The Higgs field gives mass to the elementary particles, such as the electron or the muon.
But does the Higgs yield the full mass value or does it only yield a part of the mass value?
Many state that the Higgs yields the full mass value. But why then are the electron and the muon masses different?
Or is the mass difference between electron and muon a different issue?
For leptons, yes, the full mass. (For quarks just the current mass, while QCD blows that up to a huge constituent mass, through chiral symmetry breaking, for light quarks; leave this aside for now.)
The muon couples 200 times more strongly to the Higgs than the electron does.
In your text, the EW gauge-invariant terms in the lagrangian responsible for such masses are $$ -y_e \overline{ \begin{pmatrix} \nu_{eL} \\ e_L \end{pmatrix} } \cdot \begin{pmatrix} 0 \\ \frac{h+v}{\sqrt 2} \end{pmatrix} ~e_R -y_μ \overline{ \begin{pmatrix} \nu_{μL} \\ μ_L \end{pmatrix} } \cdot \begin{pmatrix} 0 \\ \frac{h+v}{\sqrt 2} \end{pmatrix} ~μ_R+\hbox{h.c.}, $$ where the Yukawa couplings, $y_e\sim \sqrt{2} m_e/v\sim 3~10^{-6}$ and $y_μ \sim \sqrt{2} m_μ /v\sim 6~ 10^{-4}$, are dimensionless constants yielding these masses out of a common Higgs v.e.v., retrofitted to their experimental values.
There is no half-decent explanation for them, so, conceptually, they came out of a hat. Theorists have been striving for over a generation to understand them.
