A Bessel Root as a Common Scale for Electric Charge and the Electroweak Angle

A numerical construction based on the third positive zero of the spherical Bessel function j₁(x) is considered. This zero satisfies tan β = β, while its reciprocal is close to the experimental value of the squared electric charge in natural Heaviside–Lorentz normalization. If the hypothesis e² = 1/β₃ is adopted, the same Bessel root can also define an electroweak angular ratio through β₃/(2π). The resulting angle is close to 30°, and the couplings g and g′ can then be reconstructed from the standard electroweak relations without using the Koide condition. A subsequent independent substitution of the reconstructed triplet into a Koide-type ratio yields a value close to 2/3. Thus a single Bessel quantity provides both an interaction scale and a relative electroweak geometry.