From construction to application - a study in Effective Field Theories

Abstract

We explore the process of constructing low energy E↵ective Field Theories from UV complete theories consisting of fields from both the Standard Model of Particle Physics and Beyond the Standard Model. We formulate Toy Models in which a Beyond the Standard Model light scalar field interacts with the Standard Model fields via a heavy ”messenger” field carrying Standard Model quantum numbers. We consider Toy Models of two cases - (a) where the mass of the messenger field is much greater than the scale of electroweak symmetry breaking and (b) where the mass of the messenger field is of the same order of the electroweak symmetry breaking scale. Using the tools of E↵ective Field Theory, we derive the low energy e↵ective operator containing the field in di↵erent Toy Models of both cases. The low energy e↵ective operator that we get is a combination of the SM 4-Fermi e↵ective operator and the scalar along with additional coupling constants. We then try to see the e↵ect of the new low energy operator containing the scalar by looking at its contribution to the existing coupling constants in the Standard Model. As the Standard Model muon decay is a well studied process at low energies, we calculate the decay spectrum of the positron emitted if an additional particle is present in the final state products. Finally, we compare the momentum-angle spectrum of the decay positron obtained due to the contribution of the New Physics field with the experimental decay spectrum of the positron measured by the TWIST experiment at TRIUMF, Canada.