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Recent LHCb data for time-dependent CP violation in $B_d^0 \to \pi^+\pi^-$and $B^0_s\to K^+K^-$ show deviations from theoretical predictions. Besidestheir central values for $\mathcal C_{K^+K^-}$, $\mathcal S_{K^+K^-}$ and$\mathcal A^{\Delta \Gamma}_{K^+K^-}$ violate quantum mechanic CPT invariantsum rule (CPT sum rule) prediction of $|\mathcal C_{K^+K^-}|^2 + |\mathcalS_{K^+K^-}| ^2 + |\mathcal A^{\Delta \Gamma}_{K^+K^-}|^2 = 1$ (LHCb data implythe sum to be $0.67\pm 0.20$.), their values for $\mathcal C_{K^+ K^-}= 0.24\pm0.06\pm {0.02}$ and $\mathcal C_{\pi^+ \pi^-} = - 0.24\pm 0.07\pm 0.01$ alsoshow large violation of SU(3) or its U-spin sub-group symmetry (SU(3)/U)relation $\mathcal C_{K^+ K^-} /\mathcal C_{\pi^- \pi^+} = - \mathcal B(B_d^0\to \pi^- \pi^+)\tau_{B^0_s}/\mathcal B(B^0_s \to K^+ K^-)\tau_{B_d^0}$ (LHCbdata imply the ratio of left-side to right-side to be $4.67\pm 1.88$.) . TheLHCb results need to be further confirmed to be taken seriously. We suggest touse time-dependent CP violation in $B_s\to K^0\bar K^0, \pi^+\pi^-, \pi^0\pi^0$to further test the CPT sum rule. Assuming that the sum rule holds, we proposethat violation of the SU(3)/U relation may indicate a large FSI phasedifference in the $\pi^+\pi^-$ and $K^+K^-$ re-scattering. We suggest severalother U-spin pairs of $B\to PP$ decays to further test SU(3)/U relations.

Tests for CPT sum rule and U-spin violation in Time-dependent CP violation of $B^0_s \to K^+ K^-$ and $B^0_d \to \pi^+ \pi^-$