Abstract
We perform a global analysis of three-body charmless hadronic decays $B\to VP_3\to P_1P_2P_3$ 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 $P_1P_2=\pi\pi, K\pi, KK$. 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 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.
Highlights
Since the perturbative QCD (PQCD) framework for three-body B-meson decays was proposed in Ref. [1], there have been extensive applications to various channels [2–15], and rich phenomenology has been explored
As the first attempt at a global determination of two-meson distribution amplitudes (DAs), we focus on the P-wave components, and employ the leading order (LO) PQCD factorization formulas for decay amplitudes
In this work we have performed a global fit of the Gegenbauer moments in two-meson DAs to measured branching ratios and direct CP asymmetries in the threebody hadronic B-meson decays B→VP3 →P1P2P3, with V 1⁄4 ρ; φ; KÃ and P3 1⁄4 π, K, in the LO PQCD approach
Summary
Since the perturbative QCD (PQCD) framework for three-body B-meson decays was proposed in Ref. [1], there have been extensive applications to various channels [2–15], and rich phenomenology has been explored. The other coefficients Bnlðω2Þ, referred to as the Gegenbauer moments, are still quite uncertain due to a lack of systematic nonperturbative studies Note that these Gegenbauer moments differ from those in the DA for a specific resonance which strongly decays into the meson pair, because, as stated above, a two-meson DA collects contributions from a series of resonances as well as nonresonant contributions. As the first attempt at a global determination of two-meson DAs, we focus on the P-wave components, and employ the LO PQCD factorization formulas for decay amplitudes. The global fit shows that at least the linear term in one of the twist-3 dipion DAs can be constrained effectively This indicates that the determination of the ω2-dependent Gegenbauer moments in two-meson DAs is promising, when data become more precise in the future.
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