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The quark mass dependence of octet baryon magnetic polarisabilities is examined at the level of individual quark-sector contributions in the uniform background-field approach of lattice QCD. The aim is to understand the direct impact of increasing the mass of a quark flavour on the magnetic polarisability and indirect or environmental effects associated with changing the mass of spectator quarks, insensitive to the background magnetic field. Noting the need to set the electric charge of some quark flavours to zero, a fractionally charged baryon formalism is introduced. We find that increasing the mass of the charged quark flavour directly causes its contribution to the magnetic polarisability to decrease. However, increasing the mass of the spectator quark flavour indirectly acts to increase the magnetic polarisability. To gain a deeper understanding of these effects, we evaluate the predictions of the constituent quark model in this context. While the model provides a compelling explanation for the environmental effect of varying the spectator quark mass, an explanation of the direct mass dependence is more complicated as competing factors combine in the final result. The lattice results indicate the key factor is a reduction in the constituent quark magnetic moment with increasing quark mass, as it governs the strength of the magnetic transition to the nearby decuplet baryon., Comment: 13 pages, 5 figures. arXiv admin note: text overlap with arXiv:2407.01064

There is strong evidence supporting center vortices as underpinning confinement and dynamical chiral symmetry breaking -- the two key features of nonperturbative QCD. In our recent letter [ arXiv:2305.18690 ] we find that dynamical mass generation vanishes upon vortex removal in full QCD with a near-physical quark mass. In this work we extend those results and consider the influence of center vortex removal on the overlap Landau-gauge quark propagator at multiple valence quark masses on the same dynamical QCD ensemble, keeping fixed the near-physical sea quark mass. After carefully applying a smoothing process we also find that dynamical mass generation is reproduced on the corresponding vortex-only fields. This vortex-only dynamical mass shows qualitative agreement with the untouched Monte Carlo gauge field results. The results reported herein lend further credence to the important relationship between dynamical fermions and center vortices and the mediation of nonperturbative phenomena in QCD., Comment: 14 pages, 12 figures

We present an exploratory lattice QCD analysis of the $ \Omega $-baryon spectrum. Using smeared three-quark operators in a correlation matrix analysis, we report masses for the ground, first and second excited states of the $ J^P = 1/2^\pm,\, 3/2^\pm $ spectra across a broad range in the light quark mass. We investigate the parity and spin quantum numbers for the states observed on the lattice, looking to reconcile these with the resonances encountered in experiment. We find that the $ \Omega^-(2012) $ as reported by the Particle Data Group corresponds to two overlapping resonances with $ J^P = 1/2^- $ and $ 3/2^- $. We also propose quantum number assignments for the higher energy resonances, and identify successive radial excitations within the spectra., Comment: 22 pages, 13 figures. arXiv admin note: text overlap with arXiv:2312.11574

Drawing on recent advances in lattice-QCD background-field techniques, the magnetic polarisability of octet baryons is calculated from the first principles of QCD. The results are presented in the context of new constituent quark-model calculations providing a framework for understanding the lattice results and a direct comparison with simulation results at unphysical quark masses. Using smeared quark sources, low-lying Laplacian eigenmode projection and final-state Landau mode projection, considerable attention is devoted to ensuring single-state isolation in the lattice correlation functions. We also introduce new weighting methods to reduce the sensitivity to correlation-function fits, averaging over many fits based on merit drawn from the full correlated $\chi^2$ of the fits. The techniques are implemented on the $32^3 \times 64$, 2+1-flavour dynamical-fermion lattices provided by the PACS-CS collaboration following the introduction of uniform magnetic fields quantised to the lowest nontrivial values available. After some fine tuning of the constituent quark model parameters, we find the model captures the patterns observed in the lattice QCD results very well, providing important insights into the physics underpinning the magnetic polarisabilities. Finally, comparison with the most recent results from experiment proceeds through an effective field theory formalism which incorporates estimates of finite-volume corrections and small electro-quenching corrections as the results are brought to the physical point. We find excellent agreement with experiment where available, including the proton and neutron polarisabilities., Comment: 32 pages, 15 figures

The geometry of centre vortices is studied in $\mathrm{SU(3)}$ gauge theory at finite temperature to capture the key structural changes that occur through the deconfinement phase transition. Visualisations of the vortex structure in temporal and spatial slices of the lattice reveal a preference for the vortex sheet to align with the temporal dimension above the critical temperature. This is quantified through a correlation measure. A collection of vortex statistics, including vortex and branching point densities, and vortex path lengths between branching points, are analysed to highlight internal shifts in vortex behaviour arising from the loss of confinement. We find the zero-temperature inclination of branching points to cluster at short distances vanishes at high temperatures, embodying a rearrangement of branching points within the vortex structure. These findings establish the many aspects of centre vortex geometry that characterise the deconfinement phase transition in pure gauge theory., Comment: 26 pages, 25 figures including 5 interactive animations, version accepted for publication

