Search

We investigate rarely explored details of supercooled cosmological first-order phase transitions at the electroweak scale, which may lead to strong gravitational wave signals or explain the cosmic baryon asymmetry. The nucleation temperature is often used in phase transition analyses, and is defined through the nucleation condition: on average one bubble has nucleated per Hubble volume. We argue that the nucleation temperature is neither a fundamental nor essential quantity in phase transition analysis. We illustrate scenarios where a transition can complete without satisfying the nucleation condition, and conversely where the nucleation condition is satisfied but the transition does not complete. We also find that simple nucleation heuristics, which are defined to approximate the nucleation temperature, break down for strong supercooling. Thus, studies that rely on the nucleation temperature $\unicode{x2014}$ approximated or otherwise $\unicode{x2014}$ may misclassify the completion of a transition. Further, we find that the nucleation temperature decouples from the progress of the transition for strong supercooling. We advocate use of the percolation temperature as a reference temperature for gravitational wave production, because the percolation temperature is directly connected to transition progress and the collision of bubbles. Finally, we provide model-independent bounds on the bubble wall velocity that allow one to predict whether a transition completes based only on knowledge of the bounce action curve. We apply our methods to find empirical bounds on the bubble wall velocity for which the physical volume of the false vacuum decreases during the transition. We verify the accuracy of our predictions using benchmarks from a high temperature expansion of the Standard Model and from the real scalar singlet model., 39 pages (46 with appendices), 8 figures

The Fermilab Muon $g-2$ experiment recently reported its first measurement of the anomalous magnetic moment $a_\mu^{\textrm{FNAL}}$, which is in full agreement with the previous BNL measurement and pushes the world average deviation $\Delta a_\mu^{2021}$ from the Standard Model to a significance of $4.2\sigma$. Here we provide an extensive survey of its impact on beyond the Standard Model physics. We use state-of-the-art calculations and a sophisticated set of tools to make predictions for $a_\mu$, dark matter and LHC searches in a wide range of simple models with up to three new fields, that represent some of the few ways that large $\Delta a_\mu$ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large $\Delta a_\mu$ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the $\Delta a_\mu$ result can only be explained by rather small masses and/or large couplings and enhanced chirality flips, which can lead to conflicts with limits from LHC and dark matter experiments. Our results show that the new measurement excludes a large number of models and provides crucial constraints on others. Two-Higgs doublet and leptoquark models provide viable explanations of $a_\mu$ only in specific versions and in specific parameter ranges. Among all models with up to three fields, only models with chirality enhancements can accommodate $a_\mu$ and dark matter simultaneously. The MSSM can simultaneously explain $a_\mu$ and dark matter for Bino-like LSP in several coannihilation regions. Allowing under abundance of the dark matter relic density, the Higgsino- and particularly Wino-like LSP scenarios become promising explanations of the $a_\mu$ result., Comment: 106 pages, 20 figures, 5 tables; v2 added references, minor corrections to table 2 and improvements to Figs 2,3 and 4; v3 as published in JHEP

We present an updated calculation of the W boson pole mass in models beyond the Standard Model with FlexibleSUSY. The calculation has a decoupling behaviour and allows for a precise W pole mass prediction up to large new physics scales. We apply the calculation to several Standard Model extensions, including the MRSSM where we show that it can be compatible with large corrections to the W boson mass that would be needed to fit the recent 2022 CDF measurement., Comment: 23 pages, 4 figures

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a $\mathbb{Z}_2$ symmetry as a test, we explore the properties of the electroweak phase transition in general $R_\xi$ and covariant gauges, OS and $\overline{\text{MS}}$ renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether., Comment: 45 pages, 16 figures and 2 tables; version accepted for publication in JHEP; Correct the signs of mu in Table 2

