arXiv subjects

Derek B. Leinweber

Publications and source records attributed to Derek B. Leinweber.

At least 19 recordsLinked to original sources

arXiv2026

Understanding the structure of nucleon excitations from their wavefunctions

Relativistic wavefunctions of nucleon excitations are scrutinised to understand their node structure and the underlying role of local interpolating fields in generating the nucleon spectrum. In addressing quark model perspectives, approximately 4000 propagators are employed on the heaviest PACS-CS ensemble at $m_π\simeq$ 702 MeV. We examine the ground and four lowest-lying excited states at zero momentum for both positive- and negative-parity spectra, where the proton's d-quark wavefunction is calculated about the two u quarks at the origin. This is achieved using two local interpolating fields that each carry the quantum numbers of the nucleon but with differing spin-flavour structures, one of which vanishes in the nonrelativistic limit. We find that two distinct types of wavefunction nodes are manifest: "superposition nodes" formed through a linear combination of interpolating fields, and novel "built-in nodes" that are fundamentally built in to the s-wave Dirac components of an individual interpolating field. These are investigated qualitatively through visualisations in the form of both volume and surface renderings, and quantitatively by the calculation of radial wavefunctions. Combined, these findings build a comprehensive picture of the single-particle nucleon spectrum and how its properties derive from fundamental lattice operators.

hep-lat↗

arXiv2026

General Hamiltonian Approach to the $\mathbf{N}$-Body Finite-Volume Formalism: Extracting the $\mathbfω$ Resonance Parameters from Lattice QCD

We present a nonperturbative Hamiltonian framework (NPHF) to address the general $N$-body problem. This framework rigorously connects finite-volume spectra from lattice QCD to scattering observables from experiment. To demonstrate its applicability, we extract the resonance parameters of the $ω$ meson by simultaneously analyzing the isoscalar $3π$ and isovector $2π$ systems. The Hamiltonian unifies single-particle $ω$, two-particle $ρπ$, and three-particle $πππ$ dynamics within a single unitary formalism. Using leading lattice QCD spectra from the Chinese Lattice QCD Collaboration at $m_π$ = 208 and 305 MeV, we perform a fit in the isovector and isoscalar channels, accurately describe the lattice spectra and obtain robust determinations of the $ρ$ and $ω$ pole positions. This work establishes a foundational approach for extracting resonance dynamics from finite-volume spectra. Given the ubiquity of three-body dynamics in exotic hadrons, halo nuclei, and neutron star matter, this general formalism holds broad relevance across particle, nuclear, and astrophysical physics.

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arXiv2026

Lattice QCD constraints on pion electroproduction off a nucleon

Very recently, a lattice QCD collaboration has explored threshold pion electroproduction near the physical pion mass and has simulated the relevant multipole amplitudes. Different multipole amplitudes are usually entangled in experimental data, and thus extracting each of them independently from first principles provides additional essential constraints on phenomenological theories. We use nonperturbative Hamiltonian theory to investigate the electroproduction process, providing an advanced approach with additional two-particle coupled channels to acquire the physical electric dipole amplitudes from the original lattice QCD data. We note that future lattice QCD simulations of the electric dipole amplitudes at higher energies will be much closer to their physical counterparts than the current ones near threshold. In addition, we obtain a new expression which, like that of Lellouch-Lüscher, depends only on the final-state interactions but provides both the real and imaginary parts of the transition amplitudes.

hep-ph↗

arXiv2025

Pion photoproduction of nucleon excited states with Hamiltonian effective field theory

Over the past few years, Hamiltonian effective field theory has been successfully applied to studies of nucleon and hyperon excited states. By discretizing the Hamiltonian in a finite volume, one can obtain the energy spectrum and compare it with the results calculated from lattice QCD. Through the analysis of experimental data, Hamiltonian effective field theory provides a framework that connects the finite-volume spectra from lattice QCD to infinite-volume scattering observables. The model independence of the approach is well preserved under the combined constraints from lattice QCD and experimental data. Building on these developments, recent works have attempted to extend HEFT to electromagnetic processes. Meanwhile, lattice QCD has also gradually advanced into the study of electromagnetic interactions. The combination of these analyses will undoubtedly deepen our understanding of light resonances.

hep-ph↗

arXiv2025

Structure of the $Ω^{-}(2012)$ with Hamiltonian Effective Field Theory

We investigate the internal structure of the $Ω(2012)^-$ by analyzing lattice QCD simulation and experimental data within Hamiltonian effective field theory, considering both $J^P = 1/2^-$ and $3/2^-$ assignments. The couplings to the dominant decay channel $Ξ\bar{K}$ and the near-threshold channel $Ξ(1530) \bar{K}$ are determined through the quark-pair-creation model. By studying the lattice QCD spectra in these two spin-parity scenarios, we extract the masses and widths of the resonances. We notice that the $J^P = 3/2^-$ resonance is consistent with the observed $Ω(2012)^-$ while the recently reported $Ω(2109)^-$ may be a $J^P = 1/2^-$ $Ω$.

