Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition

We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describing $J^P=1^-$ and $1^+$ scattering in several coupled channels

Resonances in coupled πk,ηK scattering from lattice QCD

Coupled-channel $\pi K$ and $\eta K$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $q\bar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_\pi=391\,\mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $\pi K$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $\pi K$ and weakly to $\eta K$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $\kappa$ resonance. A bound state with $J^P=1^-$ is found very close to the $\pi K$ threshold energy, whose coupling to the $\pi K$ channel is compatible with that of the experimental $K^\star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $\pi K$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.We thank our colleagues within the Hadron Spectrum Collaboration. We also thank R. Briceno, M.R. Pennington, C.J.Shultz and A.P. Szczepaniak for fruitful discussions. Chroma [63] and QUDA [64, 65] were used to perform this work on clusters at Jefferson Laboratory under the USQCD Initiative and the LQCD ARRA project. Gauge configurations were generated using resources awarded from the U.S. Department of Energy INCITE program at Oak Ridge National Lab, the NSF Teragrid at the Texas Advanced Computer Center and the Pittsburgh Supercomputer Center, as well as at Jefferson Lab. RGE and JJD acknowledge support from U.S. Department of Energy contract DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Laboratory. JJD acknowledges support from the U.S. Department of Energy Early Career award contract DE-SC0006765. CET acknowledges partial support from the Science and Technology Facilities Council (U.K.) [grant number ST/L000385/1].This is the accepted manuscript. The final version is available at http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.054008

Decays of an exotic 1-+ hybrid meson resonance in QCD

We present the first determination of the hadronic decays of the lightest exotic $J^{PC}=1^{-+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass giving $m_\pi \sim 700$ MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically-closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad $\pi_1$ resonance decaying dominantly through the $b_1 \pi$ mode with much smaller decays into $f_1 \pi$, $\rho \pi$, $\eta' \pi$ and $\eta \pi$. A large total width is potentially in agreement with the experimental $\pi_1(1564)$ candidate state, observed in $\eta \pi$, $\eta' \pi$, which we suggest may be heavily suppressed decay channels

B1 resonance in coupled πω, πφ scattering from lattice QCD

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

An a0 resonance in strongly coupled πη, K K scattering from lattice QCD a0 RESONANCE in STRONGLY COUPLED ⋯ DUDEK, EDWARDS, and WILSON

We present the first calculation of coupled-channel meson-meson scattering in the isospin $=1$, $G$-parity negative sector, with channels $\pi \eta$, $K\overline{K}$ and $\pi \eta'$, in a first-principles 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 cusp-like structure in $\pi \eta \to \pi \eta$ close to $K\overline{K}$ threshold coupled with a rapid turn on of amplitudes leading to the $K\overline{K}$ final-state. This behavior is traced to an $a_0(980)$-like resonance, strongly coupled to both $\pi \eta$ and $K\overline{K}$, 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.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevD.93.09450

Isoscalar ππ Scattering and the σ Meson Resonance from QCD

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase shift within a first-principles 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 $\textit{S}$-wave phase shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $\textit{u}$, $\textit{d}$ quark mass corresponding to $\textit{m}_{\pi} = 236, 391$ MeV , and the resulting amplitudes are described in terms of a σ meson which evolves from a bound state below the ππ threshold at the heavier quark mass to a broad resonance at the lighter quark mass.The research was supported in part under an Advanced Scientific Computing Research (ASCR), Advanced Leadership Computing Challenge (ALCC) grant, and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This research is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Grants No. OCI-0725070 and No. ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing computing resources. Gauge configurations were generated using resources awarded from the U.S. Department of Energy Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program at Oak Ridge National Lab and also resources awarded at NERSC. R. A. B., R. G. E., and J. J. D. acknowledge support from U.S. Department of Energy Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab. J. J. D. acknowledges support from the U.S. Department of Energy Early Career Contract No. DE-SC0006765. D. J. W. acknowledges support from the Isaac Newton Trust/University of Cambridge Early Career Support Scheme [RG74916]

Coupled ππ, KK¯ scattering in P-wave and the ρ resonance from lattice QCD

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_\pi = 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $\pi\pi$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $\pi\pi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $\rho$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.We thank our colleagues within the Hadron Spectrum Collaboration, and in particular, thank B´alint Jo´o for his help. The software codes Chroma [43], QUDA [34, 35], QPhiX [44], and QOPQDP [32, 33] were used to compute the propagators required for this project. The contractions were performed on clusters at Jefferson Laboratory under the USQCD Initiative and the LQCD ARRA project. This research was supported in part under an ALCC award, and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC05-00OR22725. This research is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This work is also part of the PRAC “Lattice QCD on Blue Waters”. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. Gauge configurations were generated using resources awarded from the U.S. Department of Energy INCITE program at Oak Ridge National Lab, and also resources awarded at NERSC. RAB, RGE and JJD acknowledge support from U.S. Department of Energy contract DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Laboratory. JJD acknowledges support from the U.S. Department of Energy Early Career award contract DESC0006765. CET acknowledges partial support from the U.K. Science and Technology Facilities Council [grant number ST/L000385/1].This is the author accepted manuscript. The final version is available from APSvia http://dx.doi.org/10.1103/PhysRevD.92.09450

Glimpsing Colour in a World of Black and White

The past 40 years have taught us that nucleons are built of constituents that carry colour charges with interactions governed by Quantum Chromodynamics (QCD). How experiments (past, present and future) at Jefferson Lab probe colourless nuclei to map out these internal colour degrees of freedom is presented. When combined with theoretical calculations, these will paint a picture of how the confinement of quarks and gluons, and the structure of the QCD vacuum, determine the properties of all (light) strongly interacting states.Comment: 8 pages, 9 figures. Invited talk at the Rutherford Centennial Conference on Nuclear Physics, University of Manchester, 8-12 August 2011. To appear in the Proceeding

ππ →πγ∗ amplitude and the resonant ρ →πγ∗ transition from lattice QCD

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 finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-L\"uscher 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.Science and Technology Facilities Council (Grant ID: ST/L000385/1)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevD.93.11450