Soft supersymmetry breaking from stochastic superspace

We propose a new realization of softly broken supersymmetric theories as theories defined on stochastic superspace. At the classical level, the supersymmetry breaking is parameterized in terms of a single (in general complex) mass parameter, $\xi$, describing the stochasticity of the Grassmannian superspace coordinates. In the context of the standard model with stochastic supersymmetry, the structure of the soft breaking terms has various characteristic features that can be tested in LHC experiments. Namely, at the classical level, the $B_{\mu}$ parameter, the universal soft trilinear coupling $A_0$, the universal gaugino mass $m_{1/2}$ and the universal scalar mass $m_0$ are given solely in terms of $\xi$; there are no other arbitrary parameters. The relations are $B_\mu = \xi^*$, $A_0 = 2\xi^*$, $m_{1/2} = |\xi|/2$ and $m_0 = 0$. At the quantum level, these relations hold at a certain scale $\Lambda$ which is a second free parameter. The soft scalar masses, zero at tree-level, are induced radiatively through the renormalization group equations at one-loop. With this pattern of soft breaking terms, large supersymmetric contributions to FCNC processes are avoided. As a concrete illustration of the proposed formalism, we consider a minimal model, which is just the constrained MSSM with the stochastic superspace relations amongst the soft-breaking parameters imposed at the scale $\Lambda$. We show that this theory is phenomenologically viable for a certain region in the $(\xi,\Lambda)$ parameter space. Some sensible extensions of the minimal model are then briefly discussed.Comment: 9 pages (revtex), 4 figures. v2: Added author. The introduction has been extended and in the main text we now show that Lambda > M_GUT leads to phenomenologically acceptable outcome

Neutrino masses and sparticle spectra from stochastic superspace

Based on the stochastic superspace mechanism for softly breaking supersymmetry, we present improved sparticle spectra computations for the minimal model and examine extensions through R-parity violation and the type-I seesaw mechanism that incorporate non-zero neutrino masses for more realistic models. Performing the calculations to two-loop accuracy, we observe a global decrease in predicted sparticle masses. However this does not affect the generic features of the minimal model outlined in our earlier work, including the characteristic light stop mass. We find stop decay channels accessible at the LHC which can be used in combination with our predicted range for the stop mixing angle to falsify the minimal model with stochastic supersymmetry. We then introduce neutrino masses and mixings consistent with experiment by including purely trilinear R-parity violating superpotential terms, resulting in a viable stochastic superspace model absent a dark matter candidate. An alternative method for generating neutrino masses, namely the type-I seesaw mechanism, is found only to be viable when the neutrino Yukawa coupling is small relative to the top Yukawa and the cut-off scale is large.Comment: 11 pages, minor changes and additions, this version to appear in PR

Stochastic superspace phenomenology at the Large Hadron Collider

We analyse restrictions on the stochastic superspace parameter space arising from 1 fb$^{-1}$ of LHC data, and bounds on sparticle masses, cold dark matter relic density and the branching ratio of the process $B_s \rightarrow \mu^+ \mu^-$. A region of parameter space consistent with these limits is found where the stochasticity parameter, \xi, takes values in the range -2200 GeV < \xi < -900 GeV, provided the cutoff scale is $\mathcal{O}(10^{18})$ GeV.Comment: 9 pages, 13 figure

Soft supersymmetry breaking from stochastic superspace

© 2013 Dr. Nadine Elsie PesorA consequence of exact supersymmetry is the prediction of a mass degenerate superpartner for each standard model particle. The non-observation of such particles demands that supersymmetry manifests at low energies in softly broken form, such that new types of divergences (i.e. higher than logarithmic) are avoided. We propose a new realisation of softly broken supersymmetric theories as theories defined on stochastic superspace. With a suitably chosen probability distribution, the soft supersymmetry breaking parameters emerge upon averaging over the fluctuating superspace coordinates. At the classical level, the supersymmetry breaking is parametrised by a single mass parameter, $\xi$, which describes the stochasticity of the Grassmannian coordinates. It is therefore highly predictive, and by virtue of its characteristic structure of soft breaking terms, within reach for detection or falsification at the Large Hadron Collider. In the context of the standard model with stochastic supersymmetry, the $B_{\mu}$ parameter, the universal soft trilinear coupling $A_0$, the universal gaugino mass $m_{1/2}$ and the universal scalar mass $m_0$ are all given solely in terms of $\xi$. The relations are $B_{\mu} = \xi^*$, $A_0 = 2 \xi^*$, $m_{1/2} = |\xi|/2$ and $m_0 = 0$. At the quantum level, these relations hold at a certain scale, $\Lambda$, which is a second free parameter. The soft scalar masses, zero at tree-level, are induced radiatively through the renormalisation group equations at one-loop. Employing an analytical solution to an approximation of the one-loop renormalisation group equations, we find the parameter space of minimal stochastic supersymmetry to be highly constrained by the nature of its lightest supersymmetric particle (LSP). A viable neutralino LSP only emerges when the cutoff scale is taken to be greater than \mgut. In a more detailed analysis using sparticle spectrum calculator software to determine the mass and decay spectra, each point in parameter space is checked against known limits on relic density and rare decay processes. We then use a fast simulation of the ATLAS detector to determine which points in its parameter space are excluded by ATLAS zero lepton searches, which are amongst the most constraining limits on direct sparticle production. We find that the minimal model is definitively excluded by the recent discovery of a Higgs with mass approximately 10 \, \GeV heavier than that predicted by stochastic superspace. To address the observation of nonzero neutrino masses, we separately consider R-parity violation and the type-I seesaw mechanism as extensions to minimal model. In the former case, we are able to introduce neutrino masses and mixings consistent with experiment by including purely trilinear R-parity violating superpotential terms and assuming the less constrictive baryon triality symmetry. The latter case is found only to be viable when the neutrino Yukawa coupling is small relative to the top Yukawa, and the cutoff scale is large. However, as these models do not affect the Higgs mass prediction, they are excluded for the same reason as the minimal model. Finally, we consider the next-to-minimal supersymmetric standard model in stochastic superspace. The introduction of a gauge singlet superfield offers the possibility of increasing the mass prediction for the Higgs relative to the minimal model. Indeed, we observe a global increase such that m_h = 116.6 \div 121.0 \, \GeV. However, this is insufficient to achieve overlap with the allowed mass range from CMS and ATLAS searches