arXiv subjects

Derek B. Leinweber

Publications and source records attributed to Derek B. Leinweber.

At least 91 records · Page 5Linked to original sources

arXiv2014

Searching for low-lying multi-particle thresholds in lattice spectroscopy

We explore the Euclidean-time tails of odd-parity nucleon correlation functions in a search for the S-wave pion-nucleon scattering-state threshold contribution. The analysis is performed using 2+1 flavor 32^3 x 64 PACS-CS gauge configurations available via the ILDG. Correlation matrices composed with various levels of fermion source/sink smearing are used to project low-lying states. The consideration of 25,600 fermion propagators reveals the presence of more than one state in what would normally be regarded as an eigenstate-projected correlation function. This observation is in accord with the scenario where the eigenstates contain a strong mixing of single and multi-particle states but only the single particle component has a strong coupling to the interpolating field. Employing a two-exponential fit to the eigenvector-projected correlation function, we are able to confirm the presence of two eigenstates. The lower-lying eigenstate is consistent with a N-pi scattering threshold and has a relatively small coupling to the three-quark interpolating field. We discuss the impact of this small scattering-state contamination in the eigenvector projected correlation function on previous results presented in the literature.

hep-lat↗

arXiv2013

Exploring the Roper wave function in Lattice QCD

Using a correlation matrix analysis consisting of a variety of smearings, the CSSM Lattice collaboration has successfully isolated states associated with the Roper resonance and other "exotic" excited states such as the $Λ(1405)$ on the lattice at near-physical pion masses. We explore the nature of the Roper by examining the eigenvectors that arise from the variational analysis, demonstrating that the Roper state is dominated by the $χ_1$ nucleon interpolator and only poorly couples to $χ_2.$ By examining the probability distribution of the Roper on the lattice, we find a structure consistent with a constituent quark model. In particular, the Roper $d$-quark wave function contains a single node consistent with a $2S$ state. A detailed comparison with constituent quark model wave functions is carried out, validating the approach of accessing these states by constructing a variational basis composed of different levels of fermion source and sink smearing.

hep-lat↗

arXiv2013

Probing the proton and its excitations in full QCD

We present a first look at the application of variational techniques for the extraction of the electromagnetic properties of an excited nucleon system. In particular, we include preliminary results for charge radii and magnetic moments of the proton, its first even-parity excitation and the $Δ^{+}$.

hep-lat↗

arXiv2013

Nucleon Excited State Wave Functions from Lattice QCD

We apply the eigenvectors from a variational analysis to successfully extract the wave functions of even-parity excited states of the nucleon, including the Roper. We explore the first four states in the spectrum excited by the standard nucleon interpolating field. We find that the states exhibit a structure qualitatively consistent with a constituent quark model, where the ground, first-, second- and third-excited states have 0, 1, 2, and 3 nodes in the radial wave function of the d-quark about two $u$ quarks at the origin. Moreover the radial amplitude of the probability distribution is similar to that predicted by constituent quark models. We present a detailed examination of the quark-mass dependence of the probability distributions for these states, searching for a nontrivial role for the multi-particle components mixed in the finite-volume QCD eigenstates. Finally we examine the dependence of the d-quark probability distribution on the positions of the two u quarks. The results are fascinating, with the underlying S-wave orbitals governing the distributions even at rather large u-quark separations.

hep-lat↗

arXiv2013

Electromagnetic Form Factors for the $Λ$(1405)

Building on our successful technique to isolate the otherwise-elusive $Λ$(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 $Λ$(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.

hep-lat↗

arXiv2013

Wave Function of the Roper from Lattice QCD

We apply the eigenvectors from a variational analysis in lattice QCD to successfully extract the wave function of the Roper state, and a higher mass P_11 state of the nucleon. We use the 2+1 flavour 32^3x64 PACS-CS configurations at a near physical pion mass of 156 MeV. We find that both states exhibit a structure consistent with a constituent quark model. The Roper d-quark wave function contains a single node consistent with a 2S state, and the third state wave function contains two, consistent with a 3S state. A detailed comparison with constituent quark model wave functions is carried out, obtained from a Coulomb plus ramp potential. These results validate the approach of accessing these states by constructing a variational basis composed of different levels of fermion source and sink smearing. Furthermore, significant finite volume effects are apparent for these excited states which mix with multi-particle states, driving their masses away from physical values and enabling the extraction of resonance parameters from lattice QCD simulations.

