Heavy Particle Towers and Nonlocal QFT

A number of gravitation-motivated theories, as well as theories with new coloured fermions predict heavy particle towers with spectral densities $\rho(m^2)$ growing faster than $e^{m}$, a characteristic of nonlocalizable theories. It is shown that if a light scalar, like the Higgs boson, interacts strongly with a heavy scalar particle tower with exponentially rising degeneracy, then the local low-energy theory is equivalent to an effective nonlocal scalar QFT. For energies approaching the nonlocality scale $p^2\simeq\Lambda_{NL}^2$, the scalar propagator and scattering amplitudes are modified by nonlocal factors of the form $e^{p^2/\Lambda^2_{NL}}$. The double-Higgs production measurement at the LHC is proposed as a highly sensitive probe of nonlocality at the electroweak scale.