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11. Symmetry Breaking and The Higgs Mechanism

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Particle Physics
This chapter is in the book Particle Physics
CHAPTER11.1 THE WEAK FORCE AS A BOSON-MEDIATED INTERACTIONFermi’s original formulation of the weak interactions consisted of a four-point fermion interaction of the form 12342FGyyyy, ordueνe.This vertex contributes a factor GFto the amplitude, where GFis the coupling for the interaction, known as the Fermi constant. The value of the Fermi constant is very much smaller than the cou-plings for the electromagnetic and strong nuclear interactions, at 1.166 10−5 × GeV−2, to account for the weakness of the interaction.The theory was phenomenologically sound, and capable of reproducing the behavior of the weak interaction known at the time. There was found to be, however, a serious theoretical issue with such an interaction: the four-fermion vertex led to a non-renormalizable theory and was only viable to first-order in GF. That is to say that the inevitable infinities that arise in higher- order diagrams cannot be consistently removed in the case of the Fermi interaction. The Symmetry Breakingandthe higgS mechaniSm11PP.CH11_2PP.indd 313PP.CH11_2PP.indd 31312/5/2022 5:19:39 PM12/5/2022 5:19:39 PM
© 2023 Walter de Gruyter GmbH, Berlin/Boston

CHAPTER11.1 THE WEAK FORCE AS A BOSON-MEDIATED INTERACTIONFermi’s original formulation of the weak interactions consisted of a four-point fermion interaction of the form 12342FGyyyy, ordueνe.This vertex contributes a factor GFto the amplitude, where GFis the coupling for the interaction, known as the Fermi constant. The value of the Fermi constant is very much smaller than the cou-plings for the electromagnetic and strong nuclear interactions, at 1.166 10−5 × GeV−2, to account for the weakness of the interaction.The theory was phenomenologically sound, and capable of reproducing the behavior of the weak interaction known at the time. There was found to be, however, a serious theoretical issue with such an interaction: the four-fermion vertex led to a non-renormalizable theory and was only viable to first-order in GF. That is to say that the inevitable infinities that arise in higher- order diagrams cannot be consistently removed in the case of the Fermi interaction. The Symmetry Breakingandthe higgS mechaniSm11PP.CH11_2PP.indd 313PP.CH11_2PP.indd 31312/5/2022 5:19:39 PM12/5/2022 5:19:39 PM
© 2023 Walter de Gruyter GmbH, Berlin/Boston
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