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<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>asymmetries in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>K</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:math>decays
We consider the branching ratio and the $CP$ asymmetries in $B\ensuremath{\rightarrow}{f}_{0}(980){K}_{S}$ decay to the end of determining the deviation of the time-dependent $CP$ asymmetry from $\mathrm{sin}(2\ensuremath{\beta})$, $\ensuremath{\Delta}{S}_{{f}_{0}{K}_{S}}\ensuremath{\equiv}\ensuremath{-}{\ensuremath{\eta}}_{{f}_{0}{K}_{S}}{S}_{{f}_{0}{K}_{S}}\ensuremath{-}\mathrm{sin}(2\ensuremath{\beta})$, arising from standard model physics. We obtain $\ensuremath{\Delta}{S}_{{f}_{0}{K}_{S}}$ within the context of the QCD factorization framework for the $B\ensuremath{\rightarrow}{f}_{0}(980){K}_{S}$ decay amplitudes assuming the …