THE HIERARCHY PROBLEM AND NEW DIMENSIONS AT A MILLIMETER

We propose a new framework for solving the hierarchy problem which doe s not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak sca le, which we take as the only fundamental short distance scale in natu re. The observed weakness of gravity on distances greater than or simi lar to 1 mm is due to the existence of n greater than or equal to 2 ne w compact spatial dimensions large compared to the weak scale. The Pla nck scale M-Pl similar to G(N)(-1/2) is not a fundamental scale; its e normity is simply a consequence of the large size of the new dimension s. While gravitons can freely propagate in the new dimensions, at sub- weak energies the Standard Model (SM) fields must be localized to a 4- dimensional manifold of weak scale ''thickness'' in the extra dimensio ns. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of n = 2 new dimensions, pla nned sub-millimeter measurements of gravity may observe the transition from 1/r(2) --> 1/r(4) Newtonian gravitation. For any number of new d imensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimens ional manifold into the new dimensions, carrying away energy, and lead ing to an abrupt decrease in events with high transverse momentum p(T) greater than or similar to TeV. For certain compact manifolds, such p articles will keep circling in the extra dimensions, periodically retu rning, colliding with and depositing energy to our four dimensional va cuum with frequencies of similar to 10(12) Hz or larger. As a concrete illustration, we construct a model with SM fields localized on the 4- dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gaug e symmetry SU(4) X SU(2) X SU(2) in the bulk. (C) 1998 Published by El sevier Science B.V. All rights reserved.