Regularization in nonperturbative extensions of effective field theory

The process of renormalization in nonperturbative Hamiltonian effective field theory (HEFT) is examined in the Delta-resonance scattering channel. As an extension of effective field theory incorporating the Luscher 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 regularization. The extent to which the established features of this regularization scheme survive in HEFT is examined. In a single-channel pi N analysis, fits to experimental phase shifts withstand large variations in the regularization parameter Lambda, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the Luscher 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 finitevolume spectrum for states near the opening of the pi Delta scattering channel. Future high-quality lattice QCD results will be able to discriminate Lambda, describe the inelasticity, and constrain a description of the basis-state composition of the energy eigenstates. 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.

Automated summary

The process of renormalization in nonperturbative Hamiltonian effective field theory (HEFT) is examined in the Delta-resonance scattering channel. HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD, and examines the sensitivity of the finite-volume spectrum and state composition on the regulator.