Calculation of an $A=3$ bound-state matrix element in pionless effective field theory
Abstract
In this paper, we establish a general framework for calculating pionless matrix elements between bound-states up to next-to-leading-order. This framework is useful for pionless calculations of electroweak observables, such as H,He magnetic moments and H decay. Starting from a Bethe-Salpeter equation, we prove that for a bound-state, the three-nucleon wave-function normalization can be expressed diagrammatically in a way that is equivalent to the unit operator between two identical three-nucleon bound-states. This diagrammatic form of the identity matrix element is the foundation for constructing an matrix element of a general operator. We show that this approach can be used to calculate the energy difference between H and He due to the Coulomb interaction, and to calculate the NLO corrections to the H and He scattering amplitudes due to effective range corrections.
Keywords
Cite
@article{arxiv.1902.07677,
title = {Calculation of an $A=3$ bound-state matrix element in pionless effective field theory},
author = {Hilla De-Leon and Lucas Platter and Doron Gazit},
journal= {arXiv preprint arXiv:1902.07677},
year = {2019}
}
Comments
27 pages, 12 figures. arXiv admin note: text overlap with arXiv:1611.10004