The parity-expanded variational analysis (PEVA) technique enables the isolation of opposite-parity eigenstates at finite momentum. The approach has been used to perform the first lattice QCD calculations of excited-baryon form factors. In particular, these calculations show that the low-lying odd-parity nucleon excitations are described well by constituent quark models at moderate u and d quark masses approaching the strange quark mass. Herein, we extend the PEVA technique to establish a formalism for the determination of odd-parity nucleon electromagnetic transition form factors in lattice QCD. The formalism is implemented in the first calculation of the helicity amplitudes for transitions from the ground state nucleon to the first two odd-parity excitations. Through a comparison with constituent quark model calculations of these amplitudes, these new results give important insight into the structure of these excitations. This work is a critical step towards confronting experimental electroproduction amplitudes for the $N^*(1535)$ and $N^*(1650)$ resonances with ab-initio lattice QCD calculations., Comment: 14 pages, 12 figures

This presentation opens with a brief review of lattice QCD calculations showing the $2s$ radial excitation of the nucleon sits at approximately 2 GeV, well above the Roper resonance position. We then proceed to reconcile this observation with experimental scattering data. While the idea of dressing quark-model states in a coupled-channel analysis to describe scattering data has been around for decades, it's now possible to bring these descriptions to the finite-volume of lattice QCD for confrontation with lattice-QCD calculations. This combination of lattice QCD and experiment demands that we reconsider our preconceived notions about the quark-model and its excitation spectrum. We close with a discussion of an unanticipated resolution to the missing baryon resonances problem., Comment: 8 pages, 2 figures. To appear as a plenary contribution to the proceedings of HADRON 2023, the 20th International Conference on Hadron Spectroscopy and Structure, 5th-9th June 2023, Genova, Italy

The continued development of models that propose the existence of fractional topological objects in the Yang-Mills vacuum has called for a quantitative method to study the topological structure of $\mathrm{SU}(N)$ gauge theory. We present an original numerical algorithm that can identify distinct topological objects in the nontrivial ground-state fields and approximate the net charge contained within them. This analysis is performed for $\mathrm{SU(3)}$ colour at a range of temperatures crossing the deconfinement phase transition, allowing for an assessment of how the topological structure evolves with temperature. We find a promising consistency with the instanton-dyon model for the structure of the QCD vacuum at finite temperature. Several other quantities, such as object density and radial size, are also analysed to elicit a further understanding of the fundamental structure of ground-state gluon fields., Comment: 25 pages, 16 figures, version accepted for publication

We present a lattice QCD analysis of the $ \Delta $-baryon spectrum, with the goal of finding the position of the $ 2s $ radial excitation of the $ \Delta(1232) $ ground state. Using smeared three-quark operators in a correlation matrix analysis, we report masses for the ground, first and second excited states of the $ J^P = 3/2^+ $ spectrum across a broad range of $ m_\pi^2 $. We identify the lowest lying state as being a $ 1s $ state, consistent with the well known $ \Delta(1232) $. The first excitation is identified as a $ 2s $ state, but is found to have a mass of approximately 2.15~GeV on our $ \sim3 $ fm lattice, which does not appear to be associated with the $ \Delta(1600) $ resonance in a significant manner. We also report on the spin-$ 1/2 $ and odd-parity states accessible via our methods. The large excitation energies of the radial excitations provide a potential resolution to the long-standing missing baryon resonances problem., Comment: 16 pages, 9 figures

The first calculation of the response of the momentum space quark propagator to center vortices in the ground state fields of QCD is presented. Center vortices are identified on 2+1-flavour dynamical gauge fields with $m_\pi \simeq 156$ MeV to obtain the vortex-removed and vortex-only quark propagator. Dynamical mass generation is found to vanish upon vortex removal, while the vortex-only field is able to generate dynamical mass. These new signatures strengthen the lattice QCD evidence indicating that center vortices underpin both dynamical chiral symmetry breaking and quark confinement., Comment: 6 pages, 2 figures. Updated to include minor changes for the published version

