arXiv subjects

D. B. Leinweber

Publications and source records attributed to D. B. Leinweber.

At least 19 recordsLinked to original sources

arXiv2025

Center vortices and the $\mathrm{SU}(3)$ conformal window

A novel approach for estimating the lower end of the $\mathrm{SU}(3)$ conformal window is presented through the study of center vortex geometry and its dependence on the number of fermion flavors $N_f$. Values ranging from $N_f = 2$--$8$ are utilized to infer an upper limit for vortex behavior in the low $N_f$ phase, which may inform the transition to the conformal window. The simulations are performed at a single lattice spacing and pion mass, both fixed for all $N_f$. Visualizations of the center vortex structure in three-dimensional slices of the lattice reveal a growing roughness in the vortex matter as a function of $N_f$, embodied by an increase in the density of vortex matter in the percolating cluster and a simultaneous reduction in secondary clusters disconnected from the percolating cluster in 3D slices. This is quantified by various bulk properties, including the vortex and branching point densities. A correlation of the vortex structure reveals a turning point near $N_f \simeq 5$ past which a randomness in the vortex field becomes the dominant aspect of its evolution with $N_f$. As a byproduct, extrapolations to the vortex content of a uniform-random gauge field provide a critical point at which there must be a drastic shift in vacuum field structure. A precise estimate for the critical value is extracted as $N_f^* = 11.43(16)(17)$, close to various other estimates.

hep-lat↗

arXiv2021

Chiral extrapolation of the charged-pion magnetic polarizability with Padé approximant

The background magnetic-field formalism of Lattice QCD has been used recently to calculate the magnetic polarizability of the charged pion. These $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory. In this case, the leading term proportional to $1/M_π$ arises at tree level from $\mathcal{L}_4$. To describe the results from lattice QCD, while maintaining the exact leading terms of chiral perturbation theory, we introduce a Padé approximant designed to reproduce the slow variation observed in the lattice QCD results. Two-loop contributions are introduced to assess the systematic uncertainty associated with higher-order terms of the expansion. Upon extrapolation, the magnetic polarizability of the charged pion at the physical pion mass is found to be $β_{π^\pm}=-1.70\,(14)_{\rm stat}(25)_{\rm syst}\times 10^{-4}$ fm$^3$, in good agreement with the recent experimental measurement.

nucl-th↗

arXiv2020

Chiral extrapolation of the magnetic polarizability of the neutral pion

The magnetic polarizability of the neutral pion has been calculated in the background magnetic-field formalism of Lattice QCD. In this investigation, the chiral extrapolation of these lattice results is considered in a formalism preserving the exact leading nonanalytic terms of chiral perturbation theory. The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory and identify the leading contributions of quark-flow connected and disconnected diagrams. While electro-quenching does not impact the leading-loop contribution to the magnetic polarizability, the loops which generate the leading term have yet to be considered in lattice QCD simulations. Lattice QCD results are used to constrain the analytic terms in the chiral expansion and supplementing those with the two-loop result from chiral perturbation theory enables an evaluation of the polarizability at the physical quark mass. The resulting magnetic polarizability of the neutral pion is $β_{π^0}=3.44(19)^{\rm stat}(37)^{\rm syst}\times 10^{-4}$ fm$^3$, which lies just above the $1 σ$ error bound of the experimental measurement.

nucl-th↗

arXiv2016

Nucleon resonance structure in the finite volume of lattice QCD

An approach for relating the nucleon resonances extracted from $πN$ reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of $πN$ reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance pole positions can be related to the probability $P_{N^*}(E)$ of finding the bare state, $N^*$, in the $πN$ scattering states in infinite volume. We further demonstrate that the probability $P_{N^*}^V(E)$ of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches $P_{N^*}(E)$ as the volume increases. Our findings suggest that the comparison of $P_{N^*}(E)$ and $P_{N^*}^V(E)$ can be used to examine whether the nucleon resonances extracted from the $πN$ reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of $P_{N^*}^V(E)$ directly from lattice QCD. The practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.

hep-lat↗

arXiv2016

Singlet baryons in the graded symmetry approach to partially quenched QCD

Progress in the calculation of the electromagnetic properties of baryon excitations in lattice QCD is presenting new challenges in the determination of sea-quark loop contributions to matrix elements. A reliable estimation of the sea-quark loop contributions presents a pressing issue in the accurate comparison of lattice QCD results with experiment. In this article, an extension of the graded symmetry approach to partially quenched QCD is presented, which builds on previous theory by explicitly including flavor-singlet baryons in its construction. The formalism takes into account the interactions among both octet and singlet baryons, octet mesons, and their ghost counterparts; the latter enables the isolation of the quark-flow disconnected sea-quark loop contributions. The introduction of the flavor-singlet states anticipates the application of the method to baryon excitations such as the lowest-lying odd-parity Lambda baryon, the Lambda(1405), which is considered in detail as a worked example.

