Neutrinos with Lorentz-violating operators of arbitrary dimension

TL;DR

This paper develops a comprehensive theoretical framework for analyzing neutrino behavior under Lorentz and CPT violation, incorporating operators of arbitrary mass dimension, and applies it to experimental data to constrain possible violations.

Contribution

It classifies all Lorentz-violating terms for free fermions and adapts this to neutrino oscillations, providing a systematic way to analyze Lorentz violation effects in neutrino physics.

Findings

Constraints on Lorentz-violating coefficients from neutrino oscillation experiments.

Sensitivity to operators up to mass dimension 10 in short-baseline experiments.

Limits on Lorentz violation from supernova neutrino time-of-flight measurements.

Abstract

The behavior of fermions in the presence of Lorentz and CPT violation is studied. Allowing for operators of any mass dimension, we classify all Lorentz-violating terms in the quadratic Lagrange density for free fermions. The result is adapted to obtain the effective hamiltonian describing the propagation and mixing of three flavors of left-handed neutrinos in the presence of Lorentz violation involving operators of arbitrary mass dimension. A characterization of the neutrino coefficients for Lorentz violation is provided via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is discussed, including among others the renormalizable limit, the massless scenario, flavor-blind and oscillation-free models, the diagonalizable case, and several isotropic limits. The formalism is combined with existing data on neutrino oscillations and kinematics to extract a variety of measures of coefficients for Lorentz and CPT violation. For oscillations, we use results from the short-baseline experiments LSND and MiniBooNE to obtain explicit sensitivities to effects from flavor-mixing Lorentz-violating operators up to mass dimension 10, and we present methods to analyze data from long-baseline experiments. For propagation, we use time-of-flight measurements from the supernova SN1987A and from a variety of experiments including MINOS and OPERA to constrain oscillation-free Lorentz-violating operators up to mass dimension 10, and we discuss constraints from threshold effects in meson decays and Cherenkov emission.