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A time-dependent angular analysis of $B_s^0\to\psi(2S)\phi$ decays isperformed using data recorded by the LHCb experiment. The data set correspondsto an integrated luminosity of 3.0\invfb collected during Run 1 of the LHC. TheCP-violating phase and decay-width difference of the $B_s^0$ system aremeasured to be $\phi_s = 0.23^{+0.29}_{-0.28} \pm 0.02$ rad and $\Delta\Gamma_s= 0.066^{+0.041}_{-0.044} \pm 0.007$ ps$^{-1}$, respectively, where the firstuncertainty is statistical and the second systematic. This is the first timethat $\phi_s$ and $\Delta\Gamma_s$ have been measured in a decay containing the$\psi(2S)$ resonance.

First study of the CP-violating phase and decay-width difference in $B_s^0\to\psi(2S)\phi$ decays