Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization

Abstract

In this paper, we investigate the contributions of hard spectator scattering and annihilation in $B\to PV$ decays within the QCD factorization framework. With available experimental data on $B\to \pi K^{\ast }$, $\rho K$, $\pi \rho$ and $K\varphi$ decays, comprehensive ${\chi }^2$ analyses of the parameters $X_{A,H}^{i,f}({\rho }_{A,H}^{i,f},{\varphi }_{A,H}^{i,f})$ are performed, where $X_A^f$ ($X_A^i$) and $X_H$ are used to parameterize the endpoint divergences of the (non)factorizable annihilation and hard spectator scattering amplitudes, respectively. Based on ${\chi }^2$ analyses, it is observed that (1) The topology-dependent parameterization scheme is feasible for $B\to PV$ decays; (2) At the current accuracy of experimental measurements and theoretical evaluations, $X_H=X_A^i$ is allowed by $B\to PV$ decays, but $X_H\ne X_A^f$ at $68$ C. L.; (3) With the simplification $X_H=X_A^i$, parameters $X_A^f$ and $X_A^i$ should be treated individually. The above-described findings are very similar to those obtained from $B\to PP$ decays. Numerically, for $B\to PV$ decays, we obtain $({\rho }_{A,H}^i,{\varphi }_{A,H}^i{[}^{\circ }])=(2.87_{-1.95}^{+0.66},-145_{-21}^{+14})$ and $({\rho }_A^f,{\varphi }_A^f{[}^{\circ }])=(0.91_{-0.13}^{+0.12},-37_{-9}^{+10})$ at $68$ C. L.. With the best-fit values, most of the theoretical results are in good agreement with the experimental data within errors. However, significant corrections to the color-suppressed tree amplitude ${\alpha }_2$ related to a large ${\rho }_H$ result in the wrong sign for $A_{CP}^{dir}(B^{-}\to {\pi }^0{K}^{\ast -})$ compared with the most recent BABAR data, which presents a new obstacle in solving "$\pi \pi$" and "$\pi K$" puzzles through ${\alpha }_2$. A crosscheck with measurements at Belle (or Belle II) and LHCb, which offer higher precision, is urgently expected to confirm or refute such possible mismatch.

arXiv comment17 pages, 4 figures; Accepted for publication in PLB

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• Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays
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• Fits of Weak Annihilation and Hard Spectator Scattering Corrections in $B_{u,d}\to VV$ Decays
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• Study of $CP$ Violations in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}{f}_0(500)$ decays in the QCD factorization approach
• CP violation in the interference between $\rho (770{)}^0$ and $S$-wave in $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays and its implication for CP asymmetry in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$
• Study of localized $CP$ violation in $B^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}$ and the branching ratio of $B^{-}\to \sigma (600){\pi }^{-}$ in the QCD factorization approach
• Pure annihilation decays of $B_s^0\to a_0^{+}{a}_0^{-}$ and $B_d^0\to K_0^{\ast +}{K}_0^{\ast -}$ in the PQCD approach
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• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach