Improved global determination of two-meson distribution amplitudes from multi-body B decays

We improve the perturbative QCD (PQCD) formalism for multi-body charmless hadronic B meson decays, such as \(B\rightarrow VP_3 \rightarrow P_1P_2P_3\), by resolving the possible discrepancy in parametrizing the contribution of the P-wave resonance V to the two-meson distribution amplitudes (DAs) associated with the pairs \(P_1P_2=\pi \pi , K\pi , KK\). The determination of the Gegenbauer moments in the two-meson DAs is then updated in the global fit of the improved PQCD factorization formulas at leading order in the strong coupling \(\alpha _s\) to available data for branching ratios and polarization fractions of three- and four-body B decays. The convergence of the Gegenbauer expansion of the resultant two-meson DAs is manifest. The satisfactory quality of the fit implies the consistency of the PQCD framework for multi-body B decays and the universality of the nonperturbative two-meson DAs. In particular, the predicted longitudinal polarization fraction \(f_0(B_s^0\rightarrow K^{*0} {\bar{K}}^{*0})=28.2^{+8.8}_{-9.5} \%\) with the updated Gegenbauer moments matches well the measurement. The observable \(L_{K^{*0}{\bar{K}}^{*0}}=7.7^{+4.9}_{-3.8}\), defined as the ratio of the longitudinal amplitudes of the two U-spin related channels \(B_s^0\rightarrow K^{*0} {\bar{K}}^{*0}\) and \(B^0\rightarrow K^{*0} {\bar{K}}^{*0}\), accommodates the current data within errors. It is found that the direct CP asymmetries \({{\mathcal {A}}}^{0,||,\bot }_{\textrm{CP}}\) in the polarization states of some four-body decays \(B\rightarrow V_1V_2\rightarrow (P_1P_2)(P_3P_4)\) might be large, but the destruction among them result in small net CP violation. Our predictions can be confronted with LHCb and Belle-II data in the future.