Bayesian approach and Naturalness in MSSM analyses for the LHC

The start of LHC has motivated an effort to determine the relative probability of the different regions of the MSSM parameter space, taking into account the present, theoretical and experimental, wisdom about the model. Since the present experimental data are not powerful enough to select a small region of the MSSM parameter space, the choice of a judicious prior probability for the parameters becomes most relevant. Previous studies have proposed theoretical priors that incorporate some (conventional) measure of the fine-tuning, to penalize unnatural possibilities. However, we show that such penalization arises from the Bayesian analysis itself (with no ad hoc assumptions), upon the marginalization of the mu-parameter. Furthermore the resulting effective prior contains precisely the Barbieri-Giudice measure, which is very satisfactory. On the other hand we carry on a rigorous treatment of the Yukawa couplings, showing in particular that the usual practice of taking the Yukawas "as required", approximately corresponds to taking logarithmically flat priors in the Yukawa couplings. Finally, we use an efficient set of variables to scan the MSSM parameter space, trading in particular B by tan beta, giving the effective prior in the new parameters. Beside the numerical results, we give accurate analytic expressions for the effective priors in all cases. Whatever experimental information one may use in the future, it is to be weighted by the Bayesian factors worked out here.Comment: LaTeX, 19 pages, 3 figure

A new viable region of the inert doublet model

The inert doublet model, a minimal extension of the Standard Model by a second Higgs doublet, is one of the simplest and most attractive scenarios that can explain the dark matter. In this paper, we demonstrate the existence of a new viable region of the inert doublet model featuring dark matter masses between Mw and about 160 GeV. Along this previously overlooked region of the parameter space, the correct relic density is obtained thanks to cancellations between different diagrams contributing to dark matter annihilation into gauge bosons (W+W- and ZZ). First, we explain how these cancellations come about and show several examples illustrating the effect of the parameters of the model on the cancellations themselves and on the predicted relic density. Then, we perform a full scan of the new viable region and analyze it in detail by projecting it onto several two-dimensional planes. Finally, the prospects for the direct and the indirect detection of inert Higgs dark matter within this new viable region are studied. We find that present direct detection bounds already rule out a fraction of the new parameter space and that future direct detection experiments, such as Xenon100, will easily probe the remaining part in its entirety.Comment: 27 pages, 16 figure

On the detectability of the CMSSM light Higgs boson at the Tevatron

We examine the prospects of detecting the light Higgs h^0 of the Constrained MSSM at the Tevatron. To this end we explore the CMSSM parameter space with \mu>0, using a Markov Chain Monte Carlo technique, and apply all relevant collider and cosmological constraints including their uncertainties, as well as those of the Standard Model parameters. Taking 50 GeV < m_{1/2}, m_0 < 4 TeV, |A_0| < 7 TeV and 2 < tan(beta) < 62 as flat priors and using the formalism of Bayesian statistics we find that the 68% posterior probability region for the h^0 mass lies between 115.4 GeV and 120.4 GeV. Otherwise, h^0 is very similar to the Standard Model Higgs boson. Nevertheless, we point out some enhancements in its couplings to bottom and tau pairs, ranging from a few per cent in most of the CMSSM parameter space, up to several per cent in the favored region of tan(beta)\sim 50 and the pseudoscalar Higgs mass of m_A\lsim 1 TeV. We also find that the other Higgs bosons are typically heavier, although not necessarily much heavier. For values of the h^0 mass within the 95% probability range as determined by our analysis, a 95% CL exclusion limit can be set with about 2/fb of integrated luminosity per experiment, or else with 4/fb (12/fb) a 3 sigma evidence (5 sigma discovery) will be guaranteed. We also emphasize that the alternative statistical measure of the mean quality-of-fit favors a somewhat lower Higgs mass range; this implies even more optimistic prospects for the CMSSM light Higgs search than the more conservative Bayesian approach. In conclusion, for the above CMSSM parameter ranges, especially m_0, either some evidence will be found at the Tevatron for the light Higgs boson or, at a high confidence level, the CMSSM will be ruled out.Comment: JHEP versio

Implications for constrained supersymmetry of combined H.E.S.S. observations of dwarf galaxies, the Galactic halo and the Galactic Centre

