Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD

Abstract

We compute branching ratios of $B\to K\pi$ decays in the framework of perturbative QCD factorization theorem. Decay amplitudes are classified into the topologies of tree, penguin and annihilation, all of which contain both factorizable and nonfactorizable contributions. These contributions are expressed as the convolutions of hard $b$ quark decay amplitudes with universal meson wave functions. It is shown that (1) matrix elements of penguin operators are dynamically enhanced compared to those employed in the factorization assumption; (2) annihilation diagrams are not negligible, contrary to common belief; (3) annihilation diagrams contribute large strong phases; (4) the uncertainty of current data of the ratio $R=\mathcal{B}(B_d^0\to K^{\pm }{\pi }^{\mp })/\mathcal{B}(B^{\pm }\to K^0{\pi }^{\pm })$ and of CP asymmetries is too large to give a constraint of ${\varphi }_3$. Assuming ${\varphi }_3=90^o$ which is extracted from the best fit to the data of $R$, predictions for the branching ratios of the four $B\to K\pi$ modes are consistent with data.

Latex, 57 pages including 3 tables and 13 figures

References in corpus (3)

• Long-distance effects in $B\to V\gamma$ radiative weak decays
• Final state interaction and $B\to KK$ decays in perturbative QCD
• SU(3) Flavor Symmetry and CP Violating Rate Differences for Charmless $B\to PV$ Decays

