Supersymmetry vis-`a-vis Observation: Dark Matter Constraints, Global Fits and Statistical Issues

Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I describe the theoretical foundations of supersymmetry, issues that it can address and concrete supersymmetric models that are widely used in phenomenological studies. I discuss how the predictions of supersymmetric models may be compared with observational data from both colliders and cosmology. I show why constraints on supersymmetric parameters by direct and indirect searches of particle dark matter are of particular interest in this respect. Gamma-ray observations of astrophysical sources, in particular dwarf spheroidal galaxies, by the Fermi satellite, and recording nuclear recoil events and energies by future ton-scale direct detection experiments are shown to provide powerful tools in searches for supersymmetric dark matter and estimating supersymmetric parameters. I discuss some major statistical issues in supersymmetric global fits to experimental data. In particular, I further demonstrate that existing advanced scanning techniques may fail in correctly mapping the statistical properties of the parameter spaces even for the simplest supersymmetric models. Complementary scanning methods based on Genetic Algorithms are proposed.

💡 Research Summary

The dissertation “Supersymmetry vis‑à‑vis Observation: Dark Matter Constraints, Global Fits and Statistical Issues” presents a comprehensive study of weak‑scale supersymmetry (SUSY) as a leading extension of the Standard Model, focusing on its ability to address both particle‑physics and cosmological puzzles. After a concise review of the theoretical motivations—hierarchy problem, gauge‑coupling unification, electroweak symmetry breaking, and the need for a dark matter candidate—the work concentrates on phenomenologically viable SUSY frameworks, especially the Constrained Minimal Supersymmetric Standard Model (CMSSM).

A major part of the thesis is devoted to confronting these models with real data. Using gamma‑ray observations of the dwarf spheroidal galaxy Segue 1 obtained by the Fermi‑LAT instrument, the author constructs a likelihood function for neutralino annihilation into photons and performs a Bayesian analysis with the SuperBayeS package. The analysis incorporates cosmological relic‑density constraints, electroweak precision observables, B‑physics measurements, and collider limits on sparticle masses, thereby achieving a full global fit. The results illustrate how indirect detection can carve out significant regions of the CMSSM parameter space, especially in the (m₀, m½, tanβ) directions.

The thesis then turns to future direct‑detection experiments. By modelling the projected sensitivity of ton‑scale detectors such as XENON‑1T and LZ, the author evaluates how forthcoming nuclear‑recoil measurements could further restrict the CMSSM. The study emphasizes the importance of statistical coverage: a 95 % confidence interval derived from an inadequate sampling algorithm may fail to contain the true parameter values with the advertised probability.

A central methodological contribution is the introduction of a Genetic Algorithm (GA) based scanning technique. Traditional sampling methods (Markov Chain Monte Carlo, Nested Sampling, MultiNest) often struggle with the highly multimodal likelihood surfaces characteristic of SUSY models, leading to poor exploration of high‑likelihood islands and biased posterior estimates. The GA implementation creates an initial population of random parameter points, evaluates their fitness via the likelihood, and iteratively applies selection, crossover, and mutation operators. This evolutionary process efficiently discovers globally optimal regions and improves the uniformity of parameter‑space coverage. Comparative studies show that the GA recovers high‑likelihood points missed by conventional Bayesian scans and yields more reliable confidence intervals.

Four accompanying papers (Paper I–IV) encapsulate the research:

• Paper I: “Direct constraints on minimal supersymmetry from Fermi‑LAT observations of Segue 1” – demonstrates indirect detection constraints using Bayesian inference.
• Paper II: “A profile likelihood analysis of the constrained MSSM with genetic algorithms” – introduces the GA scanner and validates its performance.
• Paper III: “How well will ton‑scale dark matter direct detection experiments constrain minimal supersymmetry?” – projects future direct‑detection limits.
• Paper IV: “Statistical coverage for supersymmetric parameter estimation: a case study with direct detection of dark matter” – analyses the coverage problem and shows GA’s advantage.

Overall, the dissertation provides a thorough synthesis of SUSY theory, observational constraints, and advanced statistical techniques. It highlights that while supersymmetry remains an attractive solution to fundamental problems, extracting robust conclusions from the ever‑growing data sets requires careful treatment of statistical uncertainties and efficient exploration of high‑dimensional parameter spaces. The proposed GA‑based approach represents a significant methodological advance, offering improved reliability for global fits and paving the way for future studies that will combine LHC results, indirect astrophysical signals, and next‑generation direct‑detection experiments.