Prospects for measuring <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> violation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup>

This work investigates the prospects for performing a time-dependent angular analysis of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi>B</a:mi> <a:mi>s</a:mi> <a:mn>0</a:mn> </a:msubsup> <a:mo stretchy="false">→</a:mo> <a:mi>ϕ</a:mi> <a:msup> <a:mi>μ</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi>μ</a:mi> <a:mo>−</a:mo> </a:msup> </a:math> decays at hadron colliders, and introduces new optimized angular observables associated with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msubsup> <d:mi>B</d:mi> <d:mi>s</d:mi> <d:mn>0</d:mn> </d:msubsup> </d:math> -mixing in the decay rate. The time-dependent normalized decay rate and corresponding probability density function is presented both for when the flavor of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msubsup> <f:mi>B</f:mi> <f:mi>s</f:mi> <f:mn>0</f:mn> </f:msubsup> </f:math> meson at production is tagged and when it is untagged. The normalized angular terms linked to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msubsup> <h:mi>B</h:mi> <h:mi>s</h:mi> <h:mn>0</h:mn> </h:msubsup> </h:math> -mixing in the tagged (untagged) case are denoted <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi mathvariant="script">Z</j:mi> <j:mi>i</j:mi> </j:msub> </j:math> ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi mathvariant="script">H</m:mi> <m:mi>i</m:mi> </m:msub> </m:math> ), and their optimized counterparts as <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>Q</p:mi> <p:mi>i</p:mi> </p:msub> </p:math> ( <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi mathvariant="script">M</r:mi> <r:mi>i</r:mi> </r:msub> </r:math> ). The expected sensitivities of these observables at the end of Run 3, Run 4, and Run 5 of the LHC are determined using pseudoexperiments generated with a decay-time resolution, background level, and signal yield similar to those reported by the LHCb Collaboration. It is found that all observables can be extracted with Run 3 statistics, and that the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi mathvariant="script">H</u:mi> <u:mi>i</u:mi> </u:msub> </u:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi mathvariant="script">Z</x:mi> <x:mi>i</x:mi> </x:msub> </x:math> observables have similar sensitivity, despite the former being suppressed by mixing terms. Moreover, the angular observables only accessible via flavor tagging, such as the equivalent of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msubsup> <ab:mi>P</ab:mi> <ab:mn>5</ab:mn> <ab:mo>′</ab:mo> </ab:msubsup> </ab:math> in the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msubsup> <cb:mi>B</cb:mi> <cb:mi>s</cb:mi> <cb:mn>0</cb:mn> </cb:msubsup> </cb:math> system, are found to exhibit sensitivities comparable to current measurements in <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msup> <eb:mi>B</eb:mi> <eb:mn>0</eb:mn> </eb:msup> <eb:mo stretchy="false">→</eb:mo> <eb:msup> <eb:mi>K</eb:mi> <eb:mrow> <eb:mo>*</eb:mo> <eb:mn>0</eb:mn> </eb:mrow> </eb:msup> <eb:msup> <eb:mi>μ</eb:mi> <eb:mo>+</eb:mo> </eb:msup> <eb:msup> <eb:mi>μ</eb:mi> <eb:mo>−</eb:mo> </eb:msup> </eb:math> decays once Run 5 datasets are available. Fits to the observables to extract the Wilson coefficients show a significant increase in precision when either the observables accessible via time-dependent analysis, or flavor tagging, are included. A marked increase in sensitivity to <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi>C</hb:mi> <hb:mi>P</hb:mi> </hb:math> -violating short-distance effects is observed for a subset of the new optimized <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:msub> <jb:mi>M</jb:mi> <jb:mi>i</jb:mi> </jb:msub> </jb:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:msub> <lb:mi>Q</lb:mi> <lb:mi>i</lb:mi> </lb:msub> </lb:math> observables.