From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude

TL;DR

This paper develops a novel method combining S-matrix Bootstrap and optimization techniques to construct a comprehensive pion scattering amplitude that fits experimental and lattice data, aligning with QCD predictions and revealing new resonances.

Contribution

It introduces a UV complete amplitude ansatz for pion scattering that satisfies fundamental constraints and incorporates advanced numerical methods for data fitting.

Findings

Amplitude fits experimental and lattice data below 1.4 GeV

Predicts the D2 phase shift and a spin three state

Identifies a potential tetraquark resonance around 2 GeV

Abstract

We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $\pi\pi$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $\pi \pi$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $\chi$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons.