For the purpose of searching for Lorentz-invariance violation in the minimalStandard-Model Extension, we perfom a reanalysis of data obtained from the$^{133}\text{Cs}$ fountain clock operating at SYRTE. The previous study led tonew limits on eight components of the $\tilde{c}_{\mu\nu}$ tensor, whichquantifies the anisotropy of the proton kinetic energy. We recently derived anadvanced model for the frequency shift of hyperfine Zeeman transition due toLorentz violation and became able to constrain the ninth component, theisotropic coefficient $\tilde{c}_{TT}$, which is the least well-constrainedcoefficient of $\tilde{c}_{\mu\nu}$. This model is based on a second-orderboost Lorentz transformation from the laboratory frame to the Sun-centeredframe, and it gives rise to an improvement of five orders of magnitude on$\tilde{c}_{TT}$ compared to the state of the art.
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