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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

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

Computing the gluon component of momentum in the nucleon is a difficult and computationally expensive problem, as the matrix element involves a quark-line-disconnected gluon operator which suffers from ultra-violet fluctuations. But also necessary for a successful determination is the non-perturbative renormalisation of this operator. We investigate this renormalisation here by direct computation in the RI mom scheme. A clear statistical signal is obtained in the direct calculation by an adaption of the Feynman-Hellmann technique. A comparison is conducted in order to verify the energy-momentum sum rule of the nucleon.

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

We examine the phase shifts and inelasticities associated with the $N^*(1440)$ Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. All three hypotheses are able to describe the scattering data well. In the third hypothesis the Roper resonance couples the low-lying bare basis-state component associated with the ground state nucleon with the virtual meson-baryon contributions. Here the non-trivial superpositions of the meson-baryon scattering states are complemented by bare basis-state components explaining their observation in contemporary lattice QCD calculations. The merit of this scenario lies in its ability to not only describe the observed nucleon energy levels in large-volume lattice QCD simulations but also explain why other low-lying states have been missed in today's lattice QCD results for the nucleon spectrum., 14 pages, 14 figures; version to be published in Phys. Rev. D

In a recent study of the Lambda(1405), the suppression of the strange-quark contribution to the magnetic form factor was interpreted as the discovery of a dominant antikaon-nucleon composition for this low-lying state. We confirm this result by calculating the light u- and d-quark contributions to the Lambda(1405) magnetic form factor in lattice QCD in order to determine the extent to which their contributions support this exotic molecular description. Drawing on the recent graded-symmetry approach for the flavor-singlet components of the Lambda(1405), the separation of connected and disconnected contributions is performed in both the flavor-octet and singlet representations. The relationship between light-quark contributions to the Lambda(1405) magnetic form factor and the connected contributions of the nucleon magnetic form factors is established and compared with lattice calculations of the same quantities, confirming the KN molecular structure of the Lambda(1405) in lattice QCD.

With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between theory and experiment. In particular, determinations obtained via the lattice allow for a direct comparison of QCD-expectation with experimental observation. Here we present the first light quark determination of the $\rho \rightarrow \pi \gamma$ transition form factor from lattice QCD using dynamical quarks. Using the PACS-CS 2+1 flavour QCD ensembles we are able to obtain results across a range of masses, to the near physical value of $m_\pi = 157$ MeV. An important aspect of our approach is the use of variational methods to isolate the desired QCD eigenstate. For low-lying states, such techniques facilitate the removal of excited state contributions. In principle the method enables one to consider arbitrary eigenstates. We find our results are in accord with the non-relativistic quark model for heavy masses. In moving towards the light-quark regime we observe an interesting quark mass dependence, contrary to the quark model expectation. Comparison of our light-quark result with experimental determinations highlights a significant discrepancy suggesting that disconnected sea-quark loop contributions may play a significant role in fully describing this process., Comment: 9 pages, 5 figures and 1 table

The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure $\mathrm{SU}(3)$ gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under ${\cal O}(a^4)$-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling., Version accepted at Physics Letters B

With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between theory and experiment. In particular, determinations obtained via the lattice allow for a direct comparison of QCD-expectation with experimental observation. Here we present the first light quark determination of the $��\rightarrow ����$ transition form factor from lattice QCD using dynamical quarks. Using the PACS-CS 2+1 flavour QCD ensembles we are able to obtain results across a range of masses, to the near physical value of $m_��= 157$ MeV. An important aspect of our approach is the use of variational methods to isolate the desired QCD eigenstate. For low-lying states, such techniques facilitate the removal of excited state contributions. In principle the method enables one to consider arbitrary eigenstates. We find our results are in accord with the non-relativistic quark model for heavy masses. In moving towards the light-quark regime we observe an interesting quark mass dependence, contrary to the quark model expectation. Comparison of our light-quark result with experimental determinations highlights a significant discrepancy suggesting that disconnected sea-quark loop contributions may play a significant role in fully describing this process., 9 pages, 5 figures and 1 table

For almost 50 years the structure of the Lambda(1405) resonance has been a mystery. Even though it contains a heavy strange quark and has odd parity, its mass is lower than any other excited spin-1/2 baryon. Dalitz and co-workers speculated that it might be a molecular state of an antikaon bound to a nucleon. However, a standard quark-model structure is also admissible. Although the intervening years have seen considerable effort, there has been no convincing resolution. Here we present a new lattice QCD simulation showing that the strange magnetic form factor of the Lambda(1405) vanishes, signaling the formation of an antikaon-nucleon molecule. Together with a Hamiltonian effective-field-theory model analysis of the lattice QCD energy levels, this strongly suggests that the structure is dominated by a bound antikaon-nucleon component. This result clarifies that not all states occurring in nature can be described within a simple quark model framework and points to the existence of exotic molecular meson-nucleon bound states., Manuscript accepted for publication. 4 figures, 5 pages

