Upper and lower limits of the radius of elementary particles

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 $\sqrt{\langle r^2\rangle}\approx(0.62\pm0.12)\mathrm F$.