A variational analysis is performed within the framework of lattice QCD to extract the masses of the spin-3/2 positive parity $ \Delta^+ $ baryons, including radial excitations. $2+1$ flavour dynamical gauge-field configurations provided by the PACS-CS collaboration via the ILDG are considered. To improve our interpolator basis, we perform an iterative process of source and sink smearing and solve a generalised eigenvalue problem using the resulting fermion operators. We obtain a clear signal for the ground and first excited states at a light quark mass corresponding to $ m_\pi = 413 $ MeV. Furthermore, we show that one can use the eigenvectors obtained in this method to investigate the nature of these states, allowing us to classify our results as $ 1s $ and $ 2s $ states for the ground and first excited states respectively. Finally, we briefly highlight the method of Hamiltonian Effective Field Theory which can be used to make comparison with quark model expectations., Comment: 12 pages, 3 figures. Contribution to a special issue of Few Body Systems: "Emergence and Structure of Baryons -- Selected Contributions from the International Conference Baryons 2022"

An analysis of the geometry and structure of centre vortices in the presence of dynamical fermions is performed. A variety of metrics are used to measure the matrix structure of the vortex-modified gauge fields. Visualisations of centre vortices are presented and percolating clusters are identified. The size of secondary vortex clusters is analysed, with substantial differences observed between the pure Yang-Mills and dynamical fermion case. Vortex fields are represented as directed graphs, with branching points acting as the vertices. This representation leads to a novel picture of vortex branching as a binomial process. These results elucidate the change in the centre vortex vacuum induced by the introduction of dynamical fermions., Comment: 18 pages, 22 figures

Quark confinement and dynamical chiral symmetry breaking are two of the most important emergent properties of the theory of quantum chromodynamics. We review recent results studying centre vortices in SU(3) lattice gauge theory with dynamical quarks. Through a vortex identification procedure, vortex-removed and vortex-only fields are obtained from the usual Monte Carlo generated gauge fields. Several comparisons between the untouched fields and the vortex-modified fields support the notion that centre vortices are fundamental to both confinement and dynamical chiral symmetry breaking in full QCD., Comment: 10 pages, 6 figures; Proceedings of the 39th International Symposium on Lattice Field Theory, 8-13 August 2022, Bonn, Germany

COLA is a software library for lattice QCD, written in a combination of modern Fortran and C/C++. Intel and NVIDIA have dominated the HPC domain in the years leading up to the exascale era, but the status quo has changed with the arrival of Frontier and other AMD-based systems in the supercomputing Top 500. Setonix is a next generation HPE Cray EX system hosted at the Pawsey Supercomputing Centre in Perth, Australia. Setonix features AMD EPYC CPUs and AMD Instinct GPUs. This report describes some of my experiences in evolving COLA to adapt to the current hardware landscape., Comment: 10 pages, 2 figures; Proceedings of the 39th International Symposium on Lattice Field Theory, 8-13 August 2022, Bonn, Germany

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Here we examine the centre vortices identified within the ground-state fields of lattice QCD. We aim to understand the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. Using modern visualisation techniques, the centre-vortex structure of pure-gauge and dynamical-fermion fields is quantified and compared. We then explore the impact this modified structure has on measures of confinement and dynamical mass generation. The string tension of the static quark potential, positivity-violation in the gluon propagator, and dynamical mass generation in the overlap quark propagator are of particular interest. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD., Comment: 12 pages, 9 figures including 4 3D-interactive in Adobe Reader. Plenary presentation at the XVth Quark Confinement and the Hadron Spectrum conference, 1st-6th August 2022, Stavanger, Norway. arXiv admin note: text overlap with arXiv:2205.12518

The Landau-gauge quark propagator is calculated using overlap fermions on 2+1-flavour dynamical fermion gauge fields from the PACS-CS collaboration with pion mass $m_\pi \sim 156\text{ MeV}$ and spatial volume $\sim (3 \text{ fm})^3.$ The observed features of the mass and renormalisation functions are discussed, including a comparison with recent results using $\mathcal{O}(a)$-improved Wilson fermions on 2-flavour dynamical gauge fields., Comment: 8 pages, 4 figures

The impact of $SU(3)$ centre vortices on the Landau-gauge gluon propagator is calculated in the presence of dynamical fermions and compared to the pure Yang-Mills case. The presence of dynamical fermions is found to alter the behaviour of the centre vortex propagator when compared to the established pure-gauge result. The gluon spectral representation is also explored from the centre vortex perspective, where centre vortices are shown to exhibit clear signs of positivity violation, which is an indicator of confinement. Vortex removal subsequently restores positivity, demonstrating the crucial role centre vortices play in the confinement of gluons., Comment: 9 pages, 12 figures