In order to place limits on dark matter (DM) properties using $\gamma$-ray observations, previous analyses have often assumed a very simple parametrisation of the $\gamma$-ray annihilation yield; typically, it has been assumed that annihilation proceeds through a single channel only. In realistic DM models, annihilation may occur into many different final states, making this quite a rough ansatz. With additional processes like virtual internal bremsstrahlung and final state radiation, this ansatz becomes even more incorrect, and the need for scans of explicit model parameter spaces becomes clear. Here we present scans of the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM), considering $\gamma$-ray spectra from three dwarf galaxies, the Galactic Centre region and the broader Galactic halo, as obtained with the High-Energy Stereoscopic System (H.E.S.S.). We present a series of likelihood scans combining the H.E.S.S. data with other experimental results. We show that observations of the Sagittarius, Carina and Sculptor dwarf galaxies disfavour the coannihilation region of the CMSSM and models with large annihilation cross-sections. This is true even under reasonable assumptions about the DM density profiles, and constitutes the strongest constraint to date on coannihilation models within the CMSSM. The Galactic halo has a similar, but weaker, effect. The Galactic Centre search is complicated by a strong (unknown) $\gamma$-ray source, and we see no effect on the CMSSM parameter space when assuming a realistic Galactic Centre DM density profile.Comment: 18 pages, 10 figures Major changes: added H.E.S.S. results on halo and two additional dwarf galaxies, title, abstract and text changed accordingl

Combining outlier analysis algorithms to identify new physics at the LHC

The lack of evidence for new physics at the Large Hadron Collider so far has prompted the development of model-independent search techniques. In this study, we compare the anomaly scores of a variety of anomaly detection techniques: an isolation forest, a Gaussian mixture model, a static autoencoder, and a β-variational autoencoder (VAE), where we define the reconstruction loss of the latter as a weighted combination of regression and classification terms. We apply these algorithms to the 4-vectors of simulated LHC data, but also investigate the performance when the non-VAE algorithms are applied to the latent space variables created by the VAE. In addition, we assess the performance when the anomaly scores of these algorithms are combined in various ways. Using super- symmetric benchmark points, we find that the logical AND combination of the anomaly scores yielded from algorithms trained in the latent space of the VAE is the most effective discriminator of all methods tested.Melissa van Beekveld, Sascha Caron, Luc Hendriks, Paul Jackson, Adam Leinweber, Sydney Otten ... et al

Heart of Darkness: The Significance of the Zeptobarn Scale for Neutralino Direct Detection

The direct detection of dark matter through its elastic scattering off nucleons is among the most promising methods for establishing the particle identity of dark matter. The current bound on the spin-independent scattering cross section is sigma^SI < 10 zb for dark matter masses m_chi ~ 100 GeV, with improved sensitivities expected soon. We examine the implications of this progress for neutralino dark matter. We work in a supersymmetric framework well-suited to dark matter studies that is simple and transparent, with models defined in terms of four weak-scale parameters. We first show that robust constraints on electric dipole moments motivate large sfermion masses mtilde > 1 TeV, effectively decoupling squarks and sleptons from neutralino dark matter phenomenology. In this case, we find characteristic cross sections in the narrow range 1 zb 70 GeV. As sfermion masses are lowered to near their experimental limit mtilde ~ 400 GeV, the upper and lower limits of this range are extended, but only by factors of around two, and the lower limit is not significantly altered by relaxing many particle physics assumptions, varying the strange quark content of the nucleon, including the effects of galactic small-scale structure, or assuming other components of dark matter. Experiments are therefore rapidly entering the heart of dark matter-favored supersymmetry parameter space. If no signal is seen, supersymmetric models must contain some level of fine-tuning, and we identify and analyze several possibilities. Barring large cancellations, however, in a large and generic class of models, if thermal relic neutralinos are a significant component of dark matter, experiments will discover them as they probe down to the zeptobarn scale.Comment: 35 pages, 11 figures; v2: references added, figures extended to 2 TeV neutralino masses, XENON100 results included, published versio

Constraining the MSSM with universal gaugino masses and implication for searches at the LHC

