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Bootstrapping QCD Using Pion Scattering Amplitudes.

Andrea L Guerrieri1, João Penedones2, Pedro Vieira3

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This summary is machine-generated.

This study explores the S-matrix bootstrap for four-dimensional scattering amplitudes with O(3) symmetry. It maps the complex space of pion interactions, revealing unique structures and pinpointing QCD

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Quantum Field Theory

Background:

  • The S-matrix bootstrap provides a powerful, model-independent approach to studying scattering amplitudes.
  • Understanding the low-energy behavior of strongly interacting theories, like those involving pions, is crucial.
  • O(3) symmetry simplifies scattering problems, offering a tractable framework for exploration.

Purpose of the Study:

  • To investigate the allowed parameter space of scattering lengths in a four-dimensional theory with O(3) symmetry.
  • To apply the S-matrix bootstrap formalism to pion physics, incorporating their characteristic chiral zeros.
  • To map the multidimensional space of chiral zero positions, scattering lengths, and resonance masses.

Main Methods:

  • Utilizing the S-matrix bootstrap to constrain scattering amplitudes.
  • Analyzing the parameter space defined by scattering lengths and chiral zero positions.
  • Comparing theoretical predictions with experimental and theoretical expectations for Quantum Chromodynamics (QCD).

Main Results:

  • The study reveals complex structures, including 'lakes,' 'peninsulas,' and 'kinks,' within the multidimensional parameter space.
  • Specific regions of this space correspond to different interaction regimes and theoretical constraints.
  • The formalism successfully maps the interplay between scattering parameters and the properties of emergent resonances.

Conclusions:

  • The S-matrix bootstrap offers a robust method for exploring non-perturbative aspects of quantum field theories.
  • The identified structures in the parameter space provide insights into the rich phenomenology of pion interactions.
  • The apparent location of Quantum Chromodynamics (QCD) within these plots suggests the predictive power of the bootstrap approach for strongly coupled systems.