arXiv subjects

Derek B. Leinweber

Publications and source records attributed to Derek B. Leinweber.

At least 37 records · Page 2Linked to original sources

arXiv2024

Centre vortex geometry at finite temperature

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.

hep-lat↗

arXiv2024

Chiral Analysis of the Nucleon Mass and Sigma Commutator

Schemes for describing the light quark mass dependence of the nucleon mass calculated in lattice QCD are compared. The three schemes in consideration include a fully relativistic and Lorentz covariant scheme, one that is fully relativistic but not Lorentz covariant, and a semirelativistic scheme utilizing the heavy baryon approximation. Calculations of observables involving pseudoscalar meson loop diagrams generate nonanalytic terms proportional to square roots and logarithms of the quark mass. The three schemes all yield the correct model independent leading and next-to-leading nonanalytic terms of the chiral expansion of the baryon mass. Results for the masses of the other members of the octet are also presented. Here, low-energy coefficients of the analytic terms of the expansion for the nucleon and hyperons are constrained by lattice QCD results and are demonstrated to be independent of the renormalization scheme used. The differences in the leading coefficient of the chiral expansions are found to be consistent with strange quark counting. Using the schemes examined herein, we report results for the pion-nucleon sigma commutator based upon recent lattice results from the CLS Collaboration. We find $σ_{πN}=51.7 \pm 3.2 \pm 1.4$ MeV where the uncertainties are statistical and systematic respectively.

hep-ph↗

arXiv2024

Numerical evidence for fractional topological objects in SU(3) gauge theory

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.

hep-lat↗

arXiv2024

Study of the pion-mass dependence of $ρ$-meson properties in lattice QCD

We collect spectra extracted in the $I=\ell=1$ $ππ$ sector provided by various lattice QCD collaborations and study the $m_π$ dependence of $ρ$-meson properties using Hamiltonian Effective Field Theory (HEFT). In this unified analysis, the coupling constant and cutoff mass, characterizing the $ρ- ππ$ vertex, are both found to be weakly dependent on $m_π$, while the mass of the bare $ρ$, associated with a simple quark-model state, shows a linear dependence on $m_π^2$. Both the lattice results and experimental data can be described well. Drawing on HEFT's ability to describe the pion mass dependence of resonances in a single formalism, we map the dependence of the phase shift as a function of $m_π$, and expose interesting discrepancies in contemporary lattice QCD results.

hep-lat↗

arXiv2024

Structure of the $\mathbf{Λ(1670)}$ resonance

We examine the internal structure of the $Λ(1670)$ through an analysis of lattice QCD simulations and experimental data within Hamiltonian effective field theory. Two scenarios are presented. The first describes the $Λ(1670)$ as a bare three-quark basis state, which mixes with the $πΣ$, $\bar{K}N$, $ηΛ$ and $KΞ$ meson-baryon channels. In the second scenario, the $Λ(1670)$ is dynamically generated from these isospin-0 coupled channels. The $K^-p$ scattering data and the pole structures of the $Λ(1405)$ and the $Λ(1670)$ can be simultaneously described well in both scenarios. However, a comparison of the finite-volume spectra to lattice QCD calculations reveals significant differences between these scenarios, with a clear preference for the first case. Thus the lattice QCD results play a crucial role in allowing us to distinguish between these two scenarios for the internal structure of the $Λ(1670)$.

hep-ph↗

arXiv2024

Sea-quark loop contributions to the $\bar d$-$\bar u$ asymmetry in the proton

QCD interactions for equal-mass fermion flavors are flavor blind. This fact is often used to state that disconnected sea-quark loop contributions are equal for $u$ and $d$ quarks in the mass symmetric case and therefore these disconnected sea-quark loop contributions cannot contribute to the well-known $\bar d - \bar u$ asymmetry in the proton. Instead, it is argued that one must look to the connected sector of lattice QCD correlation functions to find this difference. In this presentation, we note that these statements are true provided unphysical contributions in the sea-quark loop sector are included, contributions from baryons that do not appear in the physical spectrum. To respect the Pauli principle, these unphysical contributions from the disconnected sea-quark loop sector must cancel equally unphysical contributions in the connected sector. The remaining disconnected sea-quark loop contributions no longer have a balance between $\bar d$ and $\bar u$. Upon considering only physically observed baryons in the loop contributions, we illustrate an important contribution from the sea-quark loop sector to $\bar d - \bar u$ that enhances the leading connected contribution by 12\%.

hep-ph↗

arXiv2024

Understanding the nature of baryon resonances

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.