In this work, we study the impact of electroweak and Higgs precision measurements at future electron-positron colliders on several typical supersymmetric models, including the Constrained Minimal Supersymmetric Standard Model (CMSSM), Non-Universal Higgs Mass generalisations (NUHM1, NUHM2), and the 7-dimensional Minimal Supersymmetric Standard Model (MSSM7). Using publicly-available data from the \textsf{GAMBIT} community, we post-process previous SUSY global fits with additional likelihoods to explore the discovery potential of Higgs factories, such as the Circular Electron Positron Collider (CEPC), the Future Circular Collider (FCC) and the International Linear Collider (ILC). We show that the currently allowed parameter space of these models will be further tested by future precision measurements. In particular, dark matter annihilation mechanisms may be distinguished by precise measurements of Higgs observables., Comment: 24 pages, 8 figures, 4 tables. Contribution to Snowmass 2021. Version accepted for publication in PRD

We present a likelihood analysis of the general two Higgs doublet model, using the most important currently measured flavour observables, in view of the anomalies in charged current tree-level and neutral current one-loop rare decays of $B$ mesons in $b\to c l \overline{\nu}$ and $b\to s\mu^{+}\mu^{-}$ transitions, respectively. We corroborate that the model explains the latter and it is able to simultaneously fit the experimental values of the $R(D)$ ratio at $1\sigma$, but it can not accommodate the $R(D^{*})$ and $F_{L}(D^{*})$ observables. We find that the fitted values for the angular observables in $b\to s\mu^{+}\mu^{-}$ transitions exhibit better agreement with the general two Higgs double model in comparison to the SM. We also make predictions for future collider observables $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(h\to bs)$, $\mathrm{BR}(h\to \tau\mu)$, $\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$, $\mathrm{BR}(B^{+}\rightarrow K^{+}\tau^{+}\tau^{-})$ and the flavour violating decays of the $\tau$ lepton, $\mathrm{BR}(\tau\rightarrow3\mu)$ and $\mathrm{BR}(\tau\to\mu\gamma)$. The model predicts values of $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$ and $\mathrm{BR}(B^{+}\rightarrow K^{+}\tau^{+}\tau^{-})$ that are out of reach of future experiments, but its predictions for $\mathrm{BR}(h\to bs)$ and $\mathrm{BR}(h\to \tau\mu)$ are within the future sensitivity of the HL-LHC or the ILC. We also find that the predictions for the $\tau\rightarrow3\mu$ and $\tau\to\mu\gamma$ decays are well within the projected limits of the Belle II experiment. Finally, using the latest measurement of the Fermilab Muon $g-2$ Collaboration, we performed a simultaneous fit to $\Delta a_{\mu}$ constrained by the charged anomalies, finding solutions at the $1\sigma$ level. Once the neutral anomalies are included, however, a simultaneous explanation is unfeasible., Comment: 49 pages, 18 figures, new references, fixed typos

The European physical journal / C 81(11), 992 (2021). doi:10.1140/epjc/s10052-021-09712-6, We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data., Published by Springer, Heidelberg

The excess of electron recoil events seen by the XENON1T experiment has been interpreted as a potential signal of axion-like particles (ALPs), either produced in the Sun, or constituting part of the dark matter halo of the Milky Way. It has also been explained as a consequence of trace amounts of tritium in the experiment. We consider the evidence for the solar and dark-matter ALP hypotheses from the combination of XENON1T data and multiple astrophysical probes, including horizontal branch stars, red giants, and white dwarfs. We briefly address the influence of ALP decays and supernova cooling. While the different datasets are in clear tension for the case of solar ALPs, all measurements can be simultaneously accommodated for the case of a sub-dominant fraction of dark-matter ALPs. Nevertheless, this solution requires the tuning of several a priori unknown parameters, such that for our choices of priors a Bayesian analysis shows no strong preference for the ALP interpretation of the XENON1T excess over the background hypothesis., 40 pages, 9 figures. V3 corresponds to the accepted manuscript; added appendices on the DIC and MC simulations; supplementary material now available on Zenodo at https://doi.org/10.5281/zenodo.4384061

