Abstract
We examine several issues pertaining to statistical predictivity of the string theory landscape for weak scale supersymmetry (SUSY). We work within a predictive landscape wherein super-renormalizable terms scan while renormalizable terms do not. We require stringy naturalness wherein the likelihood of values for observables is proportional to their frequency within a fertile patch of landscape including the MSSM as low energy effective theory with a pocket-universe value for the weak scale nearby to its measured value in our universe. In the string theory landscape, it is reasonable that the soft terms enjoy a statistical power-law draw to large values, subject to the existence of atoms as we know them (atomic principle). We argue that gaugino masses, scalar masses and trilinear soft terms should each scan independently. In addition, the various scalars should scan independently of each other unless protected by some symmetry. The expected non-universality of scalar masses-- once regarded as an undesirable feature-- emerges as an asset within the context of the string landscape picture. In models such as heterotic compactifications on Calabi-Yau manifolds, where the tree-level gauge kinetic function depends only on the dilaton, then gaugino masses may scale mildly, while scalar masses and A-terms, which depend on all the moduli, may scale much more strongly leading to a landscape solution to the SUSY flavor and CP problems in spite of non-diagonal K\"ahler metrics. We present numerical results for Higgs and sparticle mass predictions from the landscape within the generalized mirage mediation SUSY model and discuss resulting consequences for LHC SUSY and WIMP dark matter searches.
Highlights
The laws of physics as we know them are beset with several fine-tuning problems that can be interpreted as omissions in our present level of understanding
II: which soft terms should scan on the landscape and why? Should the soft terms be correlated and all scan together? (That is, is only a single random number needed to simulate their scan in the multiverse?) Or should they each scan independently? The second issue is, of the soft terms which ought to scan, should they scan with a common exponent n, or are there cases where different soft terms would be drawn more strongly to large values than others? (That is, should different n values apply to different soft terms, depending on the string model?) We address both these issues in
Our main goal was to examine the form of soft SUSY breaking terms that would arise in string compactifications to a 4D, N 1⁄4 1 supergravity theory including the minimal supersymmetric standard model (MSSM) as the low energy effective field theory (EFT)
Summary
The laws of physics as we know them are beset with several fine-tuning problems that can be interpreted as omissions in our present level of understanding. The minimal supersymmetric standard model (MSSM) is touted as a natural solution to the gauge hierarchy problem This is because in the MSSM log divergent contributions to the weak scale are expected to be comparable to the weak scale for soft SUSY breaking terms ∼mweak. Since in the landscape picture many of the soft terms are drawn into the tens-of-TeV range, we expect a comparable value of gravitino mass m3=2, but with TeV scale gauginos In such a case, we expect comparable gravity- and anomalymediated contributions to soft terms so that we present our numerical results within the generalized mirage mediation model GMM0 [24].
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