The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a ℤ3 conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners.

/pdf/bayesian-analysis-and-naturalness-of-next-to-minimal-3iw5k2ok7l.pdf

Bayesian analysis and naturalness of (Next-to-)Minimal Supersymmetric Models

The B − L MSSM is the MSSM with three right-handed neutrino chiral multiplets and gauged B − L symmetry. The B − L symmetry is broken by the third family right-handed sneutrino acquiring a VEV, thus spontaneously breaking R-parity. Within a natural range of soft supersymmetry breaking parameters, it is shown that a large and uncorrelated number of initial values satisfy all present phenomenological constraints; including the correct masses for the W±, Z0 bosons, having all sparticles exceeding their present lower bounds and giving the experimentally measured value for the Higgs boson. For this “valid” set of initial values, there are a number of different LSPs, each occurring a calculable number of times. We plot this statistically and determine that among the most prevalent LSPs are chargino and neutralino mass eigenstates. In this paper, the R-parity violating decay channels of charginos and neutralinos to standard model particles are determined, and the interaction vertices and decay rates computed analytically. These results are valid for any chargino and neutralino, regardless of whether or not they are the LSP. For chargino and neutralino LSPs, we will — in a subsequent series of papers — present a numerical study of their RPV decays evaluated statistically over the range of associated valid initial points.

/pdf/the-r-parity-violating-decays-of-charginos-and-neutralinos-2od9v627ow.pdf

The R -parity violating decays of charginos and neutralinos in the B-L MSSM

The R-parity violating decays of both Wino chargino and Wino neutralino LSPs are analyzed within the context of the B − L MSSM “heterotic standard model”. These LSPs correspond to statistically determined initial soft supersymmetry breaking parameters which, when evolved using the renormalization group equations, lead to an effective theory satisfying all phenomenological requirements; including the observed electroweak vector boson and Higgs masses. The explicit decay channels of these LSPs into standard model particles, the analytic and numerical decay rates and the associated branching ratios are presented. The decay lengths of these RPV interactions are discussed. It is shown that the vast majority of these decays are “prompt”, although a small, but calculable, number correspond to “displaced vertices” of various lengths. It is demonstrated that for a Wino chargino LSP, the NLSP is the Wino neutralino with a mass only slightly higher than the LSP — and vice-versa. As a consequence, we show that both the Wino chargino and Wino neutralino LSP/NLSP R-parity violating decays should be simultaneously observable at the CERN LHC.

/pdf/r-parity-violating-decays-of-wino-chargino-and-wino-1nol2125yo.pdf

$R$-parity Violating Decays of Wino Chargino and Wino Neutralino LSPs and NLSPs at the LHC

The R-parity violating decays of Bino neutralino LSPs are analyzed within the context of the B − L MSSM “heterotic standard model”. These LSPs correspond to statistically determined initial soft supersymmetry breaking parameters which, when evolved using the renormalization group equations, lead to an effective theory satisfying all phenomenological requirements; including the observed electroweak vector boson masses and the Higgs mass. The explicit RPV decay channels of these LSPs into standard model particles, the analytic and numerical decay rates and the associated branching ratios are presented. The analysis of these quantities breaks into two separate calculations; first, for Bino neutralino LSPs with mass larger than MW± and, second, when the Bino neutralino mass is smaller than the electroweak scale. The RPV decay processes in both of these regions is analyzed in detail. The decay lengths of these RPV interactions are discussed. It is shown that for heavy Bino neutralino LSPs the vast majority of these decays are “prompt”, although a small, but calculable, number correspond to “displaced” decays of various lengths. The situation is reversed for light Bino LSPs, only a small number of which can RPV decay promptly. The relation of these results to the neutrino hierarchy — either normal or inverted — is discussed in detail.

/pdf/r-parity-violating-decays-of-bino-neutralino-lsps-at-the-lhc-jzvqbmx826.pdf

$R$-parity Violating Decays of Bino Neutralino LSPs at the LHC

The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners.

/pdf/bayesian-analysis-and-naturalness-of-next-to-minimal-2300nh7ti3.pdf

Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the non-unifying puzzle model. Of the GUTs we consider, the $B-L$ MSSM GUT is the most favored, but the MSSM GUT is almost equally favored.

Panashe Fundira

Papers

Bayesian naturalness, simplicity, and testability applied to the $B−L$ MSSM GUT

Bayesian naturalness, simplicity, and testability applied to the $B-L$ MSSM GUT using GPU Monte Carlo

Bayesian naturalness, simplicity, and testability applied to the $B-L$ MSSM GUT