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

TL;DR

This paper refines the PQCD approach for multi-body B meson decays by better modeling two-meson distribution amplitudes, leading to improved fits to experimental data and consistent predictions for polarization and CP asymmetries.

Contribution

It introduces an improved parametrization of two-meson DAs in PQCD, updates Gegenbauer moments through a global fit, and demonstrates the framework's consistency with experimental results.

Findings

Gegenbauer expansion convergence is confirmed.

Predicted polarization fractions match experimental data.

Potential for large direct CP asymmetries in some decay channels.

Abstract

We improve the perturbative QCD (PQCD) formalism for multi-body charmless hadronic $B$ meson decays, such as $B\to VP_3\to P_1P_2P_3$, 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 $f_0(B_s^0\to K^{*0} {\bar K}^{*0})=28.2^{+8.8}_{-9.5} \%$ 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 $B_s^0\to K^{*0} {\bar K}^{*0}$ and $B^0\to K^{*0} {\bar K}^{*0}$, accommodates the current data within errors. It is found that the direct $CP$ asymmetries ${\cal A}^{0,||,\bot}_{\rm CP}$ in the polarization states of some four-body decays $B\to V_1V_2\to (P_1P_2)(P_3P_4)$ 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.