For the purpose of searching for Lorentz-invariance violation in the minimal Standard-Model Extension, we perfom a reanalysis of data obtained from the $^{133}text{Cs}$ fountain clock operating at SYRTE. The previous study led to new limits on eight components of the $tilde{c}_{mu u}$ tensor, which quantifies the anisotropy of the proton kinetic energy. We recently derived an advanced model for the frequency shift of hyperfine Zeeman transition due to Lorentz violation and became able to constrain the ninth component, the isotropic coefficient $tilde{c}_{TT}$, which is the least well-constrained coefficient of $tilde{c}_{mu u}$. This model is based on a second-order boost Lorentz transformation from the laboratory frame to the Sun-centered frame, 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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