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

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

Bino Dark Matter and Big Bang Nucleosynthesis in the Constrained E6SSM with Massless Inert Singlinos

We discuss a new variant of the E6 inspired supersymmetric standard model (E6SSM) in which the two inert singlinos are exactly massless and the dark matter candidate has a dominant bino component. A successful relic density is achieved via a novel mechanism in which the bino scatters inelastically into heavier inert Higgsinos during the time of thermal freeze-out. The two massless inert singlinos contribute to the effective number of neutrino species at the time of Big Bang Nucleosynthesis, where the precise contribution depends on the mass of the Z' which keeps them in equilibrium. For example for mZ' > 1300 GeV we find Neff \approx 3.2, where the smallness of the additional contribution is due to entropy dilution. We study a few benchmark points in the constrained E6SSM with massless inert singlinos to illustrate this new scenario.Comment: 24 pages, revised for publication in JHE

Supersymmetric Decays of the Z' Boson

The decay of the Z' boson into supersymmetric particles is studied. We investigate how these supersymmetric modes affect the current limits from the Tevatron and project the expected sensitivities at the LHC. Employing three representative supersymmetric Z' models, namely, E_6, U(1)_{B-L}, and the sequential model, we show that the current limits of the Z' mass from the Tevatron could be reduced substantially due to the weakening of the branching ratio into leptonic pairs. The mass reach for the E_6 Z' bosons is about 1.3-1.5 TeV at the LHC-7 (1 fb^{-1}), about 2.5 - 2.6 TeV at the LHC-10 (10 fb^{-1}), and about 4.2 - 4.3 TeV at the LHC-14 (100 fb^{-1}). A similar mass reach for the U(1)_{B-L} Z' is also obtained. We also examine the potential of identifying various supersymmetric decay modes of the Z' boson because it may play a crucial role in the detailed dynamics of supersymmetry breaking.Comment: 30 pages, including 13 figures. improvements to the presentation and references adde