Abstract
I consider an Abelian gauge theory, with a complex scalar field and massless, chiral fermions, in the limit where the couplings and the interactions induce radiative symmetry breaking, and I derive and verify the Nielsen identities that ensure the gauge independence of the physical fermion mass that emerges in the broken phase of the effective action.
Highlights
The phenomenon of symmetry breaking is fundamental in the physics of the Standard Model, which is consistently formulated as an interacting theory of massless fermions and gauge bosons, that acquire mass in the broken phase of the Higgs sector
The gauge freedom present in the original action of the Standard Model, as well as any other gauge theory of particle physics, makes the calculations of additional radiative corrections more involved, by the process of gauge fixing and the resulting gauge dependence that is present in the calculation of individual Feynman diagrams; the final result, for any physical quantity, calculated at a given order of the coupling constants, is expected to be gauge independent once all the relevant terms are accounted for
The gauge dependence of individual terms is described by the Nielsen identities [1], that are expected to hold for the generating functionals of the Green functions of such theories, and have been used in order to demonstrate the gauge independence of physical quantities such as masses, tunneling rates, and other consequences of the phenomenon of symmetry breaking in particle physics and cosmology [2, 3]
Summary
The phenomenon of symmetry breaking is fundamental in the physics of the Standard Model, which is consistently formulated as an interacting theory of massless fermions and gauge bosons, that acquire mass in the broken phase of the Higgs sector. Some comprehensive diagrammatic treatments of similar problems, in the Standard Model and other cases, exist in the literature, using the Nielsen identities or other methods [5], here, I will consider the calculation and definition of particle mass through the effective action, and derive and prove the relevant Nielsen identities at this level. This is important for the consistency of the theory, the power-counting and collection of the relevant terms of a physical calculation, as well as for the use of the effective action formalism as a tool for the study of the process and consequences of symmetry breaking.
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