The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD

Abstract

Focusing on three-pion states with maximal isospin (${\pi }^{+}{\pi }^{+}{\pi }^{+}$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

22 pages, 7 figures, 11 tables, CERN-TH-2020-147, JLAB-THY-20-3242, v2: minor edits, add references, added a curve to Fig. 2; corresponds to version published in PRL

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• Multi-particle systems on the lattice and chiral extrapolations: a brief review
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• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Solving relativistic three-body integral equations in the presence of bound states
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• Finite-volume energy shift of the three-pion ground state
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
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• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
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• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Hamiltonian effective field theory in elongated or moving finite volume
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• Charmonium ${\chi }_{c0}$ and ${\chi }_{c2}$ resonances in coupled-channel scattering from lattice QCD
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• Position-space sampling for local multiquark operators in lattice QCD using distillation and the importance of tetraquark operators for $T_{cc}(3875{)}^{+}$
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Higher order quantization conditions for two spinless particles