A timedependent angular analysis of $B_s^0\to\psi(2S)\phi$ decays is performed using data recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0\invfb collected during Run 1 of the LHC. The CPviolating phase and decaywidth difference of the $B_s^0$ system are measured 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 first uncertainty is statistical and the second systematic. This is the first time that $\phi_s$ and $\Delta\Gamma_s$ have been measured in a decay containing the $\psi(2S)$ resonance.
Definition of helicity angles. 
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Distribution of $m(\psi(2S) K ^+ K ^ )$ for the selected $ B ^0_ s \rightarrow \psi(2S)\phi$ candidates. The total fit model is shown by the solid blue line, which is composed of a sum of two Crystal Ball functions for the signal and an exponential function for the background (longdashed green line). 
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Distribution of $m(\psi(2S) K ^+ \pi^)$ of the selected $ B ^0 \rightarrow \psi(2S)K^{*}(892)^{0}$ candidates. The total fit model is shown by the solid blue line, which is composed of a sum of two Crystal Ball functions for the signal and an exponential function for the background (longdashed green line). 
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Decaytime efficiency $\varepsilon_{\rm data}^{ B ^0_ s }(t)$ in arbitrary units. 
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Decaytime and helicityangle distributions for $ B ^0_ s \rightarrow \psi(2S)\phi$ decays (data points) with the onedimensional projections of the fitted PDF. The solid blue line shows the total signal contribution, which is composed of $ C P$ even (longdashed red), $ C P$ odd (shortdashed green) and $S$wave (dashdotted purple) contributions. 
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$A_0^2$ as a function of the invariant mass squared of the dimuon system, $q^2$. Data points are taken from Ref. [38] ($ B ^0_ s \rightarrow \phi\mu^+\mu^$, circles), Ref. [3] ($ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \phi$, diamond) and this paper (square). 
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Animated gif made out of all figures. 
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Results of the maximum likelihood fit to the selected $ B ^0_ s \rightarrow \psi(2S)\phi$ candidates including all acceptance and resolution effects. The first uncertainty is statistical and the second is systematic, which will be discussed in Section 7. 
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Correlation matrix of statistical uncertainties. 
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Summary of statistical and systematic uncertainties. Fields containing a dash () correspond to systematic uncertainties that are negligible. 
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Created on 21 October 2019.