Effects of extra dimensions on unitarity and the Higgs boson mass

We study the unitarity constraint on two body Higgs boson elastic scattering in the presence of extra dimensions. The contributions from the exchange of spin-2 and spin-0 Kaluza-Klein states can have a large effect on the partial wave amplitude. The unitarity condition restricts the maximal allowed value for the ratio $r=\sqrt{s}{/M}_S$ of the center of mass energy $\sqrt{s}$ to the gravity scale $M_S$ 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.