Resolving the CP Asymmetry Puzzle in $B$ Decays with Unitarized Final-State Interactions

Abstract

A reliable description of direct CP asymmetries in hadronic $B$ decays, among the most sensitive probes of the CKM mechanism and of physics beyond the Standard Model, remains unresolved. Conventional factorization approaches adopt distinct treatments for the strong phases originating from long-distance QCD interactions, leading to predictions that differ by factors of several for identical decay channels. Existing final-state interaction (FSI) models are limited to one-loop approximations that break unitarity and rely on channel-specific phenomenological cutoffs, severely restricting the predictive capability. We introduce a unitarized FSI framework based on the Lippmann-Schwinger equation solved to all orders, restoring unitarity that is manifestly broken in one-loop treatments. Using the coupled $D\bar{D}$ system, we show that the interaction kernel can be derived from chiral effective field theory constrained by heavy-quark spin symmetry, and low-energy constants are fixed by the $\gamma\gamma\to D\bar{D}$ cross-section data from BaBar, leaving no adjustable parameter in the FSI sector when applied to $B$ decays. The resulting predictions for CP asymmetries and branching fractions show excellent agreement with the available experimental data. A defining consequence is that CP asymmetries in the pure-annihilation channels $\bar{B}^0\to D^0\bar{D}^0$ and $\bar{B}^0\to D_s^+D_s^-$, identically zero in any short-distance treatment, are dramatically enhanced by FSI, and a measured nonzero asymmetry in these modes is therefore a direct experimental signature of long-distance dynamics. We present definite predictions for the partial widths and CP asymmetries of all yet-unmeasured channels, establishing final-state interactions as a predictive, data-driven ingredient of the Standard Model with direct implications for CKM parameter extraction and BSM searches.