For the first time, centre vortices are identified on SU(3) lattice ensembles that include dynamical fermions. Using a variational method, the static quark potential is calculated on untouched, vortex-removed, and vortex-only fields. Two dynamical ensembles and one pure gauge ensemble are studied, allowing for an exploration of the impact of dynamical fermions on the centre-vortex vacuum. Novel modifications to the standard Coulomb term are introduced to describe the long range behaviour of the vortex-removed potential. These modifications remove a source of systematic error in the fitted string tension on the original ensembles. Our pure Yang-Mills result is consistent with previous studies, where projected centre-vortex fields only reproduce approximately two thirds of the string tension. Remarkably, we find that the vortex-only fields on both dynamical lattices are able to fully reproduce the respective untouched string tensions., Comment: 14 pages, 9 figures

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Using modern visualisation techniques, this presentation examines the microscopic structure of these fields. Of particular interest are the centre vortices identified within the ground-state fields of lattice QCD. Our current focus is on understanding the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD., Comment: 10 pages, 7 figures with 4 3D interactive. XXXIII International (Online) Workshop on High Energy Physics, "Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests" November 8-12, 2021. arXiv admin note: substantial text overlap with arXiv:2204.04825

The magnetic polarisability of the neutral pion has been calculated using the background field method in lattice QCD. These early results do not consider the effect of the disconnected loop contractions arising from the breaking of charge symmetry in a background magnetic field. Recent work in chiral perturbation theory has shown that these quark-self-annihilation contractions provide the leading loop-order contributions to the magnetic polarisability. A first investigation of these contractions in a background magnetic field is presented., Comment: 10 pages, 4 figures, Proceedings of the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26th - 30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

The important role of centre vortices in dynamical chiral symmetry breaking and corresponding dynamical mass generation has been demonstrated in pure gauge studies of the Landau-gauge quark propagator. We present initial results of our investigation into the impact of centre vortex removal on the Landau-gauge propagator on dynamical gauge fields. To ensure sensitivity to the topology of the gauge fields, the propagator is computed with overlap fermions. Upon removal of centre vortices we find that dynamical mass generation is suppressed. The quark renormalisation function remains remarkably flat except in the deep infrared where it exhibits significant suppression. These effects become more prominent at lighter quark masses., Comment: 8 pages, 3 figures. Proceedings of the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26th - 30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

The behaviour of centre vortices in the presence of dynamical fermions is studied for the first time in the context of the static quark potential and the Landau-gauge gluon propagator. These results indicate that in the presence of dynamical fermions, centre vortices are able to better encapsulate the long-range behaviour of QCD, compared to previous studies on pure Yang-Mills lattices. This work provides strong evidence that centre vortices are responsible for the long-range linear potential and the enhanced infrared gluon propagator, which are indicative of confinement in QCD., Comment: 8 pages, 4 figures. Proceedings of the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26th - 30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

This presentation examines the centre vortex structure of Monte-Carlo generated gauge-field configurations using modern visualisation techniques. This time, the manner in which light dynamical fermion degrees of freedom impact the centre-vortex structure is explored. Focusing on the thin vortices identified by plaquettes having a non-trivial centre phase, the vortex structure is illustrated through 3D renderings of oriented plaquettes. The impact of light dynamical fermions is not subtle, changing both the density of vortices and the complexity of the vortex structures observed. The role of vortex branching points in full QCD is highlighted in the survey of results presented., Comment: 9 pages, 5 figures with 4 3D interactive. Proceedings of the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26th - 30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

Quark confinement is perhaps the most important emergent property of the theory of quantum chromodynamics. Herein we review some key aspects of centre vortices in SU(3) lattice gauge theory. Starting from the original Monte Carlo gauge fields, a vortex identification procedure yields vortex-removed and vortex-only backgrounds. The comparison between the original `untouched' Monte Carlo gauge fields and these so called vortex-modified ensembles has provided a variety of results that support the notion that centre vortices are fundamental to confinement in pure gauge theory. For the first time we perform direct numerical tests of the response of centre vortices to the presence of dynamical quarks in SU(3)., Comment: 9 pages, 5 figures; Proceedings of 38th International Symposium on Lattice Field Theory (LATTICE2021), 26-30 July 2021, Zoom/Gather@MIT, USA

We study the application of $\mathrm{SU}(3)$ gauge field smoothing methods to $\mathrm{Z}(3)$-projected center-vortex gauge fields. Due to the proportionality of the vortex links to the identity, naive applications of these methods are either ineffectual or limited in scope, containing subtle issues which are not obviously manifest. To overcome these issues we introduce centrifuge preconditioning, a novel method applied prior to smoothing that rotates the links away from the center while preserving the fundamental structure of the vortex field. Additionally, the concept of vortex-preserved annealed smoothing is formulated to ensure the smoothing procedure maintains the underlying vortex structure. The application of these new methods in the context of annealed smoothing applied to vortex fields is shown to successfully achieve the desired smoothness condition required for the study of more advanced operators., Comment: 17 pages, 13 figures, 5 tables