We present FlexibleDecay, a tool to calculate decays of scalars in a broad class of BSM models. The tool aims for high precision particularly in the case of Higgs boson decays. In the case of scalar and pseudoscalar Higgs boson decays the known higher order SM QED, QCD and EW effects are taken into account where possible. The program works in a modified $\bar{\text{MS}}$ scheme that exhibits a decoupling property with respect to heavy BSM physics, with BSM parameters themselves treated in the $\bar{\text{MS}}/\bar{\text{DR}}$-scheme allowing for an easy connection to high scale tests for, e.g., perturbativity and vacuum stability, and the many observable calculations readily available in $\bar{\text{MS}}/\bar{\text{DR}}$ programs. Pure BSM effects are taken into account at the leading order, including all one-loop contributions to loop-induced processes. The program is implemented as an extension to FlexibleSUSY, which determines the mass spectrum for arbitrary BSM models, and does not require any extra configuration from the user. We compare our predictions for Higgs decays in the SM, singlet extended SM, type II THDM, CMSSM and MRSSM, as well as for squark decays in the CMSSM against a selection of publicly available tools. The numerical differences between our and other programs are explained. The release of FlexibleDecay officially deprecates the old effective couplings routines in FlexibleSUSY., Comment: 44 pages, 3 figures, 11 tables; version published in CPC

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at https://doi.org/10.5281/zenodo.4322283., 15 pages, 4 figures. extended discussions. closely matches version accepted for publication

We present a C++ software package called PhaseTracer for mapping out cosmological phases, and potential transitions between them, for Standard Model extensions with any number of scalar fields. PhaseTracer traces the minima of effective potential as the temperature changes, and then calculates the critical temperatures, at which the minima are degenerate. PhaseTracer is constructed with modularity, flexibility and practicality in mind. It is fast and stable, and can receive potentials provided by other packages such as FlexibleSUSY. PhaseTracer can be useful analysing cosmological phase transitions which played an important role in the very early evolution of the Universe. If they were first order they could generate detectable gravitational waves and/or trigger electroweak baryogenesis to generate the observed matter anti-matter asymmetry of the Universe. The code can be obtained from https://github.com/PhaseTracer/PhaseTracer., Comment: 32 pages, 5 figures, matches published version

We present BubbleProfiler, a C++ software package for finding field profiles in bubble walls and calculating the bounce action during phase transitions involving multiple scalar fields. Our code uses a recently proposed perturbative method for potentials with multiple fields and a shooting method for single field cases. BubbleProfiler is constructed with modularity, flexibility and practicality in mind. These principles extend from the input of an arbitrary potential with multiple scalar fields in various forms, through the code structure, to the testing suite. After reviewing the physics context, we describe how the methods are implemented in BubbleProfiler, provide an overview of the code structure and detail usage scenarios. We present a number of examples that serve as test cases of BubbleProfiler and comparisons to existing public codes with similar functionality. We also show a physics application of BubbleProfiler in the scalar singlet extension of the Standard Model of particle physics by calculating the action as a function of model parameters during the electroweak phase transition. BubbleProfiler completes an important link in the toolchain for studying the properties of the thermal phase transition driving baryogenesis and properties of gravitational waves in models with multiple scalar fields. The code can be obtained from: https://github.com/bubbleprofiler/bubbleprofiler, 43 pages, 12 figures, 1 table

Motivated by the fact that the Next-to-Minimal Supersymmetric Standard Model is one of the most plausible models that can accommodate electroweak baryogenesis, we analyze its phase structure by tracing the temperature dependence of the minima of the effective potential. Our results reveal rich patterns of phase structure that end in the observed electroweak symmetry breaking vacuum. We classify these patterns according to the first transition in their history and show the strong first-order phase transitions that may be possible in each type of pattern. These could allow for the generation of the matter-antimatter asymmetry or potentially observable gravitational waves. For a selection of benchmark points, we checked that the phase transitions completed and calculated the nucleation temperatures. We furthermore present samples that feature strong first-order phase transitions from an extensive scan of the whole parameter space. We highlight common features of our samples, including the fact that the Standard Model like Higgs is often not the lightest Higgs in the model., Comment: 41 pages, 13 figures. V3: corrected typos and extended discussion about Higgs masses. Accepted in JHEP

International audience; In Ref. (GAMBIT Collaboration: Athron et. al., Eur. Phys. J. C. arXiv:1705.07908, 2017) we introduced the global-fitting framework GAMBIT. In this addendum, we describe a new minor version increment of this package. GAMBIT 1.1 includes full support for Mathematica backends, which we describe in some detail here. As an example, we backend SUSYHD (Vega and Villadoro, JHEP 07:159, 2015), which calculates the mass of the Higgs boson in the MSSM from effective field theory. We also describe updated likelihoods in PrecisionBit and DarkBit, and updated decay data included in DecayBit.

