We perform a global analysis of three-body charmless hadronic decays $B\to V{P}_3\to P_1{P}_2{P}_3$ in the perturbative QCD (PQCD) approach, where $V$ denotes an intermediate vector resonance, and $P_i$, $i=1$, 2, 3 denote final-state pseudoscalar mesons. Fitting the PQCD factorization formulas at leading order in the strong coupling ${\alpha }_s$ to measured branching ratios and direct $CP$ asymmetries, we determine the Gegenbauer moments in the two-meson distribution amplitudes (DAs) for the meson pairs $P_1{P}_2=\pi \pi ,K\pi ,KK$. The fitted Gegenbauer moments are then employed to make predictions for those observables, whose data are excluded in the fit due to larger experimental uncertainties. A general consistency between our predictions and data is achieved, which hints at the validity of the PQCD formalism for the above three-body $B$-meson decays and the universality of the nonperturbative two-meson DAs. The obtained two-meson DAs can be applied to PQCD studies of other multi-body $B$-meson decays involving the same meson pairs. We also attempt to determine the dependence of the Gegenbauer moments on the meson-pair invariant mass, and demonstrate that this determination is promising, when data become more precise.

• Received 19 May 2021
• Accepted 7 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.096014

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society