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_\pi\approx 900$ MeV by isolating various spectra of the $\pi\pi$ system with isospin-2 including a range of total momenta and irreps. By applying the L\"uscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $\pi\pi$ scattering with isospin-2 are extracted from the spectra., Comment: 29 Pages, 5 figures

The centre vortex structure of the vacuum is visualised through the use of novel 3D visualisation techniques. These visualisations allow for a hands-on examination of the centre-vortex matter present in the QCD vacuum, and highlights some of the key features of the centre-vortex model. The connection between topological charge and singular points is also explored. This work highlights the useful role visualisations play in the exploration of the QCD vacuum., Comment: 6 pages, 9 figures. In the proceedings of CHEP 2019 - 24rd International Conference on Computing in High Energy and Nuclear Physics, Adelaide, Australia, 4-8 November 2019

The structure of the SU(3) gauge-field vacuum is explored through visualisations of centre vortices and topological charge density. Stereoscopic visualisations highlight interesting features of the vortex vacuum, especially the frequency with which singular points appear and the important connection between branching points and topological charge. This work demonstrates how visualisations of the QCD ground-state fields can reveal new perspectives of centre-vortex structure., Comment: 7 pages, 5 figures. In the proceedings of CHEP 2019 - 24rd International Conference on Computing in High Energy and Nuclear Physics, Adelaide, Australia, 4-8 November 2019

The magnetic polarisability is a fundamental property of hadrons, which provides insight into their structure in the low-energy regime. The pion magnetic polarisability is calculated using lattice QCD in the presence of background magnetic fields. The results presented are facilitated by the introduction of a new magnetic-field dependent quark-propagator eigenmode projector and the use of the background-field corrected clover fermion action. The magnetic polarisabilities are calculated in a relativistic formalism, and the excellent signal-to-noise property of pion correlation functions facilitates precise values., Comment: 7 pages, 3 Figures, 1 Table. Version published in Physics Letters B

Conventional hadron interpolating fields, which utilise gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the $SU(3) \times U(1)$ eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provides the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarisability of both the proton and neutron is calculated using this method on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarisabilities of $\beta^p = 2.79(22)({}^{+13}_{-18}) \times 10^{-4}$ fm$^3$ and $\beta^n = 2.06(26)({}^{+15}_{-20}) \times 10^{-4}$ fm$^3$, where the numbers in parantheses describe statistical and systematic uncertainties., Comment: 16 Pages, Version published in Phys. Rev. D

The recently-introduced Parity Expanded Variational Analysis (PEVA) technique allows for the isolation of baryon eigenstates on the lattice at finite momentum free from opposite-parity contamination. We find that this technique introduces a statistically significant correction in extractions of the electromagnetic form factors of the ground state nucleon. It also allows first extractions of the elastic and transition form factors of nucleon excitations on the lattice. We present the electromagnetic elastic form factors and helicity amplitudes of two odd-parity excitations of the nucleon. These results provide valuable insight into the structure of these states, and allow for a connection to be made to quark-model states in this energy region., Comment: 7 pages, 4 figures; Proceedings of the 37th annual International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

The centre vortex structure of the $SU(3)$ gauge field vacuum is explored through the use of novel visualisation techniques. The lattice is partitioned into 3D time slices, and vortices are identified by locating plaquettes with nontrivial centre phases. Vortices are illustrated by rendering vortex lines that pierce these nontrivial plaquettes. Nontrivial plaquettes with one dimension in the suppressed time direction are rendered by identifying the visible spatial link. These visualisations highlight the frequent presence of singular points and reveal an important role for branching points in $SU(3)$ gauge theory in creating high topological charge density regimes. Visualisations of the topological charge density are presented, and an investigation into the correlation between vortex structures and topological charge density is conducted. The results provide new insight into the mechanisms by which centre vortices generate nontrivial gauge field topology. This work demonstrates the utility of visualisations in conducting centre vortex studies, presenting new avenues with which to investigate this perspective of the QCD vacuum., Comment: 14 Pages, 28 figures

