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Isoscalar ππ Scattering and the σ Meson Resonance from QCD.

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This study determines the energy-dependent isoscalar pi pi elastic scattering phase shift using lattice quantum chromodynamics (QCD). We observed the sigma meson evolving from a bound state to a resonance.

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Area of Science:

  • Quantum Chromodynamics (QCD)
  • Particle Physics
  • Hadron Spectroscopy

Background:

  • Understanding the properties of mesons and their interactions is crucial in particle physics.
  • The isoscalar S-wave pi pi elastic scattering phase shift, particularly the behavior of the sigma meson, presents a long-standing challenge.
  • First-principles calculations are needed to reliably determine these properties from fundamental theory.

Purpose of the Study:

  • To determine the energy dependence of the isoscalar pi pi elastic scattering phase shift.
  • To investigate the nature of the sigma meson using a first-principles lattice QCD approach.
  • To explore the influence of quark mass on the sigma meson's properties.

Main Methods:

  • Employed a first-principles numerical lattice quantum chromodynamics (QCD) approach.
  • Computed hadronic correlation functions, including all necessary quark propagation diagrams.
  • Extracted the discrete spectrum of states from the volume dependence of the lattice spectrum to obtain the S-wave phase shift.

Main Results:

  • Successfully determined the energy dependence of the isoscalar pi pi elastic scattering phase shift up to the K K-bar threshold.
  • Observed the sigma meson evolving from a bound state below the pi pi threshold at heavier quark masses to a broad resonance at lighter quark masses.
  • Calculations were performed at two distinct light quark masses (corresponding to m_pi = 236, 391 MeV).

Conclusions:

  • This work provides the first lattice QCD determination of the energy-dependent isoscalar pi pi elastic scattering phase shift.
  • The results confirm the evolving nature of the sigma meson with changing quark mass.
  • The study demonstrates the power of lattice QCD for investigating hadron properties and interactions.