Applications of Effective Field Theory at the intersection of Nuclear and Particle Physics

Persistent Link:
http://hdl.handle.net/10150/232455
Title:
Applications of Effective Field Theory at the intersection of Nuclear and Particle Physics
Author:
de Azevedo, Regina Staropoli
Issue Date:
2012
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:
We apply effective field theory (EFT) techniques to solve problems at the intersection of nuclear and particle physics. In particular, we study three problems that span different energy scales. First, we probe scattering processes, like ππ scattering and e⁺e⁻ annihilation into pions, around the rho mass, m(p) ≃ 770 MeV, which is comparable to the characteristic QCD scale, M(QCD) ∼ 1 GeV. Second, we analyze the nucleon-nucleon potential, especially the renormalization of its binding energy, whose momentum scale, κ ∼ 45 MeV, is much smaller than the pion mass, m(π) ≃ 140 MeV, which in turn is much smaller than M(QCD). Finally, we address a decay problem of a bottomonium into charmed mesons covering two different scales larger than M(QCD), the bottom mass m(b) ∼ 4.5 GeV and the charm mass m(c) ∼ 1.5 GeV V. At energies comparable to M(QCD), rho mesons with masses parametrically comparable to the pion masses are incorporated in a controlled low-energy EFT of QCD, with the assumption that the latter has a dynamical "vector symmetry". We enlarge the "Vector EFT" of pions and rhos to include electromagnetic gauge invariance, and the connections to vector-meson-dominance models are discussed. We develop a power counting for reactions at energies near the rho mass, which requires selective resummations of the momentum expansion. We calculate the amplitudes for ππ → ππ and e⁺e⁻ → π⁺π⁻ in leading order and compare them with data. At lower energies, we use an EFT with momentum of the order of the mass of the pion, Chiral Perturbation Theory (ChPT), to develop a framework to study the renormalization of the two-nucleon problem. To eliminate the 1/r³ singularity in the isovector tensor force from the one-pion-exchange potential in leading order (LO), we add auxiliary-field potentials. The latter could possibly substitute the various counterterms necessary to renormalize the amplitude arising from the one-pion-exchange potential. By treating the short-range interaction of the nucleon-nucleon potential as the dominant piece, we provide an exact solution of the Schrödinger equation and find the binding energy of the deuteron, B, in a first approximation. The long-range interaction is treated in perturbation theory in order to calculate the first correction to B. At higher energies, we take advantage of the separation between the scales 2 m(b) ≫ m(c) ≫ M(QCD) and use a sequence of EFTs to develop a framework to study the exclusive two-body decays of bottomonium into two charmed mesons and apply it to study the decays of the C-even bottomonia. We prove that, at LO in the EFT power counting, the decay rate factorizes into the convolution of two perturbative matching coefficients and three non-perturbative matrix elements, one for each hadron. We calculate the relations between the decay rate and non-perturbative bottomonium and D-meson matrix elements at LO, with next-to-leading-log resummation. The phenomenological implications of these relations are discussed.
Type:
text; Electronic Dissertation
Keywords:
Physics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Physics
Degree Grantor:
University of Arizona
Advisor:
van Kolck, Ubirajara

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleApplications of Effective Field Theory at the intersection of Nuclear and Particle Physicsen_US
dc.creatorde Azevedo, Regina Staropolien_US
dc.contributor.authorde Azevedo, Regina Staropolien_US
dc.date.issued2012-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractWe apply effective field theory (EFT) techniques to solve problems at the intersection of nuclear and particle physics. In particular, we study three problems that span different energy scales. First, we probe scattering processes, like ππ scattering and e⁺e⁻ annihilation into pions, around the rho mass, m(p) ≃ 770 MeV, which is comparable to the characteristic QCD scale, M(QCD) ∼ 1 GeV. Second, we analyze the nucleon-nucleon potential, especially the renormalization of its binding energy, whose momentum scale, κ ∼ 45 MeV, is much smaller than the pion mass, m(π) ≃ 140 MeV, which in turn is much smaller than M(QCD). Finally, we address a decay problem of a bottomonium into charmed mesons covering two different scales larger than M(QCD), the bottom mass m(b) ∼ 4.5 GeV and the charm mass m(c) ∼ 1.5 GeV V. At energies comparable to M(QCD), rho mesons with masses parametrically comparable to the pion masses are incorporated in a controlled low-energy EFT of QCD, with the assumption that the latter has a dynamical "vector symmetry". We enlarge the "Vector EFT" of pions and rhos to include electromagnetic gauge invariance, and the connections to vector-meson-dominance models are discussed. We develop a power counting for reactions at energies near the rho mass, which requires selective resummations of the momentum expansion. We calculate the amplitudes for ππ → ππ and e⁺e⁻ → π⁺π⁻ in leading order and compare them with data. At lower energies, we use an EFT with momentum of the order of the mass of the pion, Chiral Perturbation Theory (ChPT), to develop a framework to study the renormalization of the two-nucleon problem. To eliminate the 1/r³ singularity in the isovector tensor force from the one-pion-exchange potential in leading order (LO), we add auxiliary-field potentials. The latter could possibly substitute the various counterterms necessary to renormalize the amplitude arising from the one-pion-exchange potential. By treating the short-range interaction of the nucleon-nucleon potential as the dominant piece, we provide an exact solution of the Schrödinger equation and find the binding energy of the deuteron, B, in a first approximation. The long-range interaction is treated in perturbation theory in order to calculate the first correction to B. At higher energies, we take advantage of the separation between the scales 2 m(b) ≫ m(c) ≫ M(QCD) and use a sequence of EFTs to develop a framework to study the exclusive two-body decays of bottomonium into two charmed mesons and apply it to study the decays of the C-even bottomonia. We prove that, at LO in the EFT power counting, the decay rate factorizes into the convolution of two perturbative matching coefficients and three non-perturbative matrix elements, one for each hadron. We calculate the relations between the decay rate and non-perturbative bottomonium and D-meson matrix elements at LO, with next-to-leading-log resummation. The phenomenological implications of these relations are discussed.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectPhysicsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorvan Kolck, Ubirajaraen_US
dc.contributor.committeemembervan Kolck, Ubirajaraen_US
dc.contributor.committeememberFleming, Seanen_US
dc.contributor.committeememberSu, Shufangen_US
dc.contributor.committeememberShupe, MIchaelen_US
dc.contributor.committeememberRutherfoord, Johnen_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.