hep-lat↗

arXiv2015

The spin of the proton in chiral effective field theory

Proton spin is investigated in chiral effective field theory through an examination of the singlet axial charge, $a_0$, and the two non-singlet axial charges, $a_3$ and $a_8$. Finite-range regularization is considered as it provides an effective model for estimating the role of disconnected sea-quark loop contributions to baryon observables. Baryon octet and decuplet intermediate states are included to enrich the spin and flavour structure of the nucleon, redistributing spin under the constraints of chiral symmetry. In this context, the proton spin puzzle is well understood with the calculation describing all three of the axial charges reasonably well. The strange quark contribution to the proton spin is negative with magnitude 0.01. With appropriate $Q^2$ evolution, we find the singlet axial charge at the experimental scale to be ${\hat a}_0 = 0.31^{+0.04}_{-0.05}$, consistent with the range of current experimental values.

hep-ph↗

arXiv2015

Pure sea-quark contributions to the magnetic form factors of $Σ$ baryons

We propose the pure sea-quark contributions to the magnetic form factors of $Σ$ baryons, $G_{Σ^-}^u$ and $G_{Σ^+}^d$, as priority observables for the examination of sea-quark contributions to baryon structure, both in present lattice QCD simulations and possible future experimental measurement. $G_{Σ^-}^u$, the $u$-quark contribution to the magnetic form factor of $Σ^-$, and $G_{Σ^+}^d$, the $d$-quark contribution to the magnetic form factor of $Σ^+$, are similar to the strange quark contribution to the magnetic form factor of the nucleon, but promise to be larger by an order of magnitude. We explore the size of this quantity within chiral effective field theory, including both octet and decuplet intermediate states. The finite range regularization approach is applied to deal with ultraviolet divergences. Drawing on an established connection between quenched and full QCD, this approach makes it possible to predict the sea quark contribution to the magnetic form factor purely from the meson loop. In the familiar convention where the quark charge is set to unity $G_{Σ^-}^u = G_{Σ^+}^d$. We find a value of $-0.38^{+0.16}_{-0.17}\ μ_N$, which is about seven times larger than the strange magnetic moment of the nucleon found in the same approach. Including quark charge factors, the $u$-quark contribution to the $Σ^-$ magnetic moment exceeds the strange quark contribution to the nucleon magnetic moment by a factor of 14.

hep-ph↗

arXiv2015

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modelling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behaviour of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, beta_n = 1.93(11)stat(8)sys x 10^-4 fm^3, which is in agreement with current experimental results.

hep-lat↗

arXiv2013

Strange magnetic form factor of nucleon in heavy baryon chiral effective approach at next to leading order

The strange magnetic form factor of the nucleon is studied in the heavy baryon chiral effective approach at next to leading order. The one loop contributions from kaon and intermediate octet and decuplet hyperons are included, using finite-range-regularization to deal with the ultra-violet divergences. Drawing on an established connection between quenched and full QCD, this model makes it possible to predict the strange magnetic form factor under the hypothesis that for a dipole regulator mass $Λ$ around 0.8 GeV, strangeness in the core is negligible. The strange magnetic form factor is found to be small and negative over a range of momentum transfer, while the strange magnetic moment is consistent with the best lattice QCD determinations.

hep-ph↗

arXiv2013

Chiral extrapolations for nucleon electric charge radii

Lattice simulations for the electromagnetic form factors of the nucleon yield insights into the internal structure of hadrons. The logarithmic divergence of the charge radius in the chiral limit poses an interesting challenge in achieving reliable predictions from finite-volume lattice simulations. Recent results near the physical pion mass are examined in order to confront the issue of how the chiral regime is approached. The electric charge radius of the nucleon presents a forum for achieving consistent finite-volume corrections. Newly-developed techniques within the framework of chiral effective field theory are used to achieve a robust extrapolation of the electric charge radius to the physical pion mass, and to infinite volume. The chiral extrapolations exhibit considerable finite-volume dependence; lattice box sizes of L > 7 fm are required in order to achieve a direct lattice simulation result within 2% of the infinite-volume value at the physical point. Predictions of the volume-dependence are provided to guide the interpretation of future lattice results.

hep-lat↗

arXiv2013

A finite-volume matrix Hamiltonian model for a Delta -> nucleon-pion system

A matrix Hamiltonian model is developed to address the finite-volume effects appearing in studies of baryon resonances in lattice QCD. The Hamiltonian model includes interaction terms in a transparent way, and can be readily generalized to address multi-channel problems. The eigenvalue equation of the model is exactly solvable, and can be matched onto chiral effective field theory. The model is investigated in the case of Delta -> nucleon-pion scattering. A robust method for determining the resonance parameters from lattice QCD is developed. It involves constraining the free parameters of the model based on the lattice spectrum in question. The method is tested in the context of a set of pseudodata, and a picture of the model-dependence is obtained by examining a variety of regularization schemes in the model. A comparison is made with the Luescher method, and it is found that the matrix Hamiltonian method is equally robust. Both methods are tested in a more realistic scenario, where a background interaction corresponding to direct nucleon-pion scattering is incorporated into the pseudodata. The resulting extraction of the resonance parameters associated with the Delta baryon resonance provides evidence that an effective field theory style of approach yields a successful realization of finite-volume effects in the context of baryon resonances.

