Abstract
\(\phi^{4}\)\(\overline{{MS}})\) Effective field theories are among the most powerful instruments in the toolbox of contemporary physics. Although the concept of effective field theory has been already discussed in Chap. 8, here we are going to provide a relatively elementary description of the relevant technology. Although rather unrealistic, the examples of effective field theories studied next serve the purpose of illustrating the relevant physics involved. The chapter will be closed with a discussion of the concept of naturalness, which plays a central role in modern particle physics. The reader is advised not to be scared by the technicalities of the Feynman diagram computations contained in the chapter. Most of the conclusions can be reached without caring too much about the precise value of the numerical prefactors.
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Notes
- 1.
Our choice of natural units allows us to specify the dimensions of all quantities in terms of powers of energy. Thus, for the coordinates we have \([x^{\mu}]=E^{-1}\), which we denote by \(D_{x}=-1\).
- 2.
The other known way of canceling quadratic divergences is to have supersymmetry (see Sect. 13.2 ), where the quadratically divergent corrections to the scalar masses are cancelled by the contribution of diagrams with fermion loops.
- 3.
As a matter of fact, once we decide that lepton number conservation is not a fundamental symmetry we can also introduce, in addition to the Dirac masses, Majorana mass terms for the right-handed neutrinos.
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Álvarez-Gaumé, L., Vázquez-Mozo, M.Á. (2012). Effective Field Theories and Naturalness. In: An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23728-7_12
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