Ultra-high-energy neutrino scattering in an anomalous U(1) effective field theory

TL;DR

This paper investigates how an anomalous U(1) effective field theory predicts exponential growth in ultra-high-energy neutrino scattering, with implications for IceCube data and future collider experiments.

Contribution

It demonstrates the gauge invariance of the low energy effective Lagrangian and analyzes the sensitivity of neutrino scattering cross sections to model parameters.

Findings

Exponential growth in neutrino-nucleon scattering cross section at ultra-high energies.

Stronger constraints on gauge coupling to gauge boson mass ratio from IceCube data.

Potential to probe the effect at a 10 TeV muon collider.

Abstract

A unique characteristic of exponentially growing scattering amplitude arises in an anomalous Abelian effective field theory when an extremely light Dirac neutrino mass is introduced to break the symmetry. We show that the low energy effective Lagrangian can be made explicitly gauge invariant with the help of a nonlinear representation of the Goldstone or Stueckelberg field. We study the peculiar feature of exponential growth in the ultra-high-energy neutrino-nucleon inelastic scattering. It is found that the inelastic scattering cross section is highly sensitive to the ratio of gauge coupling to the gauge boson mass, $g_X/m_X$. When the IceCube measurement of ultra-high-energy neutrinos, which is consistent with the standard model prediction up to $E_\nu \sim 6$ PeV, is taken into account, the inferred constraint on $g_X/m_X$ is more severe than that obtained from the events of mono-lepton$+$missing transverse energy at the LHC. A muon collider with a collision energy of $10$ TeV can be a good environment other than hadron colliders to probe the novel effect.