Millimetre - Range Forces in Superstring Theories with Weak - Scale Compactification

We show that theories in which supersymmetry is broken via Scherk-Schwarz com-pactification at the weak scale, possess at least one scalar particle with Compton wavelength in the millimetre range, which mediates a force with strength 1/3 of gravity. Such forces are going to be explored in upcoming experiments using micro-electromechanical systems or cantilever technology. We also present a simple way of understanding some decoupling aspects of these theories by analogy with finite-temperature field theory. 1. Light scalars and theories of supersymmetry breaking One of the most outstanding challenges of supersymmetric theories is the problem of the breaking of supersymmetry. It is directly connected with the cosmological constant problem for which no solution is in sight. In spite of this big hole in our theoretical understanding, the idea of softly broken supersymmetric theories [1] has allowed us to bypass these questions and to study phenomenological consequences of supersymmetric theories in the past 16 years. In the mean time, three distinct classes of theories have emerged for the breaking of supersymmetry:-Gravity-mediated theories.-Gauge-mediated theories.-Theories with weak-scale compactification. A main difference between these approaches is the scale of supersymmetry breaking. In gravity-mediated theories it is 10 13 GeV. In gauge-mediated ones it is anywhere from over 10 TeV to 10 12 GeV. In theories of weak-scale compactification the supersymmetry breaking scale is around the weak scale, ∼ 1 TeV [2]. The different supersymmetry breaking scales imply important differences in the pattern of sparticle masses; these differences will be tested in the next decade at the LHC. The main purpose of this paper is to point out a possible difference between these theories that may emerge at very low energies, in the near future, at " tabletop " experiments costing orders of magnitude less than the LHC. These involve macroscopic gravitational strength forces and arise as follows. In supersymmetric or superstring theories one often encounters scalar particles, called moduli, which parametrize the size and the shape of the extra compact dimensions. They couple with gravitational strength and are massless to all orders in perturbation theory. The moduli may get masses of the order of the Planck mass from non-perturbative effects; in this case they are not relevant to our considerations. It is, however, quite possible that they do not get masses until supersymmetry is broken. In this case their mass, because all –3– their couplings are gravitationally suppressed, will be of order m moduli ∼ …