I=3 Three-Pion Scattering Amplitude from Lattice QCD

Area of Science:

• Nuclear Physics
• Quantum Chromodynamics
• Particle Physics

Background:

• Analysis of two- and three-pion states is crucial for understanding the strong nuclear force.
• Recent experimental data for isosymmetric QCD with a pion mass of approximately 200 MeV provides a new avenue for theoretical investigation.

Purpose of the Study:

• To analyze the spectrum of two- and three-pion states in isosymmetric QCD.
• To investigate the scattering amplitude of three-pion systems and compare with theoretical models.
• To examine the two-pion spectrum and its consistency with chiral perturbation theory.

Main Methods:

• Utilizing the relativistic three-particle quantization condition to analyze experimental data.
• Comparing results with leading-order chiral perturbation theory predictions.
• Fitting the two-pion spectrum using an s-wave phase shift incorporating the Adler zero.

Main Results:

• Approximately 2-sigma evidence for a nonzero contact part of the three-pion (3π⁺, I=3) scattering amplitude was found.
• Good agreement between the analyzed spectrum and chiral perturbation theory at the threshold was observed.
• Some tension was noted in the energy-dependent part of the three-pion scattering amplitude.
• The two-pion (2π⁺, I=2) spectrum was well-described by an s-wave phase shift including the Adler zero.

Conclusions:

• The study provides evidence for non-trivial interactions in three-pion systems.
• The results offer insights into the low-energy behavior of quantum chromodynamics (QCD).
• The findings support the applicability of chiral perturbation theory at threshold while highlighting areas for further investigation.