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Aspects of Effective Field Theories from Scattering Amplitudes


Shen, Chia-Hsien (2017) Aspects of Effective Field Theories from Scattering Amplitudes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9VM49BW.


On-shell methods offer an alternative definition of quantum field theory at tree-level. We first determine the space of constructible theories solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory in four dimensions are constructible, but only a subset of amplitudes is constructible in non-renormalizable theories. The obstructions to effective field theories (EFTs) are then lifted for the non-linear sigma model, Dirac-Born-Infeld theory, and the Galileon, using the enhanced soft limits of their amplitudes.

We then systematically explore the space of scalar EFTs based on the soft lim- its and power counting of amplitudes. We prove that EFTs with arbitrarily soft behavior are forbidden by on-shell momentum shifts and recursion relations. The exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

Next, a new representation of the nonlinear sigma model is proposed to manifest the duality between flavor and kinematics. The action consists of only cubic interactions, which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon. The vanishing soft behavior of amplitudes is shown as a byproduct of the Weinberg soft theorem.

Finally, we derive a class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in four-dimensional quantum field theory. Our derivation combines unitarity and helicity selection rules at tree level. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Scattering Amplitudes, Effective Field Theories, S-matrices
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Cheung, Clifford W.
Group:Caltech Theory
Thesis Committee:
  • Cheung, Clifford W. (chair)
  • Wise, Mark B.
  • Porter, Frank C.
  • Trnka, Jaroslav
Defense Date:15 May 2017
Funding AgencyGrant Number
Department of EnergyDE-SC0010255
Record Number:CaltechTHESIS:06052017-000916838
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Ch. 1 adapted for Ch. 2 adapted for Ch. 3 adapted for Ch. 4 adapted for Ch. 5
Shen, Chia-Hsien0000-0002-5138-9971
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10273
Deposited By: Chia Hsien Shen
Deposited On:07 Jun 2017 21:16
Last Modified:26 Oct 2021 16:42

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