Revisiting the pure annihilation decays $B_s\to {\pi }^{+}{\pi }^{-}$ and $B^0\to K^{+}{K}^{-}$: the data and the pQCD predictions

Abstract

In this work, we recalculate the charmless pure annihilation decays $B_s\to {\pi }^{+}{\pi }^{-}$ and $B^0\to K^{+}{K}^{-}$ by using the perturbative QCD (pQCD) factorization approach, and compare the pQCD predictions with currently available experimental measurements. We used the same set of relevant input parameters and wave functions to make the calculations for the considered decay modes and found the following results: (a) one can provide a consistent pQCD interpretation for both the measured $Br(B_s^0\to {\pi }^{+}{\pi }^{-})$ and $Br(B_d^0\to K^{+}{K}^{-})$ simultaneously; (b) the pQCD predictions for $Br(B_s^0\to {\pi }^{+}{\pi }^{-})$ obtained by different authors are well consistent with each other; (c) our new pQCD prediction for $Br(B_d^0\to K^{+}{K}^{-})$ agree very well with the measured values from CDF and LHCb Collaboration; and (d) the CP-violating asymmetry ${\mathcal{A}}_{CP}(B_d^0\to K^{+}{K}^{-})\approx 16$, which is large and may be detected at the LHCb experiment.

11 pages, 1 ps figure, more discussions are made, some parts of the manuscript have been rewritten, several new references are added, several typos removed. To be published in Phys. Rev. D

References in corpus (3)

• Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach
• Branching ratios and CP asymmetries of $B\to K{\eta }^{(\prime )}$ decays in the pQCD approach
• Implications of the recent measurement of pure annihilation $B_s\to {\pi }^{+}{\pi }^{-}$ decays in QCD factorization

Cited by in corpus (65)

• The semileptonic decays $B/B_s\to (\pi ,K)(l^{+}{l}^{-},l\nu ,\nu \bar{\nu })$ in the perturbative QCD approach beyond the leading-order
• $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ and $B_s\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Improved Estimates of The $B_{(s)}\to VV$ Decays in Perturbative QCD Approach
• Analysis of Charmless Two-body B decays in Factorization Assisted Topological Amplitude Approach
• Semileptonic decays $B\to D^{(\ast )}l\nu$ in the perturbative QCD factorization approach
• Spectator Scattering and Annihilation Contributions as a Solution to the $\pi K$ and $\pi \pi$ Puzzles within QCD Factorization Approach
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Anatomy of $B\to K{\eta }^{(\prime )}$ decays in different mixing schemes and effects of next-to-leading order contributions in the perturbative QCD approach
• A Combined Fit on the Annihilation Corrections in $B_{u,d,s}$ $\to$ $PP$ Decays Within QCDF
• Semileptonic decays $B/B_s \to (η,\etar, G)(l^+l^-,l\barν,ν\barν)$ in the perturbative QCD approach beyond the leading order
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• Hochschild homology, trace map and $\zeta$-cycles
• Flavor dependence of annihilation parameters in QCD factorization
• Observation of the annihilation decay mode $B^0\to K^{+}{K}^{-}$
• Study of ${\bar{B}}_s^0\to (D_s^{+},D_s^{\ast +})l^{-}{\bar{\nu }}_l$ decays in the pQCD factorization approach
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• Rescattering Contributions to rare B-Meson Decays
• The NLO twist-3 contribution to the pion electromagnetic form factors in $k_T$ factorization
• Quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ in the perturbative QCD approach
• Semileptonic decays $B/B_s\to (D^{(\ast )},D_s^{(\ast )})l{\nu }_l$ in the PQCD approach with the lattice QCD input
• Study of $CP$ Violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays in the QCD factorization approach
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Light-front holographic distribution amplitudes of pseudoscalar mesons and their application to $B$-meson decays
• Revisiting the Annihilation Corrections in Non-leptonic ${\bar{B}}_s^0$ Decays within QCD Factorization
• Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• Two-body charmed B(Bs) decays involving a light scalar meson
• Nonleptonic charmless decays of $B_c\to TP,TV$ in the perturbative QCD approach
• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays
• Axial-vector mesons from $\tau \to AP{\nu }_{\tau }$ decays
• Branching Ratios and CP Violations of B \to K_0^*(1430) K^* Decays in the pQCD Approach
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• 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
• $B\to a_1(1260)a_1(1260)$ and $b_1(1235)b_1(1235)$ decays in the perturbative QCD approach
• Study of ${\bar{B}}_s\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ decays in the PQCD factorization approach with the lattice QCD input
• The PQCD approach towards to next-to-leading order: a short review
• The $\rho {\gamma }^{\ast }\to \pi (\rho )$ transition form factors in the Perturbative QCD factorization approach
• Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach
• The perturbative QCD predictions for the decay B^{0}_{s}\rightarrow SS(a_{0}(980),f_{0}(980),f_{0}(500))
• Nonleptonic decays of $B\to (f_1(1285),f_1(1420))V$ in the perturbative QCD approach
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• Perturbative QCD Analysis of Exclusive Processes $e^{+}{e}^{-}\to VP$ and $e^{+}{e}^{-}\to TP$
• Penguin-dominated $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays in the perturbative QCD approach
• 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
• Study of $B_s$ $\to$ ${\eta }_c(J/\psi )D$ decay with perturbative QCD approach
• Large non-factorizable contributions in $B\to a_0{a}_0$ decays
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Studies on the $B\to \kappa \bar{\kappa }$ decays in the perturbative QCD approach
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Studying the localized $CP$ violation and the branching fraction of the ${\bar{B}}^0\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• 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
• Revisiting $B_s\to PP$ and $PV$ Decays with Contributions from ${\varphi }_{B2}$ with perturbativen QCD approach
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• Doubling down on down-type diquarks
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• B\to K_1π(K) decays in the perturbative QCD approach
• Phenomenological studies on the ${\bar{B}}^0\to [K^{-}{\pi }^{+}{]}_{S/V}[{\pi }^{+}{\pi }^{-}{]}_{V/S}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Hadronic decays of $B\to a_1(1260)b_1(1235)$ in the perturbative QCD approach
• Sensitivity of Two-Body Non-Leptonic Branching Fractions to Theoretical Mass Variations in Heavy-Light Mesons
• Study of Form Factors and Observables in $B_c^{-}\to {\bar{D}}^{(\ast )0}{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c^{-}\to D^{(\ast )-}{\ell }^{+}{\ell }^{-}$ decays