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    Applications of Effective Field Theories for Precision Calculations at e⁺e⁻ Colliders

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    Author
    Fickinger, Michael
    Issue Date
    2012
    Keywords
    soft collinear effective theory
    strong coupling constant
    Physics
    effective field theory
    heavy quark fragmentation
    Advisor
    Fleming, Sean
    
    Metadata
    Show full item record
    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
    Effective field theories can be used to describe measurements at e⁺e⁻ colliders over a wide kinematic range while allowing reliable error predictions and systematic extensions. We show this in two physical situations. First, we give a factorization formula for the e⁺e⁻ thrust distribution dσ/dτ with thrust T and τ = 1 − T based on soft collinear effective theory. The result is applicable for all τ, i.e. in the peak, tail, and far-tail regions. We present a global analysis of all available thrust distribution data measured at center-of-mass energies Q = 35 to 207 GeV in the tail region, where a two parameter fit to the strong coupling constant α(s)(m(Z)) and the leading power correction parameter Ω₁ suffices. We find α(s)(m(Z)) = 0.1135 ± (0.0002)expt ± (0.0005)hadr ± (0.0009)pert, with x²/dof = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. In addition, we consider cumulants of the thrust distribution using predictions of the full spectrum for thrust. From a global fit to the first thrust moment we extract α(s)(m(Z)) and Ω₁. We obtain α(s)(m(Z)) = 0.1140 ± (0.0004)exp ± (0.0013)hadr ± (0.0007)pert which is compatible with the value from our tail region fit. The n-th thrust cumulants for n ≥ 2 are completely insensitive to Ω₁, and therefore a good instrument for extracting information on higher order power corrections, Ω'(n)/Qⁿ, from moment data. We find (˜Ω₂)^1/2 = 0.74 ± (0.11)exp ± (0.09)pert GeV. Second, we study the differential cross section dσ/dx of e⁺e⁻-collisions producing a heavy hadron with energy fraction x of the beam energy in the center-of-mass frame. Using a sequence of effective field theories we give a definition of the heavy quark fragmentation function in the endpoint region x → 1. From the perspective of our effective field theory approach we revisit the heavy quark fragmentation function away from the endpoint and outline how to develop a description of the heavy quark fragmentation function valid for all x. Our analysis is focused on Z-boson decays producing one B-meson. Finally, we will give a short outlook of how we want to apply our approach to determine the leading nonperturbative power corrections of the b-quark fragmentation function from LEP experiments.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Physics
    Degree Grantor
    University of Arizona
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