DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Yukawa coupling
Yukawa coupling Particle physics theories
predict that fermions will acquire their masses
through the Higgs mechanism, by means of a
so-called Yukawa term in the Lagrangian, where
fermions couple with a Higgs field φ. Specifically,
a fermion ψ is said to have a mass m
when the Lagrangian density that describes its
dynamics contains the term
Lm =m¯ψψ.
In some cases, however, it is not possible to have
such a term, and the corresponding fermions
would then appear massless (the symmetry rules
obeyed by the total Lagrangian are responsible
for this). Instead, a coupling such as
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Lm =f¯ψφψ
(the Yukawa coupling) with f the coupling constant,
may always be set. When the Higgs field
gets its nonzero vacuum expectation value 〈|φ|〉
in a phase transition, the above coupling reduces
to a simple mass term, and thus the fermion acquires
a mass proportional to 〈|φ|〉.
This same mechanism also allows the possibility
of fermionic currents along topological
defects in the form of zero modes. See cosmic
phase transition, fermionic zero mode, Higgs
mechanism.