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Robert G. Edwards

Publications and source records attributed to Robert G. Edwards.

At least 37 records · Page 2Linked to original sources
arXiv2022

Hadron Spectroscopy with Lattice QCD

The status and prospects for investigations of exotic and conventional hadrons with lattice QCD are discussed. The majority of hadrons decay strongly via one or multiple decay-channels, including most of the experimentally discovered exotic hadrons. Despite this difficult challenge, the properties of several hadronic resonances have been determined within lattice QCD. To further discern the spectroscopic properties of various hadrons and to help resolve their nature we present our suggestions for future analytic and lattice studies.

hep-lat↗
arXiv2021

Towards High-Precision Parton Distributions From Lattice QCD via Distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

hep-lat↗
arXiv2021

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 $m_π\sim 700$ 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 $π_1$ resonance decaying dominantly through the $b_1 π$ mode with much smaller decays into $f_1 π$, $ρπ$, $η' π$ and $ηπ$. A large total width is potentially in agreement with the experimental $π_1(1564)$ candidate state, observed in $ηπ$, $η' π$, which we suggest may be heavily suppressed decay channels.

hep-lat↗
arXiv2021

The energy-dependent $π^+ π^+ π^+$ scattering amplitude from QCD

Focusing on three-pion states with maximal isospin ($π^+π^+π^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

hep-lat↗
arXiv2020

Distillation at High-Momentum

Extraction of hadronic observables at finite-momenta from Lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronic $n$-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible, and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea, by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for $\left|\vec{p}\right|\lesssim3\text{ GeV}$ and matrix elements featuring a large momentum dependence can be resolved.

hep-lat↗
arXiv2020

Pion valence quark distribution from current-current correlation in lattice QCD

We extract the pion valence quark distribution $q^π_{\rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^π_{\rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\rm v}^π(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

hep-lat↗
arXiv2019

Hadrons and Nuclei

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD calculations related to the structure and spectroscopy of hadrons and nuclei. An overview of recent lattice calculations of the structure of the proton and other hadrons is presented along with prospects for future extensions. Progress and prospects of hadronic spectroscopy and the study of resonances in the light, strange and heavy quark sectors is summarized. Finally, recent advances in the study of light nuclei from lattice QCD are addressed, and the scope of future investigations that are currently envisioned is outlined.

hep-lat↗
arXiv2019

The $b_1$ resonance in coupled $πω$, $πϕ$ scattering from lattice QCD

We present the first lattice QCD calculation of coupled $πω$ and $πϕ$ scattering, incorporating coupled $S$ and $D$-wave $πω$ 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 $m_π\approx 391$ 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 $Γ_{R}\approx 91$ MeV. The resonance is found to couple dominantly to $S$-wave $πω$, with a much-suppressed coupling to $D$-wave $πω$, and a negligible coupling to $πϕ$ consistent with the `OZI rule'. No resonant behavior is observed in $πϕ$, indicating the absence of a putative low-mass $Z_s$ analogue of the $Z_c$ claimed in $πJ/ψ$. 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.

hep-lat↗
arXiv2019

The quark-mass dependence of elastic $πK$ scattering from QCD

We present a determination of the isospin-1/2 elastic $πK$ scattering amplitudes in S and P partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark 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 bound-state 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 $κ$/$K_0^\star(700)$-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 precisely-determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently 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.

hep-lat↗
arXiv2018

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

We present the first determination of $ρπ$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $ρπ$, 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 $m_π\sim 700$ MeV, ensuring that the $ρ$ 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.

hep-lat↗
arXiv2017

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector

We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Therefore, there is no strong indication for any bound state or narrow resonance in the channels we study.

hep-lat↗
arXiv2017

Isoscalar $ππ, K\overline{K}, ηη$ scattering and the $σ, f_0, f_2$ mesons from QCD

We present the first lattice QCD study of coupled isoscalar $ππ,K\overline{K},ηη$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_π\sim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $σ$ and $f_0(980)$ states, where the $σ$ appears as a stable bound-state below $ππ$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $ππ$ 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 $ππ$ 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.

hep-lat↗
arXiv2016

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 $S$-wave phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_π= 236, 391$ MeV and the resulting amplitudes are described in terms of a $σ$ meson which evolves from a bound-state below $ππ$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

hep-ph↗
arXiv2016

The $ππ\toπγ^\star$ amplitude and the resonant $ρ\toπγ^\star$ transition from lattice QCD

We present a determination of the $P$-wave $ππ\toπγ^\star$ 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-Lüscher formalism. We determine the amplitude for a range of discrete values of the $ππ$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $ρ$ 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 $ρ$ pole extract the $ρ\to πγ^\star$ transition form factor. This calculation, at $m_π\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

hep-ph↗
arXiv2016

An $a_0$ resonance in strongly coupled $πη$, $K\overline{K}$ scattering from lattice QCD

We present the first calculation of coupled-channel meson-meson scattering in the isospin $=1$, $G$-parity negative sector, with channels $πη$, $K\overline{K}$ and $πη'$, 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 $πη\to πη$ 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 $πη$ 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.

hep-ph↗
arXiv2015

The resonant $π^+γ\toπ^+π^0$ amplitude from Quantum Chromodynamics

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for $ππ\to πγ^\star$, as a function of the energy of the $ππ$ pair and the virtuality of the photon, in the kinematic regime where $ππ$ couples strongly to the unstable $ρ$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $m_π\approx 400$~MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $ρ$ pole and identify from its residue the $ρ\to πγ^\star$ form factor.

hep-ph↗
arXiv2015

Coupled $ππ, K\overline{K}$ 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 $m_π= 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $ππ$, $K\overline{K}$ 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 $ππ$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $ρ$ 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.

hep-ph↗