Background field methods provide an important nonperturbative formalism for the determination of hadronic properties which are complementary to matrix-element calculations. However, new challenges are encountered when utilising a fermion action exposed to additive mass renormalisations. In this case, the background field can induce an undesired field-dependent additive mass renormalisation that acts to change the quark mass as the background field is changed. For example, in a calculation utilising Wilson fermions in a uniform background magnetic field, the Wilson term introduced a field-dependent renormalisation to the quark mass which manifests itself in an unphysical increase of the neutral-pion mass for large magnetic fields. Herein, the clover fermion action is studied to determine the extent to which the removal of $\mathcal{O}(a)$ discretisation errors suppresses the field-dependent changes to the quark mass. We illustrate how a careful treatment of nonperturbative improvement is necessary to resolve this artefact of the Wilson term. Using the $32^3 \times 64$ dynamical-fermion lattices provided by the PACS-CS Collaboration we demonstrate how our technique suppresses the unphysical mass renormalisation over a broad range of magnetic field strengths., Comment: 10 pages, 7 figures, version published in Phys. Rev. D

The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has been the subject of significant interest for many years, including several investigations using lattice QCD. The majority of lattice studies have not observed a low-lying excited state energy level in the region of the Roper resonance. However, it has been claimed that chiral symmetry could play an important role in our understanding of this resonance. The purpose of this study is to systematically examine the role of chiral symmetry in the low-lying nucleon spectrum by directly comparing the clover and overlap fermion actions. To ensure any differences in results are attributable to the choice of fermion action, simulations are performed on the same set of gauge field configurations at matched pion masses. Correlation matrix techniques are employed to determine the excitation energy of the first positive-parity excited state for each action. The clover and overlap actions show a remarkable level of agreement. We do not find any evidence that fermion action chiral symmetry plays a significant role in understanding the Roper resonance on the lattice., Comment: 8 pages, 4 figures

First principles calculations of the form factors of baryon excitations are now becoming accessible through advances in Lattice QCD techniques. In this paper, we explore the utility of the parity-expanded variational analysis (PEVA) technique in calculating the Sachs electromagnetic form factors for excitations of the proton and neutron. We study the two lowest-lying odd-parity excitations and demonstrate that at heavier quark masses, these states are dominated by behaviour consistent with constituent quark models for the $N^*(1535)$ and $N^*(1650)$, respectively. We also study the lowest-lying localised even-parity excitation, and find that its form factors are consistent with a radial excitation of the ground state nucleon. A comparison of the results from the PEVA technique with those from a conventional variational analysis exposes the necessity of the PEVA approach in baryon excited-state studies., Comment: 25 pages, 37 figures, 7 tables

The gluon field configurations that form the foundation of every lattice QCD calculation contain a rich diversity of emergent nonperturbative structure. Visualisations of these phenomena not only serve to explain the concept of a nontrivial vacuum but also entertain a diverse audience from research funding panels to the next generation of science enthusiasts. In this brief review, a collection of QCD-vacuum visualisations is presented including the structure of chromo-electromagnetic fields, centre-cluster evolution at finite temperature, the structure of projected centre vortices, and novel correlations between the electromagnetic fields of QED and the chromo-electromagnetic fields of QCD in QED+QCD dynamical-fermion simulations from the QCDSF collaboration., Comment: 7 pages, 4 figures, 3D figure requires Adobe Reader 9 or later, acroread version 9.4.1 for Linux. Lattice QCD Outreach presentation to appear in the proceedings of Lattice 2018, the 36th International Symposium on Lattice Field Theory, Michigan State University, USA, 22-28 July, 2018

The structure of centre vortices in SU(3) gauge-field configurations is examined through modern visualization techniques. Centre vortices are identified through gauge transformations maximizing the centre of the gauge group. Focusing on the thin vortices identified by Wilson loops having a non-trivial centre phase, the vortex structure is illustrated through renderings of oriented spatial plaquettes. Time oriented plaquettes are illustrated by identifying spatial links associated with these non-trivial plaquettes. The results illustrate an important role for the branching of SU(3) centre vortices, possibly through monopole anti-monopole dynamics. Of particular interest is the correlation of the vortex structure and the topological-charge structure of the gauge fields, vital to dynamical chiral symmetry breaking and its associated mass generation. Singular points, where the projected vortex structure contains non-trivial centre phases in associated plaquettes spanning all four dimensions, are observed within the regions of nontrivial topological charge density calculated on the original Monte-Carlo generated configurations. The results provide new insights into the role of centre vortices in underpinning non-trivial topology in gauge fields. They reveal how the removal of centre-vortices necessarily destroys non-trivial topology and destabilizes would-be instantons under smoothing algorithms. The observed correlations further strengthen the idea that centre vortices are the seeds of dynamical chiral symmetry breaking., Comment: 7 pages, 5 figures, 3D figures require Adobe Reader 9 or later, acroread version 9.4.1 for Linux. To appear in the proceedings of Lattice 2018, the 36th International Symposium on Lattice Field Theory, Michigan State University, USA, 22-28 July, 2018

