Impact of Lorentz violation on anomalous magnetic moments of charged leptons
Andreas Crivellin, Fiona Kirk, Marco Schreck
Abstract
A bstract We address the question whether a violation of Lorentz symmetry can explain the tension between the measurement and the Standard-Model prediction of the anomalous magnetic moment of the muon, ( g − 2) μ , and whether it can significantly impact the one of the electron, ( g — 2) e . While anisotropic Lorentz-violating effects are, in general, expected to produce sidereal oscillations in observables, isotropic Lorentz violation (LV) in the charged-lepton sector could also feed into ( g — 2) e , μ . However, we find that this type of Lorentz violation, parametrised via a dim-4 field operator of the Standard-Model Extension (SME), is already strongly constrained by the absence of vacuum Čerenkov radiation and photon decay. In particular, the observations of very-high-energetic astrophysical photons at LHAASO and of high-energetic electrons (muons) by the LHC (IceCube) place the most stringent two-sided bounds on the relevant SME coefficients $$ \overset{\circ }{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>c</mml:mi><mml:mo>∘</mml:mo></mml:mover></mml:math> (e) ( $$ \overset{\circ }{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>c</mml:mi><mml:mo>∘</mml:mo></mml:mover></mml:math> (μ) ). Therefore, any explanation of the tension in ( g − 2) μ via isotropic Lorentz violation of the minimal spin-degenerate SME is excluded, and the possible size of its impact on ( g − 2) e is very limited.