Fine Tuning in Supersymmetric Models

The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the traditional measure of this fine tuning used in the literature and propose an alternative. We apply this to the MSSM and show the implications.Comment: Included in proceedings of The 14th International Conference on Supersymmetry and the Unification of Fundamental Interaction

Measuring Fine Tuning In Supersymmetry

The solution to fine tuning is one of the principal motivations for supersymmetry. However constraints on the parameter space of the Minimal Supersymmetric Standard Model (MSSM) suggest it may also require fine tuning (although to a much lesser extent). To compare this tuning with different extensions of the Standard Model (including other supersymmetric models) it is essential that we have a reliable, quantitative measure of tuning. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and the MSSM with some intriguing results.Comment: Submitted for the SUSY07 proceeding

Aspects of electroweak symmetry breaking in physics beyond the standard model

Fine tuning in the Standard Model (SM) is the basis for a widespread expectation that the minimal model for electroweak symmetry breaking, with a single Higgs boson, is not realised in nature and that new physics, in addition to (or instead of) the Higgs, will be discovered at the Large Hadron Collider (LHC). However constraints on new physics indicate that many models which go beyond the SM (BSM) may also be fine tuned (although to a much lesser extent). To test this a reliable, quantitative measure of tuning is required. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and a constrained version of the Minimal Supersymmetric Standard Model. The Exceptional Supersymmetric Standard Model (E6SSM) is another BSM motivated by naturalness. As a supersymmetric theory it solves the SM hierarchy problem and by breaking a new gauged U(1) symmetry it also solves the μ-problem of the MSSM. We investigate the Renormalisation Group Evolution of the model and test for radiative electroweak symmetry breaking in two versions of the model with different high scale constraints. First we briefly look at scenarios with non-universal Higgs masses at the GUT scale and present a particle spectrum that could be observed at the LHC. Secondly we study the constrained E6SSM (CE6SSM), with universal scalar (m0), trilinear (A0) and gaugino (M) masses. We reveal a large volume of CE6SSM parameter space where the correct breakdown of the gauge symmetry can be achieved and all experimental constraints can be satisfied. We present benchmark points corresponding to different patterns of the particle spectrum. A general feature of the benchmark spectra is a light sector of SUSY particles consisting of a light gluino, two light neutralinos and a light chargino. Although the squarks, sleptons and Z′ boson are typically much heavier, the exotic color triplet charge 1/3 fermions as well as the lightest stop can be also relatively light leading to spectacular new physics signals at the LHC

Model-independent analysis of the DAMPE excess

The Dark Matter Particle Explorer (DAMPE) recently released measurements of the electron spectrum with a hint of a narrow peak at about 1.4 TeV. We investigate dark matter (DM) models that could produce such a signal by annihilation in a nearby subhalo whilst simultaneously satisfying constraints from DM searches. In our model-independent approach, we consider all renormalizable interactions via a spin 0 or 1 mediator between spin 0 or 1/2 DM particles and the Standard Model leptons. We find that of the 20 combinations, 10 are ruled out by velocity or helicity suppression of the annihilation cross section to fermions. The remaining 10 models, though, evade constraints from the relic density, collider and direct detection searches, and include models of spin 0 and 1/2 DM coupling to a spin 0 or 1 mediator. We delineate the regions of mediator mass and couplings that could explain the DAMPE excess. In all cases the mediator is required to be heaver than about 2 TeV by LEP limits.Comment: 28 pages, 5 figures and 2 tables. v2: references added. v3: minor changes, matches published versio

FlexibleSUSY -- A spectrum generator generator for supersymmetric models

We introduce FlexibleSUSY, a Mathematica and C++ package, which generates a fast, precise C++ spectrum generator for any SUSY model specified by the user. The generated code is designed with both speed and modularity in mind, making it easy to adapt and extend with new features. The model is specified by supplying the superpotential, gauge structure and particle content in a SARAH model file; specific boundary conditions e.g. at the GUT, weak or intermediate scales are defined in a separate FlexibleSUSY model file. From these model files, FlexibleSUSY generates C++ code for self-energies, tadpole corrections, renormalization group equations (RGEs) and electroweak symmetry breaking (EWSB) conditions and combines them with numerical routines for solving the RGEs and EWSB conditions simultaneously. The resulting spectrum generator is then able to solve for the spectrum of the model, including loop-corrected pole masses, consistent with user specified boundary conditions. The modular structure of the generated code allows for individual components to be replaced with an alternative if available. FlexibleSUSY has been carefully designed to grow as alternative solvers and calculators are added. Predefined models include the MSSM, NMSSM, E$_6$SSM, USSM, R-symmetric models and models with right-handed neutrinos.Comment: 56 pages, 3 figures, 3 tables; v3: correcting typos, matches version accepted for publication by CP

Threshold Corrections in the Exceptional Supersymmetric Standard Model

We calculate threshold corrections to the running gauge and Yukawa couplings in the Exceptional Supersymmetric Standard Model (E6SSM) and analyse the more precise and reliable mass spectra in a constrained model (CE6SSM). Full expressions for the corrections are provided and the implementation into a spectrum generator is described. We find a dramatic reduction in the matching scale dependency of the masses of many states and observe a significant adjustment of the correlation of low-scale physical masses and high-scale parameters. Still, in substantial regions of parameter space the mass of the lightest Higgs is compatible with the new boson discovered at the LHC and the model satisfies limits from collider searches for squark, gluinos and Z' bosons. We study the implications for gauge coupling unification from a new dependency of the spectrum on so-called survival Higgs fields which cannot be addressed without the inclusion of the threshold corrections.Comment: 59 pages, 25 figures, v2 fixed typo and rephrased parts of section 5.3.1, v2 accepted for publication in Physical Review