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

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

Z' mass limits and the naturalness of supersymmetry

The discovery of a 125 GeV Higgs boson and rising lower bounds on the masses of superpartners have lead to concerns that supersymmetric models are now fine tuned. Large stop masses, required for a 125 GeV Higgs, feed into the electroweak symmetry breaking conditions through renormalisation group equations forcing one to fine tune these parameters to obtain the correct electroweak vacuum expectation value. Nonetheless this fine tuning depends crucially on our assumptions about the supersymmetry breaking scale. At the same time $U(1)$ extensions provide the most compelling solution to the $\mu$-problem, which is also a naturalness issue, and allow the tree level Higgs mass to be raised substantially above $M_Z$. These very well motivated supersymmetric models predict a new $Z'$ boson which could be discovered at the LHC and the naturalness of the model requires that the $Z'$ boson mass should not be too far above the TeV scale. Moreover this fine tuning appears at the tree level, making it less dependent on assumptions about the supersymmetry breaking mechanism. Here we study this fine tuning for several $U(1)$ supersymmetric extensions of the Standard Model and compare it to the situation in the MSSM where the most direct tree level fine tuning can be probed through chargino mass limits. We show that future LHC $Z'$ searches are extremely important for challenging the most natural scenarios in these models.Comment: 58 pages, 5 figures; typos corrected, references added; matches version to be published in Phys. Rev.

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

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

Phenomenological Consequences of the Constrained Exceptional Supersymmetric Standard Model

The Exceptional Supersymmetric Standard Model (E$_6$SSM) provides a low energy alternative to the MSSM, with an extra gauged U(1)$_N$ symmetry, solving the $\mu$-problem of the MSSM. Inspired by the possible embedding into an E$_6$ GUT, the matter content fills three generations of E$_6$ multiplets, thus predicting exciting exotic matter such as diquarks or leptoquarks. We present predictions from a constrained version of the model (cE$_6$SSM), with a universal scalar mass $m_0$, trilinear mass $A$ and gaugino mass $M_{1/2}$. We reveal a large volume of the cE$_6$SSM parameter space where the correct breakdown of the gauge symmetry is achieved and all experimental constraints satisfied. We predict a hierarchical particle spectrum with heavy scalars and light gauginos, while the new exotic matter can be light or heavy depending on parameters. We present representative cE$_6$SSM scenarios, demonstrating that there could be light exotic particles, like leptoquarks and a U(1)$_N$ Z' boson, with spectacular signals at the LHC.Comment: Contribution to the proceedings of SUSY 09, Boston, USA, June 2009, 4 page

Higgs mass predictions of public NMSSM spectrum generators

The publicly available spectrum generators for the NMSSM often lead to different predictions for the mass of the standard model-like Higgs boson even if using the same renormalization scheme and two-loop accuracy. Depending on the parameter point, the differences can exceed 5 GeV, and even reach 8 GeV for moderate superparticle masses of up to 2 TeV. It is shown here that these differences can be traced back to the calculation of the running standard model parameters entering all calculations, to the approximations used in the two-loop corrections included in the different codes, and to different choices for the renormalization conditions and scales. In particular, the importance of the calculation of the top Yukawa coupling is pointed out.Comment: 24 pages, no figures; v2: slightly extended discussion, matches version accepted for publication by CP