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Register a new userHow (not) to renormalize integral equations with singular potentials in effective field theory
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We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an underlying fundamental theory and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.
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We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.
We offer a brief response to the criticism put forward by Pavon Valderrama about our recent paper on How (not) to renormalize integral equations with singular potentials in effective field theory.
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.
We consider the two-nucleon weak interaction with a pionless effective field theory. Dibaryon fields are introduced to facilitate calculations and ensure precision in the initial and final state propagators. Weak interactions are accounted for with the parity-violating dibaryon-nucleon-nucleon vertices, which contain unknown weak dibaryon-nucleon-nucleon coupling constants. We apply the model to the calculation of a parity-violating observable in the neutron-proton capture at threshold. Result is obtained up to the linear order in the unknown dibaryon-nucleon-nucleon coupling constants. We compare our result to the one obtained from a hybrid calculation, and discuss the extension to weak interactions in the few-body systems.
Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations. We have studied the low-lying baryons $N^*(1535)$, $N^*(1440)$, and $Lambda(1405)$. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained at finite volume is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. The role and importance of various components of the Hamiltonian model are examined in the finite volume. The analysis of the lattice QCD data can help us to undertand the structure of these states better.
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