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Effective-Range Expansion with a Long-Range Force.

Meng-Lin Du1, Feng-Kun Guo2,3,4, Bing Wu1

  • 1University of Electronic Science and Technology of China, School of Physics, Chengdu 611731, China.

Physical Review Letters
|July 31, 2025
PubMed
Summary
This summary is machine-generated.

A new parametrization extends effective range expansion to include left-hand cuts, improving low-energy scattering analysis. This method accurately models systems with long-range forces, crucial for understanding particle and nuclear physics phenomena.

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Area of Science:

  • Nuclear Physics
  • Quantum Mechanics
  • Particle Physics

Background:

  • Effective range expansion (ERE) is limited by left-hand cuts near two-particle thresholds.
  • Left-hand cuts arise from light particle exchange, causing long-range forces in various systems.
  • This limitation hinders precise extraction of low-energy scattering observables and resonance poles.

Purpose of the Study:

  • To propose a novel parametrization for low-energy scattering amplitude that incorporates left-hand cuts.
  • To extend the capabilities of the effective range expansion for systems with Yukawa-type interactions.
  • To provide a versatile tool for analyzing diverse physical systems and phenomena.

Main Methods:

  • Developed a Padé-like approximation incorporating nonanalytic terms from the left-hand cut.
  • The parametrization accounts for both short- and long-range interactions.
  • Applied the method to systems with Yukawa-type interactions.

Main Results:

  • The new parametrization successfully extends the validity of effective range expansions.
  • It enables precise extraction of low-energy scattering observables and resonance poles.
  • The method is applicable to particle, hadronic, nuclear, cold atom, and quantum gas systems.

Conclusions:

  • The proposed parametrization is a versatile tool for low-energy scattering physics.
  • It is particularly valuable for studying near-threshold hadron resonances.
  • The method also allows extraction of exchanged particle couplings and analysis of amplitude zeros.