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Published on: November 15, 2013
Energy-Dependent π^{+}π^{+}π^{+} Scattering Amplitude from QCD
Maxwell T Hansen1,2, Raul A Briceño3,4, Robert G Edwards3
1Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland.
This study provides the first nonperturbative calculation of three-pion scattering amplitude using lattice quantum chromodynamics (QCD). The results reveal complex interactions and energy-dependent behavior in three-hadron systems.
Area of Science:
- Quantum Chromodynamics (QCD)
- Hadron Spectroscopy
- Nuclear Physics
Background:
- Understanding multi-hadron interactions is crucial in nuclear physics.
- Previous studies lacked nonperturbative, energy-dependent three-hadron scattering amplitudes.
- Lattice QCD provides a first-principles approach to strong interaction physics.
Purpose of the Study:
- To perform the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude.
- To analyze the interactions of three-pion states (π⁺π⁺π⁺) with maximal isospin.
- To connect finite-volume lattice QCD calculations with physical scattering amplitudes.
Main Methods:
- Utilizing numerical lattice QCD to extract three-hadron energies in a finite volume.
- Applying a relativistic finite-volume formalism to interpret the lattice data.
- Solving integral equations to relate the three-body K matrix to the scattering amplitude.
Main Results:
- The first nonperturbative, energy-dependent three-pion scattering amplitude was determined.
- The amplitude exhibits a complex analytic structure.
- A detailed dependence on two-pion invariant masses was observed and visualized using Dalitz-like plots.
Conclusions:
- This work establishes a novel method for calculating multi-hadron scattering amplitudes from QCD.
- The findings offer new insights into the dynamics of three-body interactions in strongly interacting systems.
- The results pave the way for future investigations of complex hadronic systems from first principles.
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