hep-ph↗

arXiv2025

Novel insight into centre-vortex geometry in four dimensions

Centre-vortex surfaces are mapped out in four dimensions within the framework of SU(3) lattice gauge theory to understand the role of secondary loops that develop in three-dimensional visualisations of centre-vortex structure, appearing separate from the percolating cluster. Loops that initially appear disconnected in three-dimensional slices can originate from the same connected surface in four dimensions depending on the surface's curvature. For the first time, these secondary loops are identified as "connected" or "disconnected" with respect to the vortex sheet, allowing new insight into the evolution of centre-vortex geometry through the finite-temperature phase transition. At low temperatures, we find that secondary loops of any length primarily lie in the same sheet percolating the four-dimensional volume. Only a handful of small secondary sheets disconnected from the percolating sheet are identified. Above the phase transition, the vortex structure is still found to be dominated by a single large sheet but one that has aligned with the temporal dimension. With the near absence of any curvature orthogonal to the temporal dimension, connected secondary loops become vanishingly rare. Other novel quantities, such as the four-dimensional density of secondary sheets and the sheet sizes themselves, are analysed to build a complete picture of centre-vortex geometry in four dimensions.

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arXiv2025

Center vortices in the novel phase of staggered fermions

The geometry of center vortices is studied in the novel lattice-artefact phase that appears with staggered fermions to elucidate any insight provided by the center-vortex degrees of freedom. For various numbers of fermion flavors, the single-site shift symmetry of the staggered-fermion action is broken in a finite region of the $(β, m)$ phase space. Simulations are performed with six degenerate fermion flavors and a range of $β$ values that span the phase boundary. Center vortices are demonstrated to capture the broken shift symmetry that manifests in the unphysical phase. This persists at the level of each individual plaquette orientation, where it is revealed that only the plaquettes that span the broken dimension are affected. Several bulk center-vortex quantities, including the vortex and branching point densities, are considered to highlight other aspects of vortex geometry sensitive to the unphysical phase. A slight preference for the plaquettes affected by the broken shift symmetry to be pierced by a vortex is observed. This translates also to a greater branching point density in three-dimensional slices that span the broken dimension. Combined, these findings provide a novel characterization of the unphysical phase in terms of the fundamental center degrees of freedom.

hep-lat↗

arXiv2025

Structure of center-vortex matter in SU(4) Yang-Mills theory

The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge $\pm 1$) and doubly charged vortices. Unlike in SU(3), where charge $+2$ vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center-vortex structures in SU(4) Yang-Mills theory.

hep-lat↗

arXiv2025

The temperature dependence of fractional topological charge objects

We present a novel method for defining the topological charge contained within distinct topological objects in the nontrivial ground-state fields of SU(N) lattice gauge theory. Such an analysis has been called for by the growing number of models for Yang-Mills topological structure which propose the existence of fractionally charged objects. This investigation is performed for SU(3) at a range of temperatures across the deconfinement phase transition, providing an assessment of how the topological structure evolves with temperature. This reveals a connection between the topological charge and holonomy of the system which must be satisfied by finite-temperature models of Yang-Mills vacuum structure. We find a promising consistency with the instanton-dyon model for SU(N) vacuum structure.

hep-lat↗

arXiv2025

SU(3) centre vortex geometry at finite temperature

The importance of examining the structure of centre-vortex matter in the ground-state fields of nonabelian gauge-field theory has been demonstrated in the recent centre-vortex based discovery of a second finite-temperature transition in QCD associated with quark deconfinement. This signals the presence of a new phase of ground-state field structure between the well separated chiral and deconfinement transitions. In this short presentation, we re-examine pure SU(3) gauge theory which provides a foundation for the development of techniques for the examination of full QCD. This time, we reconsider visualisations of the centre-vortex structure in light of the quantitative analysis that demonstrates the first order nature of the deconfinement phase transition in the pure-gauge theory. Here we consider a detailed side-by-side comparison of the field structure slightly below and slightly above the critical temperature. The abrupt changes of the field structure in the first order phase transition are easy to observe in the representative visualisations.

hep-lat↗

arXiv2025

Nucleon resonance structure to 2 GeV and the nature of the Roper

The study of the spectrum of excited states of the nucleon is vital to our understanding of how QCD is realized in the baryon spectrum. Using a simultaneous analysis of the pion nucleon scattering data up to 2 GeV as well as the results of lattice QCD calculations, we obtain new insight into the nature of the Roper resonance as well as the excited states around 1.9 GeV.

