Abstract: We explore the effects of three-loop minimal supersymmetric standard model renormalisation group equation terms and some leading two-loop threshold corrections on gauge and Yukawa unification: each being one loop higher order than current public spectrum calculators. We also explore the effect of the higher order terms (often 2-3 GeV) on the lightest CP even Higgs mass prediction. We illustrate our results in the constrained minimal supersymmetric standard model. Neglecting threshold corrections at the grand unified scale, the discrepancy between the unification scale alpha(s) and the other two unified gauge couplings changes by 0.1% due to the higher order corrections and the difference between unification scale bottom-tau Yukawa couplings neglecting unification scale threshold corrections changes by up to 1%. The difference between unification scale bottom and top Yukawa couplings changes by a few percent. Differences due to the higher order corrections also give an estimate of the size of theoretical uncertainties in the minimal supersymmetric standard model spectrum. We use these to provide estimates of theoretical uncertainties in predictions of the dark matter relic density (which can be of order one due to its strong dependence on sparticle masses) and the LHC sparticle production cross-section (often around 30%). The additional higher order corrections have been incorporated into SOFTSUSY, and we provide details on how to compile and use the program. We also provide a summary of the approximations used in the higher order corrections. Program Summary Nature of problem: Calculating supersymmetric particle spectrum and mixing parameters in the minimal supersymmetric standard model. The solution to the renormalisation group equations must be consistent with boundary conditions on supersymmetry breaking parameters, as well as the weak-scale boundary condition on gauge couplings, Yukawa couplings and the Higgs potential parameters. Program title: SOFTSUSY Catalogue identifier: ADPMv50 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPMv50.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 240528 No. of bytes in distributed program, including test data, etc.: 2597933 Distribution format: tar.gz Programming language: C++, Fortran. Computer: Personal computer. Operating system: Tested on Linux 3.4.6. Word size: 64 bits. Classification: 11.1, 11.6. External routines: At least GiNaC1.3.5 [1] and CLN1.3.1 (both freely obtainable from http://www.ginac.de). Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: ADPMv40 Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 2322 Solution method: Nested iterative algorithm. Reasons for new version: Extension to include additional two and three-loop terms. Summary of revisions: All quantities in the minimal supersymmetric standard model are extended to have three-loop renormalisation group equations (including 3-family mixing) in the limit of real parameters and some leading two-loop threshold corrections are incorporated to the third family Yukawa couplings and the strong gauge coupling. Restrictions: SOFTSUSY will provide a solution only in the perturbative regime and it assumes that all couplings of the model are real (i.e. CP-conserving). If the parameter point under investigation is non-physical for some reason (for example because the electroweak potential does not have an acceptable minimum), SOFTSUSY returns an error message. The higher order corrections included are for the real R-parity conserving minimal supersymmetric standard model (MSSM) only. Running time: A minute per parameter point. The tests provided with the package only take a few seconds to run.

Abstract: We explore the sparticle mass spectra including LSP dark matter within the framework of supersymmetric SU(4)(c) x SU(2)(L) x SU(2)(R) (422) models, taking into account the constraints from extensive LHC and cold dark matter searches. The soft supersymmetry-breaking parameters at M-GUT can be non-universal, but consistent with the 422 symmetry. We identify a variety of coannihilation scenarios compatible with LSP dark matter, and study the implications for future supersymmetry searches and the ongoing muon g-2 experiment.

Abstract: We identify the parameter regions of the phenomenological minimal supersymmetric standard model (pMSSM) with the minimal possible fine-tuning. We show that the fine-tuning of the pMSSM is not large, nor under pressure by LHC searches. Low sbottom, stop and gluino masses turn out to be less relevant for low fine-tuning than commonly assumed. We show a link between low fine-tuning and the dark matter relic density. Fine-tuning arguments point to models with a dark matter candidate yielding the correct dark matter relic density: a bino-higgsino particle with a mass of 35-155 GeV. Some of these candidates are compatible with recent hints seen in astrophysics experiments such as Fermi-LAT and AMS-02. We argue that upcoming direct search experiments, such as XENON1T, will test all of the most natural solutions in the next few years due to the sensitivity of these experiments on the spin-dependent WIMP-nucleon cross section.