Solving the Inverse Source Problem in Femtoscopy with a Toy Model

TL;DR

This paper introduces a toy model using Tikhonov regularization to reconstruct source functions from correlation data in femtoscopy, demonstrating successful recovery of Gaussian sources in a controlled setting.

Contribution

It presents a novel application of Tikhonov regularization to solve the inverse source problem in femtoscopy using a simplified model, paving the way for more realistic source function extraction.

Findings

Gaussian source functions can be accurately reconstructed from CFs.

The toy model effectively demonstrates the potential of regularization methods in femtoscopy.

Reconstruction works for different potential strengths and source shapes.

Abstract

Hadron-hadron interactions, as a non-perturbative effect, play a significant role in understanding phenomenological problems in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are generally factorized into a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about hadron-hadron interactions. However, source functions remain ambiguous and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an ``inverse problem." To address it, we propose a toy model based on the Tikhonov regularization. Employing a square potential well of four distinct potential strengths, we calculate the CFs for inputs of a Gaussian source function and its hybrid form. The obtained CFs are subsequently used to reconstruct the source functions via the Tikhonov regularization. Our results demonstrate that the Gaussian source function can be successfully reconstructed, indicating the potential of this approach for extracting realistic source functions of hadron pairs of interest in the future.