hep-ph↗

arXiv2025

Centre vortex evidence for a second finite-temperature QCD transition

Evidence for the existence of a second finite-temperature transition in quantum chromodynamics (QCD) is obtained through the study of centre vortex geometry and its evolution with temperature. The dynamical anisotropic ensembles of the FASTSUM Collaboration are utilised to conduct a comprehensive analysis at eight temperatures beyond the established chiral transition. Visualisations of the centre vortex structure in temporal and spatial slices of the lattice reveal that vortex percolation persists through the chiral transition and ceases at a temperature that is approximately twice the chiral transition temperature $T_c$. This implies that confinement is retained through temperatures up to $T \approx 2\,T_c$, pointing toward a second transition corresponding to deconfinement. The loss of percolation is quantified by the vortex cluster extent, providing a clear signal for the deconfinement transition. Additional vortex statistics, including temporal correlations, vortex and branching point densities, the number of secondary clusters and vortex chain lengths between branching points, are scrutinised as a function of temperature. All ten measures investigated herein show the characteristics of two transitions in QCD, encompassing the chiral transition at $T_c$ and the deconfinement transition at $T \approx 2\,T_c$. Performing an inflection point analysis on the vortex and branching point densities produces an estimate of $T_c$ that agrees with the known FASTSUM value. By the same procedure, a precise estimate of the deconfinement point is extracted as $T_d = 321(6)\,$MeV.

hep-lat↗

arXiv2025

Spectral parameters of the $ρ$ resonance from lattice QCD

We present a lattice QCD investigation of the $ρ$ resonance using nine $N_f = 2 + 1$ Wilson-Clover ensembles with three lattice spacings and various pion masses ranging from $135$ to $320$ MeV. For each ensemble, a large number of finite volume energy levels are determined and the energy dependence of the phase shift obtained from Lüscher's finite volume method. The mass and width of the $ρ$ resonance are then extracted by assuming the Breit-Wigner form. The mass and width are extrapolated to the physical pion mass and continuum limit ($\mathcal{O}(a^2)$) using a linear function of $a^2$ and $m^2_π$. The extrapolated values for the mass and width in the Breit-Wigner form are $(m_ρ,\,Γ_ρ) = (781.6\pm10.0,\, 146.5\pm 9.9)$ MeV, which are in good agreement with experiment. An alternative method of analysis, based on Hamiltonian effective field theory, involves directly fitting the lattice energy levels and accounting for the quark mass dependence of the hadronic loop diagrams which yield the leading and next-to-leading non-analytic behaviour. This approach also yields consistent $ρ$ parameters at the physical point. This represents the most precise determination to date of the mass and width of a hadron which is unstable under strong decay, achieved through comprehensive lattice QCD calculations and methods of analysis.

hep-lat↗

arXiv2024

Physical interpretation of the 2s excitation of the nucleon

Lattice QCD calculations of the $2s$ radial excitation of the nucleon place the state at an energy of approximately 1.9 GeV, raising the possibility that it is associated with the $N1/2^+(1880)$ and $N1/2^+(1710)$ resonances through mixing with two-particle meson-baryon states. The discovery of the $N1/2^+(1880)$ resonance in pion photoproduction but not in $πN$ scattering and the small width of the $N1/2^+(1710)$ resonance suggest that a state associated with these resonances would be insensitive to the manner in which pions are permitted to dress it. To explore this possibility, we examine the spectrum of nucleon radial excitations in both 2+1 flavour QCD and in simulations where the coupling to meson-baryon states is significantly modified through quenching. We find the energy of the $2s$ radial excitation to be insensitive to this modification for quark masses close to the physical point. This invariance provides further evidence that the $2s$ radial excitation of the nucleon is associated with the $N1/2^+(1880)$ and $N1/2^+(1710)$ resonances.

hep-lat↗

arXiv2024

Odd-Parity Nucleon Electromagnetic Transitions in Lattice QCD

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.

hep-lat↗

arXiv2024

Pion photoproduction of nucleon excited states with Hamiltonian effective field theory

We refine our previous calculation of multipole amplitude $E_{0+}$ for pion photoproduction process, $γN\rightarrowπN$. The treatment of final-state interactions is based upon an earlier analysis of pion-nucleon scattering within Hamiltonian effective field theory, supplemented by incorporating contributions from the $N^*(1650)$ and the $KΛ$ coupled channel. The contribution from the bare state corresponding to the $N^*(1650)$ significantly enhances our results. Additionally, we also compute the multipole amplitude $M_{1-}$, which is of direct relevance to the Roper resonance. The results are comparable with other dynamical coupled channel models, even though the contribution from the bare state (interpreted as a 2$s$ excitation) in this channel is small because of its large mass.

hep-ph↗

arXiv2024

Influence of center vortices on the overlap quark propagator in dynamical QCD

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.

hep-lat↗

arXiv2024

Numerical indication that center vortices drive dynamical mass generation in QCD

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 $m_π\simeq 156$ 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.

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