Evidence for the multiverse in the standard model and beyond

In any theory it is unnatural if the observed values of parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability P is introduced to numerically evaluate the degree of unnaturalness. If P is very small in all known theories, corresponding to a high degree of fine-tuning, then there is an observer naturalness problem. In addition to the well-known case of the cosmological constant, we argue that nuclear stability and electroweak symmetry breaking represent significant observer naturalness problems. The naturalness probability associated with nuclear stability depends on the theory of flavor, but for all known theories is conservatively estimated as P-nuc less than or similar to(10(-3)-10(-2)), and for simple theories of electroweak symmetry breaking P-EWSB less than or similar to(10(-2)-10(-1)). This pattern of unnaturalness in three different arenas, cosmology, nuclear physics, and electroweak symmetry breaking, provides evidence for the multiverse, since each problem may be easily solved by environmental selection. In the nuclear case the problem is largely solved even if the multiverse distribution for the relevant parameters is relatively flat. With somewhat strongly varying distributions, it is possible to understand both the close proximity to neutron stability and the values of m(e) and m(d)-m(u) in terms of the electromagnetic mass difference between the proton and neutron, delta(EM)similar or equal to 1 +/- 0.5 MeV. It is reasonable that multiverse distributions are strong functions of Lagrangian parameters, since they depend not only on the landscape of vacua, but also on the population mechanism, integrating out other parameters, and on a density of observers factor. In any theory with mass scale M that is the origin of electroweak symmetry breaking, strongly varying multiverse distributions typically lead either to a little hierarchy v/M approximate to(10(-2)-10(-1)), or to a large hierarchy v < M. In certain multiverses, where electroweak symmetry breaking occurs only if M is below some critical value, we find that a little hierarchy develops with the value of v(2)/M-2 suppressed by an extra loop factor, as well as by the strength of the distribution. Since the correct theory of electroweak symmetry breaking is unknown, our estimate for P-EWSB is theoretical. The LHC will lead to a much more robust determination of P-EWSB, and, depending on which theory is indicated by the data, the observer naturalness problem of electroweak symmetry breaking may be removed or strengthened. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data.