hep-lat↗

arXiv2013

Variational Approach to the Calculation of gA

We present a lattice QCD calculation of the nucleon axial charge, gA, using a variational approach. After a brief outline of how the variational method is applied to the calculation of form factors, we present results for gA using this method. We find that ground state dominance is rapid, evident in the early onset of a clear plateau in the correlation function ratio proportional to gA. Through a comparison with results obtained via traditional methods, we show how excited state effects can suppress gA by as much as 8% if sources are not properly tuned.

hep-lat↗

arXiv2013

Structure and Flow of the Nucleon Eigenstates in Lattice QCD

A determination of the excited energy eigenstates of the nucleon, $s=c{1}{2}$, $I={1}{2}$, $N^{\pm}$, is presented in full QCD using 2+1 flavor PACS-CS gauge configurations. The correlation-matrix method is used and is built using standard nucleon interpolators employing smearings at the fermion sources and sinks. We develop and demonstrate a new technique that allows the eigenvectors obtained to be utilized to track the propagation of the intrinsic nature of energy-states from one quark mass to the next. This approach is particularly useful for larger dimension correlation matrices where more near-degenerate energy-states can appear in the spectrum.

hep-lat↗

arXiv2013

Multi-Particle Baryon Spectroscopy

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.

hep-lat↗

arXiv2012

Low-lying Odd-parity States of the Nucleon in Lattice QCD

The world's first examination of the odd-parity nucleon spectrum at light quark masses in 2+1 flavor lattice QCD is presented. Configurations generated by the PACS-CS collaboration and made available through the ILDG are used, with the lightest pion mass at 156 MeV. A novel method for tracking the individual energy eigenstates as the quark mass changes is introduced. The success of this approach reveals the flow of the states towards the physical masses. Using the correlation matrix method, the two lowest-energy states revealed are found to be in accord with the physical spectrum of Nature.

hep-lat↗

arXiv2012

Accessing High Momentum States In Lattice QCD

Two measures are defined to evaluate the coupling strength of smeared interpolating operators to hadronic states at a variety of momenta. Of particular interest is the extent to which strong overlap can be obtained with individual high-momentum states. This is vital to exploring hadronic structure at high momentum transfers on the lattice and addressing interesting phenomena observed experimentally. We consider a novel idea of altering the shape of the smeared operator to match the Lorentz contraction of the probability distribution of the high-momentum state, and show a reduction in the relative error of the two-point function by employing this technique. Our most important finding is that the overlap of the states becomes very sharp in the smearing parameters at high momenta and fine tuning is required to ensure strong overlap with these states.

hep-lat↗

arXiv2012

Bosonic stringlike behavior and the Ultraviolet filtering of QCD

The gluonic action density is calculated in static mesons at finite temperature just below the deconfinement point. Our focus is to elucidate the role of vacuum ultraviolet fluctuations which are filtered using an improved smearing algorithm. In the intermediate source separation distance, where the free string picture poorly describes the flux tube width profile, we find upon reducing the vacuum action towards the classical instanton vacuum, the characteristics of the flux tube converge and compare favorably with the predictions of the free bosonic string. This result establishes a connection between the free string action and vacuum gauge fields and reveals the important role of ultraviolet physics in understanding the lattice data at this temperature scale. As a by-product of these calculations, we find the broadening of the QCD flux tube to be independent of the ultraviolet filtering at large distances. Our results exhibit a linearly divergent pattern in agreement with the string picture predictions.

