Search for CP Violation in the Decays $D^0\rightarrow K^0_S P^0$

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Throughout this Letter the charge-conjugate decay mode is also implied unless stated otherwise

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We use A C ​ P K ¯ 0 = Γ ⁡ ( K ¯ 0 → f ¯ ) − Γ ⁡ ( K 0 → f ) Γ ⁡ ( K ¯ 0 → f ¯ ) + Γ ⁡ ( K 0 → f ) A^{\bar{K}^{0}}_{CP}~=~\frac{\Gamma(\bar{K}^{0}\rightarrow\bar{f})-\Gamma(K^{0}\rightarrow f)}{\Gamma(\bar{K}^{0}\rightarrow\bar{f})+\Gamma(K^{0}\rightarrow f)} . Hence, A C ​ P K ¯ 0 = − A L A^{\bar{K}^{0}}_{CP}=-A_{L} where A L A_{L} is the symbol for the asymmetry used in Ref. PDG2010

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The leading-order prediction for A F ​ B c ​ c ¯ A^{c\bar{c}}_{FB} at s \sqrt{s} =10.6 GeV is about − 0.029 cos θ CMS / ( 1 + cos 2 θ CMS ) -0.029\cos\theta^{\rm CMS}/(1+\cos^{2}\theta^{\rm CMS}) . See for example O. Nachtmann, Elementary Particle Physics, Springer-Verlag (1989)

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The systematic uncertainty due to the A ϵ π s + A^{\pi^{+}_{s}}_{\epsilon} determination in the two measurements are only partially correlated due to the use of slightly different data set and different tracking algorithms. The difference in the results when treating the systematic uncertainties as completely correlated or completely uncorrelated is negligible. To be conservative, we quote the result treating the systematic uncertainties as uncorrelated

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