We present the GAMBIT modules SpecBit, DecayBit and PrecisionBit. Together they provide a new framework for linking publicly available spectrum generators, decay codes and other precision observable calculations in a physically and statistically consistent manner. This allows users to automatically run various combinations of existing codes as if they are a single package. The modular design allows software packages fulfilling the same role to be exchanged freely at runtime, with the results presented in a common format that can be easily passed to downstream dark matter, collider and flavour codes. These modules constitute an essential part of the broader GAMBIT framework, a major new software package for performing global fits. In this paper we present the observable calculations, data, and likelihood functions implemented in the three modules, as well as the conventions and assumptions used in interfacing them with external codes. We also present 3-BIT-HIT, a command-line utility for computing mass spectra, couplings, decays and precision observables in the MSSM, which shows how the three modules can be easily used independently of GAMBIT., 67 pages, 9 figures, updated to match version published in EPJC

The radiatively-induced mass splitting between components of an electroweak multiplet is typically of order 100 MeV. This is sufficient to endow the charged components with macroscopically-observable lifetimes, and ensure an electrically-neutral dark matter particle. We show that a commonly used iterative procedure to compute radiatively-corrected pole masses can lead to very different mass splittings than a non-iterative calculation at the same loop order. By estimating the uncertainties of the two one-loop results, we show that the iterative procedure is significantly more sensitive to the choice of renormalisation scale and gauge parameter than the non-iterative method. This can cause the lifetime of the charged component to vary by up to 12 orders of magnitude if iteration is employed. We show that individual pole masses exhibit similar scale-dependence regardless of the procedure, but that the leading scale-dependent terms cancel when computing the mass splitting if and only if the non-iterative procedure is employed. We show that this behaviour persists at two-loop order: the precision of the mass splitting improves in the non-iterative approach, but our results suggest that higher-order corrections do not reduce the uncertainty in the iterative calculation enough to resolve the problem at two-loop order. We conclude that the iterative procedure should not be used for computing pole masses in situations where electroweak mass splittings are phenomenologically relevant., 21 pages, 6 figures, submitted to EPJC

We study the decays of the lightest CP–even Higgs boson into a pair of pseudoscalar Higgs states within U(1)N extensions of the MSSM.

The Exceptional Supersymmetric Standard Model (E$_6$SSM) is a low energy alternative to the MSSM with an extra $U(1)$ gauge symmetry and three generations of matter filling complete 27-plet representations of $E_6$. This provides both new D and F term contributions that raise the Higgs mass at tree level, and a compelling solution to the $\mu$-problem of the MSSM by forbidding such a term with the extra $U(1)$ symmetry. Instead, an effective $\mu$-term is generated from the VEV of an SM singlet which breaks the extra $U(1)$ symmetry at low energies, giving rise to a massive $Z^\prime$. We explore the phenomenology of the constrained version of this model (cE$_6$SSM) in substantially more detail than has been carried out previously, performing a ten dimensional scan that reveals a large volume of viable parameter space. We classify the different mechanisms for generating the measured relic density of dark matter found in the scan, including the identification of a new mechanism involving mixed bino/inert-Higgsino dark matter. We show which mechanisms can evade the latest direct detection limits from the LUX 2016 experiment. Finally we present benchmarks consistent with all the experimental constraints and which could be discovered with the XENON1T experiment., Comment: 26 pages, 4 figures

