
Antoni J. Woss, Christopher E. Thomas, Jozef J. Dudek, Robert G. Edwards and David J. Wilson (for the Hadron Spectrum Collaboration).
arxiv.org/abs/1904.04136
A preprint with members of the Hadron Spectrum Collaboration has appeared
In this article, we present the first lattice QCD calculation of coupled $\pi\omega$ and $\pi\phi$ scattering, incorporating coupled $S$ and $D$wave $\pi\omega$ in $J^P=1^+$. Finitevolume spectra in three volumes are determined via a variational analysis of matrices of twopoint correlation functions, computed using large bases of operators resembling singlemeson, twomeson and threemeson structures, with the lightquark mass corresponding to a pion mass of $m_\pi \approx 391$ MeV. Utilizing the relationship between the discrete spectrum of finitevolume energies and infinitevolume scattering amplitudes, we find a narrow axialvector 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 muchsuppressed 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 lowmass $Z_s$ analogue of the $Z_c$ claimed in $\pi J/\psi$. In order to minimally present the contents of a unitary threechannel scattering matrix, we introduce an $n$channel generalization of the traditional twochannel Stapp parameterization.


David J. Wilson, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards and Christopher E. Thomas (for the Hadron Spectrum Collaboration).
arxiv.org/abs/arXiv:1904.03188
A preprint with members of the Hadron Spectrum Collaboration has appeared
We present a determination of the isospin$\frac{1}{2}$ elastic $\pi K$ scattering amplitudes in $S$ and $P$ partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of realvalued energy points, are obtained as a function of lightquark mass, corresponding to four pion masses between 200 and 400 MeV. Below the first inelastic threshold, the $P$wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable boundstate at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $\kappa$/$K_0^\star(700)$like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of preciselydetermined lattice QCD amplitudes on the real energy axis are not sufficient to modelindependently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.


Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards and David J. Wilson (for the Hadron Spectrum Collaboration).
Published in Phys.Rev.D 97, 054513 (2018)
A recent article with members of the Hadron Spectrum Collaboration was promoted as an Editors' Suggestion in Physical Review D.
In this article, we present the first lattice QCD study of coupled isoscalar $\pi\pi,K\overline{K},\eta\eta$ $S$ and $D$wave scattering extracted from discrete finitevolume spectra computed on lattices which have a value of the quark mass corresponding to $m_\pi\sim391$~MeV. In the $J^P=0^+$ sector we find analogues of the experimental $\sigma$ and $f_0(980)$ states, where the $\sigma$ appears as a stable boundstate below $\pi\pi$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $\pi\pi$ cross section in the vicinity of the $K\overline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2'(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $\pi\pi$ and the heavier state to $K\overline{K}$. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.


Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards and David J. Wilson (for the Hadron Spectrum Collaboration).
Published in Phys.Rev.Lett. 118 (2017) no.2, 022002
A recent article with members of the Hadron Spectrum Collaboration was featured on the cover of Physical Review Letters.
In this article, we present for the first time a determination of the energy dependence of the isoscalar $\pi\pi$ elastic scattering phase shift within a firstprinciples numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the
Swave phase shift up to the $K\bar{K}$ threshold. Calculations are performed at two values of the u,d quark mass corresponding to
$m_\pi=236,391$ MeV, and the resulting amplitudes are described in terms of a $\sigma$ meson which evolves from a bound state below the
$\pi\pi$ threshold at the heavier quark mass to a broad resonance at the lighter quark mass.


Graham Moir, Michael Peardon, Sinéad M. Ryan, Christopher E. Thomas and David J. Wilson (for the Hadron Spectrum Collaboration).
Published in JHEP 1610 (2016) 011
In this study, we present the first lattice QCD study of coupledchannel $D\pi$, $D\eta$ and $D_{s}\bar{K}$ scattering in isospin1/2 in three partial waves. Using distillation, we compute matrices of correlation functions with bases of operators capable of resolving both meson and mesonmeson contributions to the spectrum. These correlation matrices are analysed using a variational approach to extract the finitevolume energy eigenstates. Utilising Lüscher's method and its extensions, we constrain scattering amplitudes in $S$, $P$ and $D$wave as a function of energy. By analytically continuing the scattering amplitudes to complex energies, we investigate the $S$matrix singularities. Working at $m_\pi \approx 391$ MeV, we find a pole corresponding to a $J^{P} = 0^{+}$ nearthreshold bound state with a large coupling to $D\pi$. We also find a deeply bound $J^{P} = 1^{}$ state, and evidence for a $J^{P} = 2^{+}$ narrow resonance coupled predominantly to $D\pi$.


Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, Christian J. Shultz, Christopher E. Thomas and David J. Wilson (for the Hadron Spectrum Collaboration).
Published in Phys.Rev. D93 (2016) no.11, 114508
In this paper, we present a determination of the $P$wave $\pi\pi\to\pi\gamma^\star$ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finitevolume are extracted from threepoint correlation functions, and from these we determine the infinitevolume amplitude using a generalization of the LellouchLüscher formalism. We determine the amplitude for a range of discrete values of the $\pi\pi$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $\rho$ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the $\rho$ pole extract the $\rho\to \pi \gamma^\star$ transition form factor. This calculation, at $m_\pi\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.


Jozef J. Dudek, Robert G. Edwards and David J. Wilson (for the Hadron Spectrum Collaboration)
Published in Phys.Rev. D93 (2016) no.9, 094506
In this article, we present the first calculation of coupledchannel mesonmeson scattering in the isospin $=1$, $G$parity negative sector, with channels $\pi\eta$, $K\bar K$ and $\pi\eta^\prime$, in a firstprinciples approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the $S$matrix, and find that the $S$wave features a prominent cusplike structure in $\pi\eta \to \pi\eta$ close to $K\bar{K}$ threshold coupled with a rapid turn on of amplitudes leading to the $K\bar K$ finalstate. This behavior is traced to an $a_0(980)$like resonance, strongly coupled to both $\pi\eta$ and $K\bar K$, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of $D$wave scattering suggests a narrow tensor resonance at higher energy.
