The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and $CPT$ violation. Two Lorentz and $CPT$ violation signatures were searched for a nonzero $\Delta {\omega }_a(={\omega }_a^{{\mu }^{+}}-{\omega }_a^{{\mu }^{-}})$ and a sidereal variation of ${\omega }_a^{{\mu }^{\pm }}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_Z=-(1.0\pm 1.1)\times {10}^{-23}\mathrm{GeV}$; $(m_{\mu }{d}_{Z0}+H_{XY})=(1.8\pm 6.0)\times {10}^{-23}\mathrm{GeV}$; and the 95% confidence level limits ${\check{b}}_{\perp }^{{\mu }^{+}}<1.4\times {10}^{-24}\mathrm{GeV}$ and ${\check{b}}_{\perp }^{{\mu }^{-}}<2.6\times {10}^{-24}\mathrm{GeV}$.

• Received 29 September 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.091602