Curious Link of Exclusive and Inclusive CPV in Charmless 3-body B$^+$ Decays

The LHCb experiment has measured CP violation (CPV) across the Dalitz plot of charmless decays of B+ mesons to 3 charged tracks, namely in Kππ, KKK, πππ and πKK final states, with strikingly large CPV that vary strongly with Dalitz variables. Identifying these processes with b → sqq, sss and b → dqq, dss, where q = u, d, then the “sum rule” that requires two-loop absorptive parts by unitarity works well for inclusive b → s CPV, but less well for inclusive b → d case. We elucidate the situation, and argue that the 30 year old unitarity/CPT argument is valid to this day, while affirming quark-hadron duality.