  In the bound state in continuum (BIC) the mass of a composite particle is
greater than the total mass of its constituent particles. The BIC states that
are stable due to confinement mechanisms, have been found in various fields but
particle physics has evolved without analyzing these states. The work's idea is
to apply the BIC phenomenon to some elementary particles. The study focuses on
a composite fermion of the three light leptons, $(e^{-}e^{+}e^{\pm})_{BIC}$. In
the present theory the free electron and free positron is treated as different
particles, each being characterized by the complete set of the Dirac plane
waves. Using the Bethe-Salpeter equation, the wave function of the fermion with
the mass of 207 electron masses was found numerically. The results obtained
predict the particle radius equal to 65.9 Fm. The representation of muons as
the composite fermions formed by the three electron-like leptons in the BIC
states, is analyzed.
