Utilising optimised operators and distillation to extract scattering phase shifts

In this investigation, we examine how the precision of energy spectra and scattering phase shifts, extracted in lattice QCD, depend upon the degree of distillation type smearing. We use the variational method to extract energy spectra for the isospin-1, J$^{PC}$ = 1$^{−−}$ channel and use the Lüscher method to compute scattering amplitudes, relevant for the ρ resonance, in ππ elastic scattering. Optimised interpolating operators for a single ground state pion are constructed and these are used to construct two pion operators. Calculations are performed on an anisotropic lattice with a pion mass of m$_{π}$ = 236MeV. We provide a comprehensive comparison of energy spectra and scattering phase shifts across distillation spaces of varying rank.AW is supported by the U.K. Science and Technology Facilities Council (STFC). CET acknowledges support from STFC [grant ST/L000385/1]. Computations were performed at Jefferson Laboratory under the USQCD Initiative and the LQCD ARRA project. The software codes Chroma, QUDA, QPhiX, and QOPQDP were used to compute the propagators required for this 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. DE-AC05-00OR22725. 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 the Oak Ridge Leadership Computing Facility, the NERSC, the NSF Teragrid at the TACC and the Pittsburgh Supercomputer Center, as well as at Jefferson Lab

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

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

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection.

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10(3) to 10(4) times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beam-pointing, and pulse-width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD

We present the first determination of $\rho \pi$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $\rho \pi$, we calculate partial-wave amplitudes with $J \le 3$ and determine the degree of dynamical mixing between the coupled $S$ and $D$-wave channels with $J^P=1^+$. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that $m_\pi \sim 700$ MeV, ensuring that the $\rho$ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states