dark matter and from 195 TeV
(the oft-quoted value of 340 TeV assumes $\Omega_{DM} h^2 = 1$) to 140 TeV for
the self-conjugate case. For composite dark matter, for which the unitarity
limit on the radius was thought to be mass-independent, we show that the
largest allowed mass is 1 PeV. In addition, we find important new effects for
annihilation in the late universe. For example, while the production of
high-energy light fermions in WIMP annihilation is suppressed by helicity, we
show that bound-state formation changes this. Coupled with rapidly improving
experimental sensitivity to TeV-range gamma rays, cosmic rays, and neutrinos,
our results give new hope to attack the thermal-WIMP mass range from the
high-mass end.
