Abstract
We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass M≈200 MeV in Hörz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.142002]. Using the relativistic three-particle quantization condition, we find ∼2σ evidence for a nonzero value for the contact part of the 3π^{+} (I=3) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold and some tension in the energy dependent part of the 3π^{+} scattering amplitude. We also find that the 2π^{+} (I=2) spectrum is fit well by an s-wave phase shift that incorporates the expected Adler zero.
Highlights
Introduction.—Lattice QCD (LQCD) provides a powerful tool for ab initio calculations of strong-interaction scattering amplitudes
Precise results were presented for the spectrum of 2πþ and 3πþ states in OðaÞ-improved isosymmetric QCD with pions having close to physical mass, M ≈ 200 MeV [58]
Sixteen 2πþ levels and eleven 3πþ levels were obtained below the respective inelastic threshpoldffiffisffiffiffiffiffiaffiffitffiffiffiffiffiEffiffi Ã2 1⁄4 4M and EÃ 1⁄4 5M, Here, EÃ2 and EÃ 1⁄4 E2 − P⃗ 2 are the corresponding center-of-mass energies, with E the total three-particle energy
Summary
Introduction.—Lattice QCD (LQCD) provides a powerful (if indirect) tool for ab initio calculations of strong-interaction scattering amplitudes. The application to LQCD results has, so far, been restricted to the energy of the three-particle ground state, either using the threshold expansion [55,56,57], or, more recently, the FVU approach for 3πþ [51]. Formalism and implementation.—All approaches to determining three-particle scattering amplitudes using LQCD proceed in two steps, which we outline here.
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