Spectator Scattering and Annihilation Contributions as a Solution to the $\pi K$ and $\pi \pi$ Puzzles within QCD Factorization Approach

Abstract

The large branching ratios for pure annihilation ${\bar{B}}_s^0$ $\to$ ${\pi }^{+}{\pi }^{-}$ and ${\bar{B}}_d^0$ $\to$ $K^{+}{K}^{-}$ decays reported by CDF and LHCb collaborations recently and the so-called $\pi K$ and $\pi \pi$ puzzles indicate that spectator scattering and annihilation contributions are important to the penguin-dominated, color-suppressed tree dominated, and pure annihilation nonleptonic $B$ decays. Combining the available experimental data for $B_{u,d}$ $\to$ $\pi \pi$, $\pi K$ and $K\bar{K}$ decays, we do a global fit on the spectator scattering and annihilation parameters $X_H({\rho }_H$, ${\varphi }_H)$, $X_A^i({\rho }_A^i,{\varphi }_A^i)$ and $X_A^f({\rho }_A^f,{\varphi }_A^f)$, which are used to parameterize the endpoint singularity in amplitudes of spectator scattering, nonfactorizable and factorizable annihilation topologies within the QCD factorization framework, in three scenarios for different purpose. Numerically, in scenario II, we get $({\rho }_A^i,{\varphi }_A^i{[}^{\circ }])=(2.88_{-1.30}^{+1.52},-103_{-40}^{+33})$ and $({\rho }_A^f,{\varphi }_A^f{[}^{\circ }])=(1.21_{-0.25}^{+0.22},-40_{-8}^{+12})$ at the $68\%$ confidence level, which are mainly demanded by resolving $\pi K$ puzzle and confirm the presupposition that $X_A^i\ne X_A^f$. In addition, correspondingly, the $B$-meson wave function parameter ${\lambda }_B$ is also fitted to be $0.18_{-0.08}^{+0.11}MeV$, which plays an important role for resolving both $\pi K$ and $\pi \pi$ puzzles. With the fitted parameters, the QCDF results for observables of $B_{u,d}$ $\to$ $\pi \pi$, $\pi K$ and $K\bar{K}$ decays are in good agreement with experimental measurements. Much more experimental and theoretical efforts are expected to understand the underlying QCD dynamics of spectator scattering and annihilation contributions.

26 pages, 8 figures, 5tables; version accepted for publication in Phys. Rev. D

References in corpus (5)

• Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach
• Branching fractions, polarisation and asymmetries of B -> VV decays
• B- -> pi- pi0/rho- rho0 to NNLO in QCD factorization
• Resolving B-CP Puzzles in QCD Factorization
• Revisiting the Annihilation Corrections in Non-leptonic ${\bar{B}}_s^0$ Decays within QCD Factorization

Cited by in corpus (15)

• A Combined Fit on the Annihilation Corrections in $B_{u,d,s}$ $\to$ $PP$ Decays Within QCDF
• Observation of the annihilation decay mode $B^0\to K^{+}{K}^{-}$
• Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization
• Transverse-momentum-dependent wave functions with Glauber gluons in $B\to \pi \pi$, $\rho \rho$ decays
• Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays
• Study of the weak annihilation contributions in charmless $B_s\to VV$ decays
• 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
• Branching ratio and $CP$ violation of $B\to K\pi$ decays in a modified perturbative QCD 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
• Study of $B\to PP$ decays in the modified perturbative QCD approach
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• Charmless $B_c\to VV$ decays in the QCD factorization approach
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• Study of the ${\rm Y}(1S)$ $\to$ $DP$ decays