Building on our successful technique to isolate the otherwise-elusive $\Lambda$(1405) using correlation matrix techniques and multiple source and sink smearings, we present calculations of the quark sector contributions to the electric form factors of the $\Lambda$(1405). Using the PACS-CS $(2+1)$-flavour full-QCD ensembles available through the ILDG, our calculations reveal behaviour consistent with the development of a non-trivial molecular $\overline{K}N$ bound-state component as one approaches the physical values of the $u$ and $d$ quark masses., Comment: 7 pages, 3 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

Building on our successful technique to isolate the otherwise-elusive $��$(1405) using correlation matrix techniques and multiple source and sink smearings, we present calculations of the quark sector contributions to the electric form factors of the $��$(1405). Using the PACS-CS $(2+1)$-flavour full-QCD ensembles available through the ILDG, our calculations reveal behaviour consistent with the development of a non-trivial molecular $\overline{K}N$ bound-state component as one approaches the physical values of the $u$ and $d$ quark masses., 7 pages, 3 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We study the phase structure of QCD at high temperature and density by lattice QCD simulations adopting a histogram method. We try to solve the problems which arise in the numerical study of the finite density QCD, focusing on the probability distribution function (histogram). As a first step, we investigate the quark mass dependence and the chemical potential dependence of the probability distribution function as a function of the Polyakov loop when all quark masses are sufficiently large, and study the properties of the distribution function. The effect from the complex phase of the quark determinant is estimated explicitly. The shape of the distribution function changes with the quark mass and the chemical potential. Through the shape of the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quark region is determined for the 2+1-flavor case., 7 pages, 12 figures, proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australia

We study the phase structure of QCD in the $T-\mu$ plane using a histogram method and the reweighting technique by performing phase quenched simulations of two-flavor QCD with RG-improved gauge action and O($a$) improved Wilson quark action. Taking the effects of the complex phase of the quark determinant using the cumulant expansion method, we calculate the probability distribution function of plaquette and phase-quenched determinant as a function of $T$ and $\mu$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function., Comment: 7 pages, 13 figures, contribution to "The 30th International Symposium on Lattice Field Theory", June 24-29, 2012, Cairns, Australia

Center vortices are studied in SU(3) gauge theory using Maximal Center Gauge (MCG) fixing. Stout link smearing and over-improved stout link smearing are used to construct a preconditioning gauge field transformation, applied to the original gauge field before fixing to MCG. We find that preconditioning successfully achieves higher gauge fixing maxima. We observe a reduction in the number of identified vortices when preconditioning is used, and also a reduction in the vortex-only string tension., Comment: 9 pages, 4 figures

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 mesonbaryon 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 σN, πN and a0N channels are constructed. Despite the introduction of qualitatively different operators, no novel energy levels are extracted near the regime of the Roper resonance. Refereed/Peer-reviewed

In 2 + 1 flavour lattice QCD the spectrum of the nucleon is presented for both parities using local meson-baryon type interpolating fields in addition to the standard three-quark nucleon interpolators. The role of local five-quark operators in extracting the nucleon excited state spectrum via correlation matrix techniques is explored on dynamical gauge fields with $m_\pi$ = 293 MeV, leading to the observation of a state consistent with the S-wave $N\pi$ scattering threshold in the negative-parity sector. Furthermore, the robustness of the variational technique is examined by studying the spectrum on a variety of operator bases. Fitting a single-state ansatz to the eigenstate-projected correlators provides robust energies for the low-lying spectrum that are essentially invariant despite being extracted from qualitatively different bases., Comment: 13 Pages, 12 Figures, Updated version as appears in PRD

The role of 5-quark operators in extracting the nucleon excited state spectrum via correlation matrix techniques is explored. In particular, the coupling of meson-baryon operators to nucleon resonance states and scattering states is studied. Results are presented for 2+1 flavour dynamical ensembles in both the positive and negative parity channels. Fitting a single-state ansatz to the eigenstate-projected correlators provides robust energies for the low-lying spectrum that are essentially invariant across a variety of different operator bases. In particular, the resonant state energies obtained both with and without the use of meson-baryon operators agree, demonstrating that resonance energies can be reliably extracted solely using 3-quark operators., 3 figures, 7 pages. Proceedings of the 32nd International Symposium on Lattice Field Theory; 23-28 June, 2014, Columbia University, New York

PoS: Proceedings of Science, 164, ISSN:1824-8039, PoS LATTICE2012

In Nature the excited states of the hadron spectrum appear as resonances. Consequently, there has been significant interest in studying the excited baryon spectrum using lattice QCD. With this in mind we perform spectroscopic calculations with five-quark interpolating fields. Stochastic estimation techniques are used in order to calculate the loop propagators, with dilution in spin, colour and time implemented as a means of variance reduction. We present effective mass plots extracted from these five-quark interpolators, and examine the contributions from fully-connected and loop-containing pieces of the correlation function, keeping in mind their use in future corre- lation matrix studies., Comment: 6 Pages, 3 Figures, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australia, PoS(Lattice 2012)250