Dale S. Roberts

Wave function of the Roper from lattice QCD

Abstract 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 3 × 64 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.

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

Accessing high momentum states in lattice QCD

u

N* Spectroscopy from Lattice QCD: The Roper Explained

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.

Quark propagation in the instantons of 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.

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

Derek Leinweber, Waseem Kamleh, Adrian Kiratidis, Zhan-Wei Liu, Selim Mahbub, Dale Roberts, Finn Stokes, Anthony W. Thomas and Jiajun Wu

The wave function of the Roper resonance

We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use over-improved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.

Proton Wave Functions in a Uniform Magnetic Field

Centre for Theoretical Chemistry and Physics and Institute of Natural Sciences,Massey University (Albany), Private Bag 102904, North Shore City 0745, New ZealandWe calculate the probability distributions of quarks in the ground state of the proton, and howthey are a ected in the presence of a constant background magnetic eld. We focus on wave functionsin the Landau and Coulomb gauges. We observe the formation of a scalar u-ddiquark clustering.The overall distortion of the quark probability distribution under a very large magnetic eld, asdemanded by the quantisation conditions on the eld, is quite small. The e ect is to elongate thedistributions along the external eld axis while localizing the remainder of the distribution.

Shape of the proton in a uniform magnetic field

We apply the eigenvectors from a variational analysis to successfully extract the wave function of the Roper state, and the next P11 state of the nucleon, associated with the N ? (1710). 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 N ? (1710) contains two, consistent with a 3S state. A detailed investigation of the mass dependence of the wave functions of these states is carried out at four quark masses. The lightest mass provides a pion mass of 156 MeV, just slightly above the physical mass of 139.6 MeV. The ground state wave function shows little mass dependence, consistent with prior wave function investigations. The wave functions of the Roper and second excited state show finite volume effects which become prominent at heavier quark masses than for the ground state.

Exploring the Roper resonance in Lattice QCD

The wave function of the d‐quark in the ground state of the proton, and how it is affected in the presence of a uniform background magnetic field is calculated in lattice QCD. We focus on the wave functions in the Landau and Coulomb gauges. When the quarks are annihilated at different lattice sites, we observe the formation of a scalar u‐d diquark pair within the proton in the Landau gauge, which is not present in the Coulomb gauge. The overall distortion of the wave function under a very large magnetic field, as demanded by the quantisation conditions on the field, is quite small.