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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/193879 |
| Date | January 2008 |
| Creators | Long, Bingwei |
| Contributors | van Kolck, Ubirajara, van Kolck, Ubirajara, Barrett, Bruce, Dienes, Keith, Fleming, Sean, Su, Shufang |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| 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. |
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