Supersymmetry Breaking in the Anthropic Landscape

In this paper I attempt to address a serious criticism of the “Anthropic Landscape” and “Discretuum” approach to cosmology, leveled by Banks, Dine and Gorbatov. I argue that in this new and unfamiliar setting, the gauge Hierarchy may not favor low energy supersymmetry. 1 The Banks Dine Gorbatov Argument Let’s begin by reviewing a successful use of the anthropic principle. In 1987 Steven Weinberg predicted that if the anthropic principle was correct, the cosmological constant should not be very much smaller than the bound provided by galaxy formation [2]. The argument is straightforward: a much smaller value would require fine tuning of the type which the anthropic principle was supposed to eliminate. Since the anthropic upper bound was only a couple of orders of magnitude above the empirical upper bound, Weinberg argued that the anthropic principle predicted that a cosmological constant would soon be discovered. And it was. It is worth noting that there are also anthropic bounds on the weak scale that might be strong enough to require a gauge hierarchy like the one we actually observe. Increasing the Higgs expectation value keeping everything else fixed would among other things, increase the strength of gravity, making stars, galaxies and the universe evolve much faster. Alternatively we could try to keep particle masses fixed by decreasing Yukawa couplings. This would decrease the strength of weak interactions, thereby having many effects on the creation of heavy elements in stars as well as the primary mechanism for dispersing the elements, namely, supernovae. Banks, Dine and Gorbatov (BDG) [1] have recently argued that similar logic can be applied to proton stability and that the exceptionally long life of the proton falsifies the Anthropic Principle. The context of the Banks Dine Gorbatov argument is the “Landscape” or “Discretuum” hypothesis [3, 4, 5, 6]. They argue (correctly I think) that the anthropic bound on the proton lifetime is about 10 years. Therefore the vast majority of anthropically acceptable landscape sites have proton lifetimes many orders of magnitude shorter than the experimental lower limit 10 years. One way out of the Banks Dine Gorbatov argument is to note that in the nonsupersymmetric standard model, there is no mechanism for proton decay. If the scale signaling the breakdown of the standard model is high enough, there is no problem. Thus BDG begin by first arguing that the vast majority of anthropically acceptable vacua have a very low supersymmetry breaking scale. Their argument goes as follows: Without supersymmetry both the cosmological constant and the Higgs mass scale, μ must be fine tuned. The combined fine tuning is about one part in 10. If the supersymmetry breaking scale is called M then the natural scale for radiative corrections to the cosmological constant is of order M. If the actual cosmological constant is λ then