We present FlexibleEFTHiggs, a method for calculating the SM-like Higgs pole mass in SUSY (and even non-SUSY) models, which combines an effective field theory approach with a diagrammatic calculation. It thus achieves an all order resummation of leading logarithms together with the inclusion of all non-logarithmic 1-loop contributions. We implement this method into FlexibleSUSY and study its properties in the MSSM, NMSSM, E6SSM and MRSSM. In the MSSM, it correctly interpolates between the known results of effective field theory calculations in the literature for a high SUSY scale and fixed-order calculations in the full theory for a sub-TeV SUSY scale. We compare our MSSM results to those from public codes and identify the origin of the most significant deviations between the DR-bar programs. We then perform a similar comparison in the remaining three non-minimal models. For all four models we estimate the theoretical uncertainty of FlexibleEFTHiggs and the fixed-order DR-bar programs thereby finding that the former becomes more precise than the latter for a SUSY scale above a few TeV. Even for sub-TeV SUSY scales, FlexibleEFTHiggs maintains the uncertainty estimate around 2-3 GeV, remaining a competitive alternative to existing fixed-order computations., 51 pages, corrected eq. (27), made minor corrections to some plots and text

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., Comment: 52 pages, 11 figures and 3 tables, Published in JHEP

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 version

We explore the relic density of dark matter and the particle spectrum within a constrained version of an $E_6$ inspired SUSY model with an extra $U(1)_N$ gauge symmetry. In this model a single exact custodial symmetry forbids tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. We present a set of benchmark points showing scenarios that have a SM-like Higgs mass of 125 GeV and sparticle masses above the LHC limits. They lead to striking new physics signatures which may be observed during run II of the LHC and can distinguish this model from the simplest SUSY extensions of the SM. At the same time these benchmark scenarios are consistent with the measured dark matter abundance and necessarily lead to large dark matter direct detection cross sections close to current limits and observable soon at the XENON1T experiment., Comment: 9 pages, no figures, 3 tables; references updated and minor corrections, branching ratios added to Table 3, matches version published in Phys. Lett. B

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 CPC

We present the Bayesian naturalness prior to quantify electroweak fine tuning in the NMSSM. The naturalness prior arises automatically as an Occam razor in Bayesian model comparison quantifying the plausability of electroweak symmetry breaking within the model. The prior incorporates the most widely used fine tuning measures as special cases. In particular, it captures features the Barbieri-Ellis-Giudice, and the Electroweak Fine Tuning measures. We present the amount of Bayesian fine tuning over parameter space slices of the Constrained MSSM, the Constrained NMSSM, and an 11 parameter NMSSM scenario. According to the naturalness prior the constrained models are less tuned than other fine-tuning measures indicate.

The hints for a new resonance at 750 GeV from ATLAS and CMS have triggered a significant amount of attention. Since the simplest extensions of the standard model cannot accommodate the observation, many alternatives have been considered to explain the excess. Here we focus on several proposed renormalisable weakly-coupled models and revisit results given in the literature. We point out that physically important subtleties are often missed or neglected. To facilitate the study of the excess we have created a collection of 40 model files, selected from recent literature, for the Mathematica package SARAH. With SARAH one can generate files to perform numerical studies using the tailor-made spectrum generators FlexibleSUSY and SPheno. These have been extended to automatically include crucial higher order corrections to the diphoton and digluon decay rates for both CP-even and CP-odd scalars. Additionally, we have extended the UFO and CalcHep interfaces of SARAH, to pass the precise information about the effective vertices from the spectrum generator to a Monte-Carlo tool. Finally, as an example to demonstrate the power of the entire setup, we present a new supersymmetric model that accommodates the diphoton excess, explicitly demonstrating how a large width can be obtained. We explicitly show several steps in detail to elucidate the use of these public tools in the precision study of this model., 184 pages, 24 figures; model files available at http://sarah.hepforge.org/Diphoton_Models.tar.gz; v2: added a few clarifications and references

The existence of weak scale supersymmetry (SUSY) is theoretically well motivated, because of its ability to stabilise the electro-weak symmetry breaking (EWSB) scale. One of the benefits of weak scale SUSY with conserved R-parity is that the lightest supersymmetric particle (LSP) is absolutely stable and provides a weakly interacting massive particle (WIMP) candidate capable of accounting for the observed cold dark matter (CDM) relic density ΩCDMh ≈ 0.1. In particular, the lightest neutralino in SUSY models is an excellent such candidate, providing its mass, composition and interactions are suitably tuned to result in the correct value of ΩCDMh. The Minimal Supersymmetric Standard Model (MSSM) [1] provides the simplest supersymmet