Feroz, F., Cranmer, K., Hobson, M., Ruiz de Austri, R., & Trotta, R. (2011). Challenges of profile likelihood evaluation in multi-dimensional SUSY scans. J. High Energy Phys., 06(6), 042–23pp.
Abstract: Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MULTINEST, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration previously used in the literarture is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MULTINEST configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MULTINEST is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.
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Roszkowski, L., Ruiz de Austri, R., & Trotta, R. (2010). Efficient reconstruction of constrained MSSM parameters from LHC data: A case study. Phys. Rev. D, 82(5), 055003–12pp.
Abstract: We present an efficient method of reconstructing the parameters of the constrained MSSM from assumed future LHC data, applied both on their own right and in combination with the cosmological determination of the relic dark matter abundance. Focusing on the ATLAS SU3 benchmark point, we demonstrate that our simple Gaussian approximation can recover the values of its parameters remarkably well. We examine two popular noninformative priors and obtain very similar results, although when we use an informative, naturalness-motivated prior, we find some sizeable differences. We show that a further strong improvement in reconstructing the SU3 parameters can by achieved by applying additional information about the relic abundance at the level of WMAP accuracy, although the expected data from Planck will have only a very limited additional impact. Further external data may be required to break some remaining degeneracies. We argue that the method presented here is applicable to a wide class of low-energy effective supersymmetric models, as it does not require one to deal with purely experimental issues, e.g., detector performance, and has the additional advantages of computational efficiency. Furthermore, our approach allows one to distinguish the effect of the model's internal structure and of the external data on the final parameters constraints.
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Bertone, G., Cerdeño, D. G., Fornasa, M., Ruiz de Austri, R., & Trotta, R. (2010). Identification of dark matter particles with LHC and direct detection data. Phys. Rev. D, 82(5), 055008–7pp.
Abstract: Dark matter (DM) is currently searched for with a variety of detection strategies. Accelerator searches are particularly promising, but even if weakly interacting massive particles are found at the Large Hadron Collider (LHC), it will be difficult to prove that they constitute the bulk of the DM in the Universe Omega(DM). We show that a significantly better reconstruction of the DM properties can be obtained with a combined analysis of LHC and direct detection data, by making a simple Ansatz on the weakly interacting massive particles local density rho(0)((chi) over bar1), i.e., by assuming that the local density scales with the cosmological relic abundance, (rho(0)((chi) over bar1)/rho(DM)) = (Omega(0)((chi) over bar1)/Omega(DM)). We demonstrate this method in an explicit example in the context of a 24-parameter supersymmetric model, with a neutralino lightest supersymmetric particle in the stau coannihilation region. Our results show that future ton-scale direct detection experiments will allow to break degeneracies in the supersymmetric parameter space and achieve a significantly better reconstruction of the neutralino composition and its relic density than with LHC data alone.
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