The decay-time-dependent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> asymmetry in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msubsup><c:mi>B</c:mi><c:mi>s</c:mi><c:mn>0</c:mn></c:msubsup><c:mo stretchy="false">→</c:mo><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi><c:mo stretchy="false">(</c:mo><c:mo stretchy="false">→</c:mo><c:msup><c:mi>μ</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>μ</c:mi><c:mo>−</c:mo></c:msup><c:mo stretchy="false">)</c:mo><c:msup><c:mi>K</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>K</c:mi><c:mo>−</c:mo></c:msup></c:math> decays is measured using proton-proton collision data, corresponding to an integrated luminosity of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>6</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:msup><i:mi>fb</i:mi><i:mrow><i:mo>−</i:mo><i:mn>1</i:mn></i:mrow></i:msup></i:math>, collected with the LHCb detector at a center-of-mass energy of 13 TeV. Using a sample of approximately 349 000 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>B</k:mi><k:mi>s</k:mi><k:mn>0</k:mn></k:msubsup></k:math> signal decays with an invariant <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>K</m:mi><m:mo>+</m:mo></m:msup><m:msup><m:mi>K</m:mi><m:mo>−</m:mo></m:msup></m:math> mass in the vicinity of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>ϕ</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1020</o:mn><o:mo stretchy="false">)</o:mo></o:math> resonance, the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>C</s:mi><s:mi>P</s:mi></s:math>-violating phase <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>ϕ</u:mi><u:mi>s</u:mi></u:msub></u:math> is measured, along with the difference in decay widths of the light and heavy mass eigenstates of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:msubsup><w:mrow><w:mi>B</w:mi></w:mrow><w:mrow><w:mi>s</w:mi></w:mrow><w:mrow><w:mn>0</w:mn></w:mrow></w:msubsup><w:mtext>−</w:mtext><w:msubsup><w:mrow><w:mover accent="true"><w:mrow><w:mi>B</w:mi></w:mrow><w:mrow><w:mo stretchy="false">¯</w:mo></w:mrow></w:mover></w:mrow><w:mrow><w:mi>s</w:mi></w:mrow><w:mrow><w:mn>0</w:mn></w:mrow></w:msubsup></w:mrow></w:math> system, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="normal">Δ</ab:mi><ab:msub><ab:mi mathvariant="normal">Γ</ab:mi><ab:mi>s</ab:mi></ab:msub></ab:math>, and the difference of the average <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mi>B</eb:mi><eb:mi>s</eb:mi><eb:mn>0</eb:mn></eb:msubsup></eb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>B</gb:mi><gb:mn>0</gb:mn></gb:msup></gb:math> meson decay widths, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi mathvariant="normal">Γ</ib:mi><ib:mi>s</ib:mi></ib:msub><ib:mo>−</ib:mo><ib:msub><ib:mi mathvariant="normal">Γ</ib:mi><ib:mi>d</ib:mi></ib:msub></ib:math>. The values obtained are <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>ϕ</mb:mi><mb:mi>s</mb:mi></mb:msub><mb:mo>=</mb:mo><mb:mo>−</mb:mo><mb:mn>0.039</mb:mn><mb:mo>±</mb:mo><mb:mn>0.022</mb:mn><mb:mo>±</mb:mo><mb:mn>0.006</mb:mn><mb:mtext> </mb:mtext><mb:mtext> </mb:mtext><mb:mi>rad</mb:mi></mb:math>, <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi mathvariant="normal">Δ</ob:mi><ob:msub><ob:mi mathvariant="normal">Γ</ob:mi><ob:mi>s</ob:mi></ob:msub><ob:mo>=</ob:mo><ob:mn>0.0845</ob:mn><ob:mo>±</ob:mo><ob:mn>0.0044</ob:mn><ob:mo>±</ob:mo><ob:mn>0.0024</ob:mn><ob:mtext> </ob:mtext><ob:mtext> </ob:mtext><ob:msup><ob:mi>ps</ob:mi><ob:mrow><ob:mo>−</ob:mo><ob:mn>1</ob:mn></ob:mrow></ob:msup></ob:math>, and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mrow><sb:msub><sb:mrow><sb:mi mathvariant="normal">Γ</sb:mi></sb:mrow><sb:mrow><sb:mi>s</sb:mi></sb:mrow></sb:msub><sb:mo>−</sb:mo><sb:msub><sb:mrow><sb:mi mathvariant="normal">Γ</sb:mi></sb:mrow><sb:mrow><sb:mi>d</sb:mi></sb:mrow></sb:msub><sb:mo>=</sb:mo><sb:mo>−</sb:mo><sb:mn>0.005</sb:mn><sb:msubsup><sb:mrow><sb:mn>6</sb:mn></sb:mrow><sb:mrow><sb:mo>−</sb:mo><sb:mn>0.0015</sb:mn></sb:mrow><sb:mrow><sb:mo>+</sb:mo><sb:mn>0.0013</sb:mn></sb:mrow></sb:msubsup><sb:mo>±</sb:mo><sb:mn>0.0014</sb:mn><sb:mtext> </sb:mtext><sb:mtext> </sb:mtext><sb:msup><sb:mrow><sb:mi>ps</sb:mi></sb:mrow><sb:mrow><sb:mo>−</sb:mo><sb:mn>1</sb:mn></sb:mrow></sb:msup></sb:mrow></sb:math>, where the first uncertainty is statistical and the second systematic. These are the most precise single measurements to date and are consistent with expectations based on the Standard Model and with the previous LHCb analyses of this decay. These results are combined with previous independent LHCb measurements. The phase <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>ϕ</wb:mi><wb:mi>s</wb:mi></wb:msub></wb:math> is also measured independently for each polarization state of the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msup><yb:mi>K</yb:mi><yb:mo>+</yb:mo></yb:msup><yb:msup><yb:mi>K</yb:mi><yb:mo>−</yb:mo></yb:msup></yb:math> system and shows no evidence for polarization dependence. © 2024 CERN, for the LHCb Collaboration 2024 CERN