hep-lat↗

arXiv2013

Finite-volume corrections to charge radii

The finite-volume nature of lattice QCD entails a variety of effects that must be handled in the process of performing chiral extrapolations. Since the pion cloud that surrounds hadrons becomes distorted in a finite volume, hadronic observables must be corrected before one can compare with the experimental values. The electric charge radius of the nucleon is of particular interest when considering the implementation of finite-volume corrections. It is common practice in the literature to transform electric form factors from the lattice into charge radii prior to analysis. However, there is a fundamental difficulty with using these charge radii in a finite-volume extrapolation. The subtleties are a consequence of the absence of a continuous derivative on the lattice. A procedure is outlined for handling such finite-volume corrections, which must be applied directly to the electric form factors themselves rather than to the charge radii.

hep-lat↗

arXiv2012

Baryon resonances and hadronic interactions in a finite volume

In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy spectrum of the finite-volume lattice with the asymptotic behaviour of the S-matrix. A new technique for comparing energy eigenvalues with scattering phase shifts is introduced, which involves the construction of an exactly solvable matrix Hamiltonian model. The model framework is applied to the case of $Δ\rightarrow Nπ$ decay, but is easily generalized to include multi-channel scattering. Extracting resonance parameters involves matching the energy spectrum of the model to that of a lattice QCD calculation. The resulting fit parameters are then used to generate phase shifts. Using a sample set of pseudodata, it is found that the extraction of the resonance position is stable with respect to volume for a variety of regularization schemes, and compares favorably with the well-known Luescher method. The model-dependence of the result is briefly investigated.

hep-lat↗

arXiv2012

Chiral extrapolation of nucleon magnetic moments at next-to-leading-order

Nucleon magnetic moments display a rich nonanalytic dependence on the quark mass in both quenched and full QCD. They provide a forum for a detailed examination of the connection between quenched and full QCD made possible through the formalism of finite-range regularised chiral effective field theory. By defining meson-cloud and core contributions through the careful selection of a regularisation scale, one can correct the meson cloud of quenched QCD to make full QCD predictions. Whereas past success is based on unquenching the leading-order loop contributions, here we extend and test the formalism including next to leading-order (NLO) loop contributions. We discuss the subtleties associated with working at NLO and illustrate the role of higher-order corrections.

hep-ph↗

arXiv2012

Chiral extrapolations for nucleon magnetic moments

Lattice QCD simulations have made significant progress in the calculation of nucleon electromagnetic form factors in the chiral regime in recent years. With simulation results achieving pion masses of order ~180 MeV, there is an apparent challenge as to how the physical regime is approached. By using contemporary methods in chiral effective field theory, both the quark-mass and finite-volume dependence of the isovector nucleon magnetic moment are carefully examined. The extrapolation to the physical point yields a result that is compatible with experiment, albeit with a combined statistical and systematic uncertainty of 10%. The extrapolation shows a strong finite-volume dependence; lattice sizes of L > 5 fm must be used to simulate results within 2% of the infinite-volume result for the magnetic moment at the physical pion mass.

hep-lat↗

arXiv2011

Chiral extrapolation beyond the power-counting regime

Chiral effective field theory can provide valuable insight into the chiral physics of hadrons when used in conjunction with non-perturbative schemes such as lattice QCD. In this discourse, the attention is focused on extrapolating the mass of the rho meson to the physical pion mass in quenched QCD (QQCD). With the absence of a known experimental value, this serves to demonstrate the ability of the extrapolation scheme to make predictions without prior bias. By using extended effective field theory developed previously, an extrapolation is performed using quenched lattice QCD data that extends outside the chiral power-counting regime (PCR). The method involves an analysis of the renormalization flow curves of the low energy coefficients in a finite-range regularized effective field theory. The analysis identifies an optimal regulator, which is embedded in the lattice QCD data themselves. This optimal regulator is the regulator value at which the renormalization of the low energy coefficients is approximately independent of the range of quark masses considered. By using recent precision, quenched lattice results, the extrapolation is tested directly by truncating the analysis to a set of points above 380 MeV, while being blinded of the results probing deeply into the chiral regime. The result is a successful extrapolation to the chiral regime.

hep-lat↗

arXiv2010

Excited States of the Nucleon in 2+1 Flavor QCD

Recent developments on the determination of the spin-1/2 spectrum of the nucleon in full QCD are presented. Our focus is on the PACS-CS 2+1 flavor configurations made available through the ILDG. Using correlation matrix techniques, in which a wide variety of gauge-invariant Gaussian-smeared fermion-propagator sources and sinks are considered, excited states are determined. We consider several correlation matrices of various sizes, each constructed with a different set of basis interpolators, in order to demonstrate the invariance of the eigenstates on the basis choice. Of particular interest is the approach to the elusive Roper resonance and we report preliminary results in full QCD.

hep-lat↗

arXiv2010

Power Counting Regime of Chiral Effective Field Theory and Beyond

Chiral effective field theory complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of chiral effective field theory, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory beyond the PCR are reported.

hep-lat↗