Some inverse problems in particle physics

Area of Science:

• Particle Physics
• Computational Physics

Background:

• Inverse problems are fundamental in particle phenomenology.
• Extracting Parton Distribution Functions (PDFs) and spectral functions are key research areas.

Purpose of the Study:

• To investigate methods for extracting Parton Distribution Functions (PDFs) and spectral functions.
• To compare Backus-Gilbert, Gaussian Processes, and Neural Network approaches for inverse problems in particle physics.

Main Methods:

• Focus on two examples: Parton Distribution Function (PDF) extraction and spectral function extraction.
• Utilize experimental data, pseudo-PDFs, and quasi-PDFs from lattice Quantum Chromodynamics (QCD).
• Detail three distinct methodologies: Backus-Gilbert, Gaussian Processes, and Neural Network parametrizations.

Main Results:

• Comparative analysis of the three inverse problem-solving approaches.
• Demonstration of the application of these methods to specific problems in particle phenomenology.
• Insights into the strengths and limitations of each method for data analysis.

Conclusions:

• The choice of method depends on the specific inverse problem and available data.
• Neural Network parametrizations offer a flexible approach for complex data fitting.
• Further research is needed to optimize these methods for precision physics.