hep-lat↗

arXiv2023

Low-lying odd-parity nucleon resonances as quark-model like states

Recent lattice QCD results for the low-lying odd-parity excitations of the nucleon near the $N^{*}(1535)$ and $N^{*}(1650)$ resonance positions have revealed that the lattice QCD states have magnetic moments consistent with predictions from a constituent-quark-model. Using Hamiltonian Effective Field Theory (HEFT) to describe pion-nucleon scattering in the $I(J^{P}) = \frac{1}{2}(\frac{1}{2}^{-})$ channel, we represent these two quark-model like states as two single-particle bare basis states, dressed and mixed by meson-baryon scattering channels. By constraining the free parameters of the Hamiltonian with $S_{11}$ pion-nucleon scattering data, we perform the first calculation of the finite-volume spectrum using two bare-baryon basis states. By comparing this spectrum to contemporary lattice QCD results at three lattice volumes, we analyse the eigenvectors of the Hamiltonian to gain insight into the structure and composition of these two low-lying resonances. We find that an interpretation of the two low-lying nucleon resonances as quark-model like states dressed by meson-baryon interactions is consistent with both the $S_{11}$ scattering data and lattice QCD. We introduce a novel HEFT formalism for estimating scattering-state contaminations in lattice QCD correlation functions constructed with standard three-quark operators. Not only are historical lattice QCD results described with excellent accuracy, but correlation functions with large scattering-state contaminations are identified.

hep-lat↗

arXiv2023

Effects of multiple single-particle basis states in scattering systems

Low-lying baryon resonances have been explored using Hamiltonian Effective Field Theory (HEFT), in a formalism where resonances with a three-quark component are described by both two-particle meson-baryon states and a bare basis state. Here, we investigate the use of multiple bare states in the Hamiltonian, to extend the formalism to higher energy ranges, and represent a larger portion of the low-lying baryon spectrum. Introducing a second bare state into a toy model extension of the low-energy $Δ(1232)$ system, we explore the influence of the second bare state on the position of poles in the infinite-volume $T$-matrix. Considering the same system in a finite-volume, we analyse the finite-volume energy spectrum in the presence of a second bare state, providing insight into the interplay between two bare basis states, representing quark-model states, and the relationship between infinite-volume poles and finite-volume eigenstates.

nucl-th↗

arXiv2023

Centre vortex structure in the presence of dynamical fermions

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.

hep-lat↗

arXiv2023

Emergent phenomena from centre vortices in dynamical QCD

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.

hep-lat↗

arXiv2022

Regularisation in Nonperturbative Extensions of Effective Field Theory

The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $Δ$-resonance scattering channel. As an extension of effective field theory incorporating the Lüscher formalism, HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD. HEFT also provides phenomenological insight into the basis-state composition of the finite-volume eigenstates via the state eigenvectors. The Hamiltonian matrix is made finite through the introduction of finite-range regularisation. The extent to which the established features of this regularisation scheme survive in HEFT is examined. In a single-channel $πN$ analysis, fits to experimental phase shifts withstand large variations in the regularisation parameter, $Λ$, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the Lüscher formalism ensures the eigenvalues are insensitive to $Λ$ variation in the single-channel case, the eigenstate composition varies with $Λ$; the admission of short distance interactions diminishes single-particle contributions to the states. In the two-channel $πN$, $πΔ$ analysis, $Λ$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $Λ$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $πΔ$ scattering channel. Finally, HEFT has the unique ability to describe the quark-mass dependence of the finite-volume eigenstates. The robust nature of this capability is presented and used to confront current state-of-the-art lattice QCD calculations.

hep-lat↗

arXiv2022

Emergent phenomena from centre vortices

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).

hep-lat↗

arXiv2021

Towards high partial waves in lattice QCD with a dumbbell-like operator

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 $m_π\approx 900$ MeV by isolating various spectra of the $ππ$ system with isospin-2 including a range of total momenta and irreps. By applying the Lüscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $ππ$ scattering with isospin-2 are extracted from the spectra.

hep-lat↗

arXiv2021

Hamiltonian effective field theory in elongated or moving finite volume

We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively. We also consider the combination of the two systems when directions of the elongation and the moving momentum are aligned. This extension should also be applicable in any Hamiltonian formalism. As a demonstration, we analyze lattice QCD results for the spectrum of an isospin-2 $ππ$ scattering system and determine the $s$, $d$, and $g$ partial-wave scattering information. The inclusion of lattice simulation results from moving frames significantly improves the uncertainty in the scattering information.

hep-lat↗

arXiv2020

Emergent Structure in QCD

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.

hep-lat↗

arXiv2020

Visualisations of Centre Vortices

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.

hep-lat↗

arXiv2020

Visualisation of Centre Vortex Structure

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.

hep-lat↗