Using a Markov chain Monte Carlo approach, we find the allowed parameter space of a MSSM model with seven free parameters. In this model universality conditions at the GUT scale are imposed on the gaugino sector. We require in particular that the relic density of dark matter saturates the value extracted from cosmological measurements assuming a standard cosmological scenario. We characterize the parameter space of the model that satisfies experimental constraints and illustrate the complementarity of the LHC searches, B-physics observables and direct dark matter searches for further probing the parameter space of the model. We also explore the different decay chains expected for the coloured particles that would be produced at LHC.Comment: 29 pages, 11 figure

A novel determination of the local dark matter density

We present a novel study on the problem of constructing mass models for the Milky Way, concentrating on features regarding the dark matter halo component. We have considered a variegated sample of dynamical observables for the Galaxy, including several results which have appeared recently, and studied a 7- or 8-dimensional parameter space - defining the Galaxy model - by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. The main result of this analysis is a novel determination of the local dark matter halo density which, assuming spherical symmetry and either an Einasto or an NFW density profile is found to be around 0.39 GeV cm$^{-3}$ with a 1-$\sigma$ error bar of about 7%; more precisely we find a $\rho_{DM}(R_0) = 0.385 \pm 0.027 \rm GeV cm^{-3}$ for the Einasto profile and $\rho_{DM}(R_0) = 0.389 \pm 0.025 \rm GeV cm^{-3}$ for the NFW. This is in contrast to the standard assumption that $\rho_{DM}(R_0)$ is about 0.3 GeV cm$^{-3}$ with an uncertainty of a factor of 2 to 3. A very precise determination of the local halo density is very important for interpreting direct dark matter detection experiments. Indeed the results we produced, together with the recent accurate determination of the local circular velocity, should be very useful to considerably narrow astrophysical uncertainties on direct dark matter detection.Comment: 31 pages,11 figures; minor changes in the text; two figures adde

Statistical coverage for supersymmetric parameter estimation: a case study with direct detection of dark matter

Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the employed statistical framework and scanning algorithm. In frequentist parameter estimation, a central requirement for properly constructed confidence intervals is that they cover true parameter values, preferably at exactly the stated confidence level when experiments are repeated infinitely many times. Since most widely-used scanning techniques are optimised for Bayesian statistics, one needs to assess their abilities in providing correct confidence intervals in terms of the statistical coverage. Here we investigate this for the Constrained Minimal Supersymmetric Standard Model (CMSSM) when only constrained by data from direct searches for dark matter. We construct confidence intervals from one-dimensional profile likelihoods and study the coverage by generating several pseudo-experiments for a few benchmark sets of pseudo-true parameters. We use nested sampling to scan the parameter space and evaluate the coverage for the benchmarks when either flat or logarithmic priors are imposed on gaugino and scalar mass parameters. The sampling algorithm has been used in the configuration usually adopted for exploration of the Bayesian posterior. We observe both under- and over-coverage, which in some cases vary quite dramatically when benchmarks or priors are modified. We show how most of the variation can be explained as the impact of explicit priors as well as sampling effects, where the latter are indirectly imposed by physicality conditions. For comparison, we also evaluate the coverage for Bayesian credible intervals, and observe significant under-coverage in those cases.Comment: 30 pages, 5 figures; v2 includes major updates in response to referee's comments; extra scans and tables added, discussion expanded, typos corrected; matches published versio

A Bayesian view of the current status of dark matter direct searches

Bayesian statistical methods offer a simple and consistent framework for incorporating uncertainties into a multi-parameter inference problem. In this work we apply these methods to a selection of current direct dark matter searches. We consider the simplest scenario of spin-independent elastic WIMP scattering, and infer the WIMP mass and cross-section from the experimental data with the essential systematic uncertainties folded into the analysis. We find that when uncertainties in the scintillation efficiency of Xenon100 have been accounted for, the resulting exclusion limit is not sufficiently constraining to rule out the CoGeNT preferred parameter region, contrary to previous claims. In the same vein, we also investigate the impact of astrophysical uncertainties on the preferred WIMP parameters. We find that within the class of smooth and isotropic WIMP velocity distributions, it is difficult to reconcile the DAMA and the CoGeNT preferred regions by tweaking the astrophysics parameters alone. If we demand compatibility between these experiments, then the inference process naturally concludes that a high value for the sodium quenching factor for DAMA is preferred.Comment: 37 pages, 14 figures and 7 tables. Replacement for matching the version accepted for publicatio