The recently-introduced Parity Expanded Variational Analysis (PEVA) technique allows for the isolation of baryon eigenstates at finite momentum free from opposite-parity contamination. In this paper, we establish the formalism for computing form factors of spin-1/2 states using PEVA. Selecting the vector current, we compare the electromagnetic form factors of the ground state nucleon extracted via this technique to a conventional parity-projection approach. Our results show a statistically significant discrepancy between the PEVA and conventional analyses. This indicates that existing calculations of matrix elements of ground state baryons at finite momentum can be affected by systematic errors of ~20% at physical quark masses. The formalism introduced here provides an effective approach to removing these systematic errors., Comment: 15 pages, 17 figures

It has become increasingly important to include one or more individual flavours of dynamical fermion in lattice QCD simulations. This is due in part to the advent of QCD+QED calculations, where isospin symmetry breaking means that the up, down, and strange quarks must be treated separately. These single-flavour pseudofermions are typically implemented as rational approximations to the inverse of the fermion matrix, using the technique known as Rational Hybrid Monte Carlo (RHMC). Over the years, a wide range of methods have been developed for accelerating simulations of two degenerate flavours of pseudofermion, while there are comparatively fewer such techniques for single-flavour pseudofermions. Here, we investigate two different filtering methods that can be applied to RHMC for simulating single-flavour pseudofermions, namely polynomial filtering (PF-RHMC), and filtering via truncations of the ordered product (tRHMC). A novel integration step-size tuning technique based on the characteristic scale is also introduced. Studies are performed on two different lattice volumes, demonstrating that one can achieve significant reductions in the computational cost of single-flavour simulations with these filtering techniques., Comment: 14 pages, 17 figures, 20 tables; to be submitted to Computer Physics Communications

The impact of $SU(3)$ centre vortices on the gluon propagator in Landau gauge is investigated on original, vortex-removed and vortex-only lattice gauge field configurations. Vortex identification is found to partition the gluon propagator into short range strength on the vortex removed configurations and long range strength on the vortex only configurations. The effect of smoothing vortex-only configurations is also studied, and a regime for recovering the form of the smoothed original propagator from vortex-only configurations is introduced. The results reinforce the significance of centre vortices in a fundamental understanding of QCD vacuum structure., Comment: 9 pages, 9 figures, 1 table, version accepted for publication

An approach for relating the nucleon excited states extracted from lattice QCD and the nucleon resonances of experimental data has been developed using the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in the finite volume of the lattice, the eigenstates of the Hamiltonian model can be related to the energy eigenstates observed in Lattice simulations. By taking the infinite-volume limit of HEFT, information from the lattice is linked to experiment. The approach opens a new window for the study of experimentally-observed resonances from the first principles of lattice QCD calculations. With the Hamiltonian approach, one not only describes the spectra of lattice-QCD eigenstates through the eigenvalues of the finite-volume Hamiltonian matrix, but one also learns the composition of the lattice-QCD eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the composition of the states in terms of the meson-baryon basis states considered in formulating the effective field theory. One also learns the composition of the resonances observed in Nature. In this paper, we will focus on recent breakthroughs in our understanding of the structure of the $N^*(1535)$, $N^*(1440)$ and $\Lambda^*(1405)$ resonances using this method., Comment: 20 pages, 9 figures, Proceedings of The 11th International Workshop on the Physics of Excited Nucleons, August 20 - 23, 2017, at the University of South Carolina, Columbia, SC

The application of a uniform background magnetic field makes standard quark operators utilising gauge-covariant Gaussian smearing inefficient at isolating the ground state nucleon at nontrivial field strengths. In the absence of QCD interactions, Landau modes govern the quark energy levels. There is evidence that residual Landau mode effects remain when the strong interaction is turned on. Here we introduce novel quark operators constructed from the two-dimensional $U(1)$ Laplacian eigenmodes that describe the Landau levels of a charged particle on a periodic finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Using asymmetric source and sink operators, we are able to encapsulate the predominant effects of both the QCD and QED interactions in the interpolating fields for the neutron. The neutron magnetic polarizability is calculated using these techniques on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. In conjunction with a chiral effective-field theory analysis, we obtain a neutron magnetic polarizability of $\beta^n = 2.05(25)(19) \times 10^{-4}$ fm$^3$, where the numbers in parentheses describe statistical and systematic uncertainties., Comment: v2:Improved discussion on crucial points, systematics; new version to match published version

