A new implication for strong interactions if large, direct CP violation in Bbar^0(B^0) -> pi^+pi^- is confirmed

We show that the large, direct CP-violation parameter $A_{\pi\pi}=-C_{\pi\pi}$, reported by the BELLE collaboration in the decays Bbar^0(B^0) -> \pi^+\pi^-, implies an unusual situation in which the presence of a very large difference between two strong-interaction phases ~ -110 deg. plays an essential role. We make the demonstration within a model of strong, two-body quasi-elastic interactions between physical hadrons. The model can accommodate a large difference between two strong-interaction phases, for which it provides a natural enhancement.