arXiv subjects

Curtis D. Abell

Publications and source records attributed to Curtis D. Abell.

7 recordsLinked to original sources

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↗

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↗

arXiv2020

Partial Wave Mixing in Hamiltonian Effective Field Theory

The spectrum of excited states observed in the finite volume of lattice QCD is governed by the discrete symmetries of the cubic group. This finite group permits the mixing of orbital angular momentum quanta in the finite volume. As experimental results refer to specific angular momentum in a partial-wave decomposition, a formalism mapping the partial-wave scattering potentials to the finite volume is required. This formalism is developed herein for Hamiltonian effective field theory, an extension of chiral effective field theory incorporating the Lüscher relation linking the energy levels observed in finite volume to the scattering phase shift. The formalism provides an optimal set of rest-frame basis states maximally reducing the dimension of the Hamiltonian, and it should work in any Hamiltonian formalism. As a first example of the formalism's implementation, lattice QCD results for the spectrum of an isospin-2 $ππ$ scattering system are analyzed to determine the $s$, $d$, and $g$ partial-wave scattering information.

hep-lat↗

arXiv2019

Partial Wave Mixing in Hamiltonian Effective Field Theory

Within general partial-wave mixing, a method for reducing the high dimension of the finite-volume Hamiltonian from Hamiltonian effective field theory is proposed. This method provides a new viewpoint on partial-wave mixing, and a set of matrices that can reflect the degree of partial-wave mixing. An example of isospin-2 $ππ$ scattering is used to examine the consistency between this method and Lüscher's method.

hep-lat↗

arXiv2019

Partial Wave Mixing in Hamiltonian Effective Field Theory

We explore partial-wave mixing in the finite volume based on HEFT, and provide the P-Matrix to show the degree of partial-wave mixing. An example of isospin-2 $ππ$ scattering is used to check the consistency between HEFT and Lüscher's method.

hep-lat↗