Filtering algorithms for two degenerate quark flavours have advanced to the point that, in 2+1 flavour simulations, the cost of the strange quark is significant compared with the light quarks. This makes efficient filtering algorithms for single flavour actions highly desirable, in particular when considering 1+1+1 flavour simulations for QED+QCD. Here we discuss methods for filtering the RHMC algorithm that are implemented within BQCD, an open-source Fortran program for Hybrid Monte Carlo simulations., Comment: 8 pages, 3 figures, proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

The introduction of a uniform background magnetic field breaks three-dimensional spatial symmetry for a charged particle and introduces Landau mode effects. Standard quark operators are inefficient at isolating the nucleon correlation function at nontrivial field strengths. We introduce novel quark operators constructed from the two-dimensional Laplacian eigenmodes that describe a charged particle on a finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Preliminary results are obtained for the neutron and proton magnetic polarisabilities using these methods., Comment: 8 pages, 5 figures, proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

Variational analysis techniques in lattice QCD are powerful tools that give access to the full spectrum of QCD. At zero momentum, these techniques are well established and can cleanly isolate energy eigenstates of either positive or negative parity. In order to compute the form factors of a single energy eigenstate, we must perform a variational analysis at non-zero momentum. When we do this with baryons, we run into issues with parity mixing in the Dirac spinors, as boosted baryons are not eigenstates of parity. Due to this parity mixing, care must be taken to ensure that the projected correlation functions provided by the variational analysis correspond to the same states at zero momentum. This can be achieved through the parity-expanded variational analysis (PEVA) technique, a novel method developed at the University of Adelaide for ensuring the successful and consistent isolation of boosted baryons. Utilising this technique, we are able to compute the form factors of baryon excitations without contamination from other states. We present world-first calculations of excited state nucleon form factors using this new technique., Comment: proceedings for INPC2016, 5 pages, 4 figures. arXiv admin note: text overlap with arXiv:1701.07177

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV., Comment: 8 pages, 4 figures. Proceedings of the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18 - 24 June 2017, Granada, Spain

An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra. In particular, this new formulation only requires propagator inversions from two distinct locations, at fixed physical separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_\pi\approx 900$~MeV by isolating the spectra of $A^+_1$, $E^+$ and $T^+_2$ of the $\pi\pi$ system with isospin-2 in the rest frame., Comment: 8 pages, 3 figures, Contribution to the conference Lattice2017

The influence of centre vortices on dynamical chiral symmetry breaking is investigated through the light hadron spectrum on the lattice. Recent studies of the quark propagator and other quantities have provided evidence that centre vortices are the fundamental objects underpinning dynamical chiral symmetry breaking in SU(3) gauge theory. For the first time, we use the chiral overlap fermion action to study the low-lying hadron spectrum on lattice ensembles consisting of Monte Carlo, vortex-removed, and vortex-projected gauge fields. We find that gauge field configurations consisting solely of smoothed centre vortices are capable of reproducing all the salient features of the hadron spectrum, including dynamical chiral symmetry breaking. The hadron spectrum on vortex-removed fields shows clear signals of chiral symmetry restoration at light values of the bare quark mass, while at heavy masses the spectrum is consistent with a theory of weakly-interacting constituent quarks.

The positive-parity nucleon spectrum is studied in 2 + 1 flavour lattice QCD in an attempt to discover novel low-lying energy eigenstates in the region of the Roper resonance. In this work, we employ standard three-quark interpolating fields and introduce new local five-quark meson-baryon operators that hold the possibility of revealing new states that have been missed in previous studies. Motivated by phenomenological arguments, five-quark interpolators based on the $\sigma{N}$, $\pi{N}$ and $a_0{N}$ channels are constructed. Despite the introduction of qualitatively different operators, no novel energy levels are extracted near the regime of the Roper resonance., Comment: INPC 2016 Conference proceedings; 7 pages, 2 Figures, 1 Table

The magnetic moment and magnetic polarisability of the neutron and proton are investigated using the uniform background-field method and lattice QCD. The results are calculated using 32^3 x 64 dynamical QCD lattices provided by the PACS-CS collaboration through the ILDG. Methods of isolating the energy of the hadrons accounting for Landau level energies are explored. Effective energy shifts are formed from combinations of correlation functions and their efficiency in isolating the magnetic moment and polarisability terms is determined., Comment: 8 pages, 7 figures, Proceedings of the 26th International Nuclear Physics Conference (INPC2016), Adelaide, Australia, 11-16 Sep 2016