The Hierarchy Problem and New Dimensions at a Millimeter

TL;DR

This paper proposes that the electroweak scale is the fundamental short-distance scale and introduces $n\ge2$ large extra dimensions of radius $R\sim$ mm, with the $(4+n)$-dimensional Planck mass near the weak scale. SM fields are confined to a 4D throat in the extra dimensions while gravitons propagate in all dimensions, making 4D gravity appear weak due to the large extra-dimensional volume. The authors construct a concrete 6D model where fermions, Higgs, and gauge fields are localized on a vortex throat, yielding a realistic SM-like spectrum and a rich array of phenomenological consequences, including sub-mm deviations of gravity, graviton-induced missing energy at colliders, and possible repetitive energy exchange with the bulk. If correct, this framework eliminates the hierarchy problem without SUSY, predicts testable signatures at the LHC/NLC and gravity experiments, and invites further exploration of higher-dimensional localization mechanisms and cosmology.

Abstract

We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances $\gsim$ 1 mm is due to the existence of $n \geq 2$ new compact spatial dimensions large compared to the weak scale. The Planck scale $M_{Pl} \sim G_N^{-1/2}$ is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. 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 dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of $n=2$ new dimensions, planned sub-millimeter measurements of gravity may observe the transition from $1/r^2 \to 1/r^4$ Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum $p_T \gsim$ TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of $ \sim 10^{12}$ Hz or larger. As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry $SU(4) \times SU(2) \times SU(2)$ in the bulk.