The \(b_1\) resonance in coupled \(\pi\omega\), \(\pi\phi\) scattering from lattice QCD

• Published in: arXiv.org 2019-04
• Main Authors: Woss, Antoni J, Thomas, Christopher E, Dudek, Jozef J, Edwards, Robert G, Wilson, David J
• Format: Article
• Language: English
• Subjects: Correlation analysis; Coupling; Mathematical analysis; Operators (mathematics); Parameterization; Personal computers; Quantum chromodynamics; Resonance scattering
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1904.04136

We present the first lattice QCD calculation of coupled \(\pi\omega\) and \(\pi\phi\) scattering, incorporating coupled \(S\) and \(D\)-wave \(\pi\omega\) in \(J^P=1^+\). Finite-volume spectra in three volumes are determined via a variational analysis of matrices of two-point correlation functions, computed using large bases of operators resembling single-meson, two-meson and three-meson structures, with the light-quark mass corresponding to a pion mass of \(m_\pi \approx 391\) MeV. Utilizing the relationship between the discrete spectrum of finite-volume energies and infinite-volume scattering amplitudes, we find a narrow axial-vector resonance (\(J^{PC}=1^{+-}\)), the analogue of the \(b_1\) meson, with mass \(m_{R}\approx1380\) MeV and width \(\Gamma_{R}\approx 91\) MeV. The resonance is found to couple dominantly to \(S\)-wave \(\pi\omega\), with a much-suppressed coupling to \(D\)-wave \(\pi\omega\), and a negligible coupling to \(\pi\phi\) consistent with the `OZI rule'. No resonant behavior is observed in \(\pi\phi\), indicating the absence of a putative low-mass \(Z_s\) analogue of the \(Z_c\) claimed in \(\pi J/\psi\). In order to minimally present the contents of a unitary three-channel scattering matrix, we introduce an \(n\)-channel generalization of the traditional two-channel Stapp parameterization.