UCLA

This dissertation explores the effects of higher-dimension operators in scattering amplitudes,and how such amplitudes can be used to gain insight into areas of physics ranging from elementary particle interactions to the tidal responses of black holes and neutron stars. Chapter 1 provides a brief introduction to higher-dimension operators and the Effective Field Theories (EFTs) which are their natural environment. In Chapter 2, we prove a theorem stating that operators which are "longer" in a specific sense cannot renormalize "shorter" operators at low loop levels. This result applies very generally, and can apply at high loop levels given the appropriate operators. We also discuss how the theorem applies to specifically to the Standard Model Effective Field Theory (SMEFT). In Chapter 3, we extend this discussion of renormalization within the SMEFT by calculating a large class of one loop amplitudes of dimension-six SMEFT operators and showing how to use these amplitudes to compute two-loop anomalous dimensions. Finally, in Chapter 4 we turn the calculation of amplitudes with higher-dimension operators to the purpose of calculating the effects of tides on the gravitational potential between, for example, orbiting black holes and neutron stars. This work, which includes in principle the leading effect of tidal operators at all loops, has direct relevance for gravitational wave detectors.