Two-Pole Nature of the Λ(1405) Resonance from Lattice QCD.

This Letter presents the first lattice QCD computation of the coupled channel πΣ-K[over ¯]N scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance Λ(1405) with strangeness S=-1 and isospin, spin, and parity quantum numbers I(J^{P})=0(1/2^{-}). However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to m_{π}≈200 MeV and m_{K}≈487 MeV, this study finds the amplitudes exhibit a virtual bound state below the πΣ threshold in addition to the established resonance pole just below the K[over ¯]N threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity.

The large N c limit of QCD on the lattice.

We review recent progress in the study of the large N c limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of O ( N c - 1 ) corrections for values of N c ≳ 3 . Some concrete examples of the topics we include are tests of large- N c factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the Δ I = 1 / 2 rule in kaon decays.

I=3 Three-Pion Scattering Amplitude from Lattice QCD.

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.