Abstract
Lorentz invariance may only be broken far above the electroweak scale, since violations are experimentally stringently constrained. Therefore, the Standard-Model Extension parameterizing Lorentz violation (LV) via (higher-dimensional) field theory operators is manifestly SU(2)L gauge-invariant. As a consequence, LV in neutrinos implies LV in charged leptons and vice versa. This allows us to obtain estimated sensitivities for flavour-changing operators in the charged-lepton sector from neutrino oscillations as well as sensitivities for flavour-diagonal neutrino effects from high-precision electron experiments. We also apply this method to an analysis of time-of-flight data for neutrinos (detected by IceCube) and photons from gamma ray bursts where discrepancies have been observed. Our conclusion is that an explanation of the arrival time difference between neutrino and photon events by dim-5 operators in the neutrino sector would lead to unacceptably large LV effects in the charged-lepton sector.
Highlights
A multitude of tests of Lorentz invariance have been carried out over the past decades
Our conclusion is that an explanation of the arrival time difference between neutrino and photon events by dim-5 operators in the neutrino sector would lead to unacceptably large Lorentz violation (LV) effects in the charged-lepton sector
This consideration will demonstrate that LV in the neutrino sector, as studied in the context of the former OPERA excess [24] and recently deduced from data on IceCube neutrino events in refs. [25, 26], would imply LV for charged leptons that clashes with existing experimental constraints
Summary
As motivated in the introduction, LV is usually assumed to occur at very high energies. The effective framework valid at low energies, the SME, includes LV operators of mass dim-3 and 4, classified in ref. (aΨ)μAB and (cΨ)μAνB are understood as generalizations of the LV coefficients within the minimal SME [15, 16]. They can be written as infinite series involving four-derivatives:. The operator in eq (2.3a) (eq (2.3b)) is C -odd (C -even) [22] which implies that the coefficients enter with opposite (same) signs in the dispersion relations of fermions and antifermions As the operator has an odd (even) number of Lorentz indices, it is CPT -odd (CPT -even), i.e., it generates (no) CPT violation. Note that since the neutrino is contained within the lepton doublet, any modification of neutrino properties affects charged leptons.
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