Implications of $\textit{SU}(2)_L$ gauge invariance for constraints on Lorentz violation

TL;DR

This paper explores how $SU(2)_L$ gauge invariance constrains Lorentz violation (LV) in the Standard-Model Extension, linking neutrino and charged-lepton sectors, and derives new bounds on LV effects from experimental data.

Contribution

It demonstrates that gauge invariance imposes strong correlations between neutrino and charged-lepton LV, leading to novel bounds and constraining explanations of neutrino-photon time delays.

Findings

Tight bounds on neutrino LV from charged-lepton constraints

LV explanations for neutrino-photon time delays are ruled out

New limits on dim-5 operators in neutrino sector

Abstract

Lorentz invariance is one of the basic ingredients of quantum field theories and violations of it are stringently constrained experimentally. Therefore, the possibility of Lorentz violation (LV) is usually realized at very high energy scales, resulting in a strong suppression of it (by the new scale) in experiments. The Standard-Model Extension (SME) parameterizes LV in a model-independent way, respecting $SU(2)_L$ gauge invariance. This means, e.g., that the neutrino and charged-lepton sectors are linked to each other. Hence, on the one hand, any modification of neutrino properties simultaneously gives rise to effects for charged leptons, which is why the tight limits on flavour-off-diagonal LV for neutrinos imply new bounds on modifications of charged leptons. On the other hand, LV for left-handed charged leptons implies LV for neutrinos. Since LV modifications of the charged-lepton sector are, in general, even more constraining than effects in the flavour-diagonal neutrino sector, we obtain novel tight bounds on LV in the latter. Subsequently, we apply the same approach 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 finding 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.