The vast majority of hadrons are resonances, seen experimentally through decays into a multitude of other hadrons in various angular distributions and corresponding to pole singularities in scattering amplitudes. Resonances which decay into two pseudoscalar mesons (mesons with JP=0–, where J is spin and P is parity) have been studied extensively using first-principles lattice QCD calculations over the last decade. However, all but the simplest resonances have decay channels which involve hadrons with non-zero spin and, in particular, those with ‘unnatural’ spin parity, JP=0–, 1+, 2–, are forbidden to decay to two psuedoscalars. Calculations of these scattering channels are significantly more complicated.
In a recent publication [arXiv:1904.04136, Phys. Rev. D 100, 054506 (2019)], we studied the axial-vector resonance (JP=1+). Experimentally its decay channels include πω and πφ, where π is a pseudoscalar meson (JP=0–) and ω, φ are vector mesons (JP=1–). The non-zero spin of the vector mesons means that the decay may feature a superposition of orbital angular momentum L=0 (S-wave) and L=2 (D-wave). Working with heavier-than-physical light quarks such that the π mass is 391 MeV, we performed the first lattice QCD computation of the relevant coupled scattering amplitudes – the resulting squared-amplitudes for πω in S-wave and D-wave, and πφ in D-wave are shown in the figure below (upper panels) labelled by 2S+1LJ. Notably, we observe a bump-like enhancement in S-wave πω, suggestive of a narrow resonance, and we indeed find a pole in the analytic continuation of the amplitudes to complex energies (lower panel) – the real and imaginary parts are related to the mass (mR) and width (ΓR) respectively, and the strengths of the coupling to each channel (|c|) are also shown. Interestingly, the absence of significant enhancement in S-wave πφ suggests no evidence for a ZS, proposed as an analogue of the enigmatic Zc(3900) observed in πJ/ψ. This work opens the door to investigating the π1(1600) exotic light resonance, nucleon resonances such as the Roper, and puzzling structures observed in the charmonium and bottomonium sectors.