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 \(e^{p^2/\Lambda_{NL}^2}\). The double-Higgs production measurement at the LHC is proposed as a highly sensitive probe of nonlocality at the electroweak scale.