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

Abstract

The LHCb experiment has measured CP violation (CPV) across the Dalitz plot of charmless decays of B+ mesons to 3 charged tracks, namely in K{\pi}{\pi}, KKK, {\pi}{\pi}{\pi} and {\pi}KK final states, with strikingly large CPV that vary strongly with Dalitz variables. Identifying these processes with b -> sqq(bar), sss(bar) and b -> dqq(bar), dss(bar), 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.

Comments: 12 pages, 7 figures, to appear in proceedings of HADRON2019, held August 2019 in Guilin, China