Author
Balalhabashi, JaberIssue Date
2022Advisor
van Kolck, UbirajaraFleming, Sean
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
Low-energy scattering in the quantum regime can reveal a lot about the long-range interactions of particles. An efficient tool for studying these reactions is effective field theory (EFT) in which the physics of short-range interactions are encapsulated inthe effective parameters of long-range interactions. In this thesis, EFTs are applied to various shallow quantum scattering states. Since resonances are of particular importance to the scattering of particles in quantum mechanics, low-energy EFTs are built for two-body scattering which includes a low-energy S-wave resonance. Manifestly renormalized scattering amplitudes up to next-to-leading order are constructed in a systematic expansion. The starting point is the most general Lagrangian with only short-range contact interactions that are organized into various orders to generate a systematic expansion for an S matrix with two low-energy poles. The pole positions are restricted to the lower half of the complex momentum plane by renormalization at leading order, where the common feature is a non-positive effective range. The use of contact interactions is limited to the broad resonances due to complications of resummation, therefore the study of S-wave scattering systems is extended to other types of resonances by using an auxiliary field with the quantum numbers of the resonance. For a narrow resonance, the amplitude is perturbative except in the immediate vicinity of the resonance poles, and it naturally has a zero in the low-energy region, analogous to the Ramsauer-Townsend effect. For a broad resonance, the leading-order amplitude is nonperturbative almost everywhere in the regime of validity of the EFT. An additional fine-tuning leading to a low-energy amplitude zero even for a broad resonance is also considered. In all cases when the auxiliary field is not a ghost, the requirement of renormalizability ensures the resonance poles are in the lower half of the complex momentum plane, as expected from other arguments. The systematic convergence of EFT results for resonances with or without auxiliary field is examined and compared with an underlying toy model — a spherical well with a delta shell at its border. Finally, auxiliary fields (dibaryons) along with perturbative pions are used for the uncoupled P-wave channels of two-nucleon scattering. Reasonable fit to phase shifts is obtained up to a center-of-mass momentum of about 400 MeV.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegePhysics