Regularisation in Nonperturbative Extensions of Effective Field Theory

Abstract

The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $\Delta$-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 $\pi N$ analysis, fits to experimental phase shifts withstand large variations in the regularisation parameter, $\Lambda$, 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 $\Lambda$ variation in the single-channel case, the eigenstate composition varies with $\Lambda$; the admission of short distance interactions diminishes single-particle contributions to the states. In the two-channel $\pi N$, $\pi \Delta$ analysis, $\Lambda$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $\Lambda$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $\pi \Delta$ 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.

21 pages, 22 figures

References in corpus (5)

• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• Scalar mesons in a finite volume
• Dynamical Coupled-Channel Model of $\pi N$ Scattering in the W $\le$ 2 GeV Nucleon Resonance Region
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Hamiltonian effective field theory in elongated or moving finite volume

Cited by in corpus (6)

• Structure of the $\mathbf{\Lambda }(1670)$ resonance
• Pion photoproduction of nucleon excited states with Hamiltonian effective field theory
• Structure of the ${\Omega }^{-}(2012)$ with Hamiltonian Effective Field Theory
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• $\Delta$ baryon spectroscopy in lattice QCD
• Odd-Parity Nucleon Electromagnetic Transitions in Lattice QCD