hep-lat↗

arXiv2012

Roper Resonance in 2+1 Flavor QCD

The low-lying even-parity states of the nucleon are explored in lattice QCD using the PACS-CS collaboration 2+1-flavor dynamical-QCD gauge-field configurations made available through the International Lattice Datagrid (ILDG). The established correlation-matrix approach is used, in which various fermion source and sink smearings are utilized to provide an effective basis of interpolating fields to span the space of low-lying energy eigenstates. Of particular interest is the nature of the first excited state of the nucleon, the $N{1/2}^{+}$ Roper resonance of $P_{11}$ pion-nucleon scattering. The Roper state of the present analysis approaches the physical mass, displaying significant chiral curvature at the lightest quark mass. These full QCD results, providing the world's first insight into the nucleon mass spectrum in the light-quark regime, are significantly different from those of quenched QCD and provide interesting insights into the dynamics of QCD.

hep-lat↗

arXiv2011

Isolating the Λ(1405) in Lattice QCD

The negative-parity ground state of the Λ baryon lies surprisingly low in mass. At 1405.1 MeV, it lies lower than the negative-parity ground state nucleon, even though it has a valence strange quark. Using the PACS-CS (2+1)-flavour full-QCD ensembles available through the ILDG, we employ a variational analysis using source and sink smearing to isolate this elusive state. We find three low-lying odd-parity states, and for the first time reproduce the correct level ordering with respect to the nearby scattering thresholds.

hep-lat↗

arXiv2011

Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD

We calculate the probability distributions of quarks in the ground state of the proton, and how they are affected in the presence of a constant background magnetic field. We focus on wave functions in the Landau and Coulomb gauges. We observe the formation of a scalar u-d diquark clustering. The overall distortion of the quark probability distribution under a very large magnetic field, as demanded by the quantisation conditions on the field, is quite small. The effect is to elongate the distributions along the external field axis while localizing the remainder of the distribution.

hep-lat↗

arXiv2011

Gluonic profile of the static baryon at finite temperature

The gluon flux distribution of a static three quark system has been revealed at finite temperature in the pure SU(3) Yang-Mills theory. An action density operator is correlated with three Polyakov loops representing the baryonic state at a temperatures near the end of the QCD plateau, T/T_c = 0.8, and another just before the deconfinement point, T/T_c = 0.9. The flux distributions at short distance separations between the quarks display an action-density profile consistent with a filled Delta shape iso-surface. However the Delta-shaped action iso-surface distributions are found to persist even at large inter-quark separations for both temperatures. The action density distribution in the quark plane exhibits a nonuniform pattern for all quark separations considered. This result contrasts the well-known Y-shaped uniform action density gluonic-flux profile obtained using the Wilson-loop as a quark source operator at zero temperature. We systematically measure and compare the main aspects of the profile of the flux distribution at the two considered temperature scales for three sets of isosceles triangle quark configurations. The radii, amplitudes and rate of change of the width of the flux distribution are found to reverse their behavior as the temperature increase from the end of the QCD plateau region towards the deconfinement point. Remarkably, we find the mean square width of the flux distribution shrinks and localizes for quark separations larger than 1.0 fm at T/T_c = 0.8 which results in an identifiable Y-shaped radius profile. Near the deconfinement point, the action-density delocalizes and the width broadens linearly at large quark separations.

hep-lat↗

arXiv2011

Chiral effective field theory beyond the power-counting regime

Novel techniques are presented, which identify the chiral power-counting regime (PCR), and realize the existence of an intrinsic energy scale embedded in lattice QCD results that extend outside the PCR. The nucleon mass is considered as a benchmark for illustrating this new approach. Using finite-range regularization, an optimal regularization scale can be extracted from lattice simulation results by analyzing the renormalization of the low energy coefficients. The optimal scale allows a description of lattice simulation results that extend beyond the PCR by quantifying and thus handling any scheme-dependence. Preliminary results for the nucleon magnetic moment are also examined, and a consistent optimal regularization scale is obtained. This indicates the existence of an intrinsic scale corresponding to the finite size of the source of the pion cloud.

hep-lat↗

arXiv2011

On the ground state of Yang-Mills theory

We investigate the overlap of the ground state meson potential with sets of mesonic-trial wave functions corresponding to different gluonic distributions. We probe the transverse structure of the flux tube through the creation of non-uniform smearing profiles for the string of glue connecting two color sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube operators are found to optimize the overlap with the ground state and display interesting features in the ground state overlap.

hep-lat↗