We study the unitarity constraint on the two body Higgs boson elastic
scattering in the presence of extra dimensions. The contributions from exchange
of spin-2 and spin-0 Kaluza-Klein states can have large effect on the partial
wave amplitude. Unitarity condition restrict the maximal allowed value for the
ratio r of the center of mass energy to the gravity scale to be less than
one. Although the constraint on the standard Higgs boson mass for r of order
one is considerably relaxed, for small r the constraint is similar to that in
the Standard Model. The resulting bound on the Higgs boson mass is not
dramatically altered if perturbative calculations are required to be valid up
to the maximal allowed value for r.Comment: References added, RevTex, 9 pages with two figure
