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Rigorous Bounds on the Analytic S Matrix.

Andrea Guerrieri1, Amit Sever1

  • 1School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel.

Physical Review Letters
|January 14, 2022
PubMed
Summary

We used the S-matrix bootstrap method to find numerical bounds for particle scattering. This approach rigorously uses fundamental properties of scattering amplitudes in multiple dimensions.

Area of Science:

  • Theoretical physics
  • Quantum field theory
  • High-energy physics

Background:

  • The S-matrix bootstrap is a powerful theoretical framework.
  • Analyticity, crossing, and unitarity are fundamental properties of scattering amplitudes.

Purpose of the Study:

  • To apply a dual S-matrix bootstrap approach in d≥3 space-time dimensions.
  • To derive rigorous numerical bounds on the quartic coupling for scalar particle scattering.

Main Methods:

  • Utilizing a dual S-matrix bootstrap approach.
  • Relying on rigorously proven analyticity, crossing, and unitarity properties.
  • Numerical computations in four dimensions.

Main Results:

  • Rigorous upper and lower numerical bounds were established for the quartic coupling.

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  • Demonstrated the efficacy of the S-matrix bootstrap for quantitative predictions.

    • Conclusions:

    • The S-matrix bootstrap provides a viable method for bounding physical parameters.
    • The approach is applicable in dimensions d≥3, with a specific application in d=4.