Alternative to χ² minimization for ρ(770) pole extraction

Determine whether a parameter-estimation method distinct from χ² minimization—specifically, simulation-based inference using deep neural networks trained on pseudodata generated from K-matrix parameterizations of ππ P-wave scattering—can mitigate inconsistencies in ππ phase-shift data and yield accurate determinations of the ρ(770) resonance pole position via analytic continuation to the relevant unphysical Riemann sheet.

Background

The pole position of the ρ(770) resonance is a universal parameter extracted from ππ scattering amplitudes by fitting models to data and performing analytic continuation. Standard practice employs χ² minimization to estimate model parameters; however, long-standing inconsistencies have been observed between pole positions extracted from specific ππ datasets (e.g., Protopopescu and Estabrooks) and global values compiled by the PDG, suggesting potential issues in data or model specification.

Simulation-based inference (SBI) provides an alternative approach that uses model-generated pseudodata and neural networks to infer parameter posteriors. The paper investigates whether SBI can deliver more robust pole estimates under model misspecification, motivating the explicit question of whether methods other than χ² minimization can mitigate data inconsistencies in ρ(770) pole extraction.