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    Non-Perturbative Effective Field Theories in Strong-Interaction Physics

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    Author
    Long, Bingwei
    Issue Date
    2008
    Keywords
    Delta resonances
    Effective field theory
    Neutron-antineutron oscillation
    Non-perturbative
    Singular potentials
    Advisor
    van Kolck, Ubirajara
    Committee Chair
    van Kolck, Ubirajara
    
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    Publisher
    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 or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    The idea of effective field theory (EFT) was developed decades ago in low-energy strong-interaction - hadronic and nuclear - physics. After introducing chiral perturbation theory (ChPT), we focus in this dissertation on three non-perturbative cases that standard ChPT cannot deal with by itself. First, we investigate pion-nucleon (πN) scattering around the delta resonance, which is an important non-perturbative feature of low-energy nuclear physics. We show that in order to describe πN scattering around the delta peak, a power counting is necessary that goes beyond the power counting of ChPT. Using this new power counting, we calculate the phase shifts in the spin-3/2 P-wave channel up to next-to-next-to-leading order (NNLO). Second, in order to clarify the issue of renormalization and power counting of nucleon-nucleon potentials, we use a toy model to illustrate how to build effective theories for singular potentials, which some nuclear potentials belong to. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. Finally, we illustrate how non-perturbative EFT can be used to study neutron-antineutron oscillation inside the deuteron. We build an EFT for a model-independent, systematic study of two-unit baryon-number (|ΔB| = 2) violation in the context of nuclear physics. To cope with the non-perturbative deuteron structure, we apply the pionless version of this EFT to calculate deuteron decay. The decay width is obtained up to next-to-leading order. We show that the contribution of direct two-nucleon annihilation to the deuteron decay appears only at NNLO.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Physics
    Graduate College
    Degree Grantor
    University of Arizona
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