ar X iv : h ep - p h / 99 04 23 6 v 1 6 A pr 1 99 9 UCB – PTH – 99 / 13 LBNL – 43085 hep - ph / 9904236 April 1999

If spacetime contains large compact extra dimensions, the fundamental mass scale of nature, Λ, may be close to the weak scale, allowing gravitational physics to significantly modify electroweak symmetry breaking. Operators of the form (1/Λ2)|φ†Dμφ|2 and (1/Λ)φWμνB φ, where Wμν and B μν are the SU(2) and U(1) field strengths and φ is the Higgs field, remove the precision electroweak bound on the Higgs boson mass for values of Λ in a wide range: 4 TeV ∼ Λ ∼ 11TeV. Within this framework, there is no preference between a light Higgs boson, a heavy Higgs boson, or a non-linearly realized SU(2)× U(1) symmetry beneath Λ. If there is a Higgs doublet, then operators of the form (1/Λ)φφ(G, F ), where Gμν and Fμν are the QCD and electromagnetic field strengths, modify the production of the Higgs boson by gluon-gluon fusion, and the decay of the Higgs boson to γγ, respectively. At Run II of the Tevatron collider, a γγ signal for extra dimensions will be discovered if Λ is below 2.5 (1) TeV for a Higgs boson of mass 100 (300) GeV. Furthermore, such a signal would point to gravitational physics, rather than to new conventional gauge theories at Λ. The discovery potential of the LHC depends sensitively on whether the gravitational amplitudes interfere constructively or destructively with the standard model amplitudes, and ranges from Λ = 3 – 10 (2 – 4) TeV for a light (heavy) Higgs boson.