Amplitudes and the Riemann Zeta Function

Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses m(n)(2) = mu(2)(n), where zeta(1/2 +/- i mu(n)) = 0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of zeta. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/mu(2)(n).

Automated summary

The physical properties of scattering amplitudes are linked to the Riemann zeta function, with real masses corresponding to the Riemann hypothesis, locality of the amplitude relating to the meromorphicity of the zeta function, and universal coupling between massive and massless states reflecting the simplicity of zeros of the zeta function. Additionally, unitarity bounds from dispersion relations for the forward amplitude translate to the positivity of odd moments of the sequence of 1/mu(2)(n).