Abstract:
Expression are found for the upper and lower limits of the radius of elementary particles.
These expressions contain the value of the modulus of the form factor on the cut. To this
end, the solution was found of the corresponding extremal problem of the theory of analytic
functions. If the modulus of the form factor of a $\pi$-meson can be expressed by a resonance
formula of the Breit–Wigner type corresponding to a $\rho$-meson, the results obtained show
that the radius of the $\pi$-meson is $\sqrt{\langle r^2\rangle}\approx(0.62\pm0.12)\mathrm F$.