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• Two-body charmed B(Bs) decays involving a light scalar meson
• Branching ratios, $CP$ asymmetries and polarizations of $B\to \psi (2S)V$ decays
• Resonance contributions $\varphi (1020,1680)\to K\bar{K}$ for the three-body decays $B\to K\bar{K}h$
• Nonleptonic charmless decays of $B_c\to TP,TV$ in the perturbative QCD approach
• Implications of Family Nonuniversal $Z^{\prime }$ Model on B -->K_0^* pi Decays
• Three-parton contribution to pion form factor in kT factorization
• The Effects of a Family Non-universal Z' Boson in the \bar{B}_s->πK, πK*, ρK Decays and B_d-\bar{B_d} mixing
• Study of Bc->KK decay with perturbative QCD approach
• Charmless hadronic $B_c\to VA,AA$ decays in the perturbative QCD approach
• Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
• Comment on "Gauge Invariance and $k_T$-Factorization of Exclusive Processes"
• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Resonant state $D_0^{\ast }(2400)$ in the quasi-two-body $B$ meson decays
• Reinvestigating the $B$ $\to$ $PP$ decays by including the contributions from ${\varphi }_{B2}$
• Rare decays of B-> J/ψD^(*) and B->η_c D^(*)in pQCD Approach
• What can we learn from $B\to a_1(1260)(b_1(1235))\pi (K)$ decays?
• $B\to K{K}^{\ast }$ Decays in the Perturbative QCD Approach
• ${\bar{B}}_{d,s}\to D_{d,s}^{\ast }V$ and ${\bar{B}}_{d,s}^{\ast }\to D_{d,s}V$ decays within QCD Factorization and Possible Puzzles
• Reexamining charmless B\to PV decays in QCD factorization approach
• Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays
• The effects of a family non-universal Z-prime boson on B--->pipi decays
• Measurements of Branching Fractions and CP-Violating Asymmetries in B Meson Decays to Charmless Two-Body States Containing a K0
• Search for Direct CP Violation in B -> K pi Decays
• Phenomenological studies on the $B_{d,s}^0\to J/\psi f_0(500)[f_0(980)]$ decays
• Implications of new data in charmless B decays
• Baryonic D Decay $D_s^{+}\to p\bar{n}$ and Its Implication
• K_1(1270)-K_1(1400) mixing and the fourth generation SM effects in B-->K_1l^+l^- decays
• B\to πϕin SM and MSSM
• Study of CP-violating asymmetries in B^0 --> pi^+pi^-, K^+pi^- decays
• Study of $B_c\to DS$ Decays in PQCD Approach
• Study of the weak annihilation contributions in charmless $B_s\to VV$ decays
• Branching Ratios and CP Violations of B \to K_0^*(1430) K^* Decays in the pQCD Approach
• Okubo-Zweig-Iizuka-rule violation and B\to η^{(\prime)}K branching ratios
• Exclusive processes $e^{+}{e}^{-}\to VP$ in $k_T$ factorization
• Flavor Physics at the CEPC: a General Perspective
• Analysis of Supersymmetric Effects on B -> phi K Decays in the PQCD Approach
• Weak phases from topological-amplitude parametrization
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• Charmless $B_s\to PP,PV,VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II
• Revisiting $K\pi$ puzzle in the pQCD factorization approach
• Fits of Weak Annihilation and Hard Spectator Scattering Corrections in $B_{u,d}\to VV$ Decays
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Systematic Error on Weak Phase $\gamma$ from $B\to {\pi }^{+}{\pi }^{-}$ and $B\to K\pi$
• NLO contributions to $B\to K{K}^{\ast }$ Decays in the pQCD approach
• Space- and time-like electromagnetic pion form factors in light-cone pQCD
• Constraints on SUSY Gluonic Dipole Interaction from B\to KπDecays
• Non-leptonic decays of Charmed mesons into two Pseudoscalars
• Direct CP Violation in Untagged B-Meson Decays
• Recent Developments on the CKM Matrix
• Study of the $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay with perturbative QCD approach
• Power corrections to quasi-distribution amplitudes of a heavy meson
• Charmonium decays of beauty baryons in the perturbative QCD approach
• Investigation of $B_{u,d}\to (\pi ,K)\pi$ decays within unparticle physics
• $B\to a_1(1260)a_1(1260)$ and $b_1(1235)b_1(1235)$ decays in the perturbative QCD approach
• To understand the rare decay $B_s\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$
• What can we learn from $B\to$ $\rho (\omega )K$ decays?
• Study of $B\to K_0^{\ast }(1430)K^{(\ast )}$ decays in QCD Factorization Approach
• Cabibbo-Kobayashi-Maskawa-favored $B$ decays to a scalar meson and a $D$ meson
• The PQCD approach towards to next-to-leading order: a short review
• Study of ${\bar{B}}_s\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ decays in the PQCD factorization approach with the lattice QCD input
• Axial-vector $f_1(1285)-f_1(1420)$ mixing and $B_s\to J/\psi (f_1(1285),f_1(1420))$ decays
• Charmless $B\to PP,PV,VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects
• Physics Opportunities at a Photon-Photon Collider
• Study of the $K_1(1270)-K_1(1400)$ mixing in the decays $B\to J/\Psi K_1(1270),J/\Psi K_1(1400)$
• Determination of gamma from charmless B^+/- -> M^0 M^+/- decays using U-spin
• R-Parity violation in B --> pi+ pi- decay
• Pion and Kaon form factors in the perturbative QCD approach
• Charmless Two-body $B(B_s)\to PP,VP$ decays In Soft-Collinear-Effective-Theory
• Three-parton contribution to the $B\to \pi$ form factors in $k_T$ factorization
• Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons
• Study Pure Annihilation Decays $B_s^0({\bar{B}}_s^0)\to D^{\pm }{\pi }^{\mp }$ in PQCD Approach
• $B$-to-Glueball form factor and Glueball production in $B$ decays
• Study of scalar meson a_0(1450) from B \to a_0(1450)K^* Decays
• Restoration of $k_T$ factorization for low $p_T$ hadron hadroproduction
• Effect of resonance for $CP$ asymmetry of the decay process ${\bar{B}}_s\to P{\pi }^{+}{\pi }^{-}$ in perturbative QCD
• Asymmetries from the interference between Cabibbo-favored and doubly-Cabibbo-suppressed D decays
• Large Strong Phases and CP Violation in the Annihilation Processes ${\bar{B}}^0\to K^{+}{K}^{-}$, $K^{\ast \pm }{K}^{\mp }$, $K^{\ast +}{K}^{\ast -}$
• Nonleptonic decays of $B\to (f_1(1285),f_1(1420))V$ in the perturbative QCD approach
• Space-and Time-like Electromagnetic Kaon Form Factors
• Helicity conservation and factorization-suppressed charmless B decays
• Weak Annihilation Topologies and Final State Interactions in D -> PP Decays
• High Energy Photon-Photon Collisions at a Linear Collider
• $CP$ violation induced by the double resonance for pure annihilation decay process in Perturbative QCD
• $B\to D{K}_{0,2}^{\ast }$ Decays: PQCD analysis to determine CP violation phase angle $\gamma$
• Calculation of the $B\to K_{0,2}^{\ast }(1430)f_0(980)/\sigma$ 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))
• Generalized analysis on $B\to K^{\ast }\rho$ within and beyond the Standard Model $-$ Can it help understand the $B\to K\pi$ puzzle?
• The role of $D_{(s)}^{\ast }$ and their contributions in $B_{(s)}\to D_{(s)}h{h}^{\prime }$ decays
• Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach
• CP asymmetry in B \to phi K_S in a SUSY SO(10) GUT
• The study of $B\to J/\Psi {\eta }^{(\prime )}$ decays and determination of $\eta -{\eta }^{\prime }$ mixing angle
• Study of Nonleptonic $B_{(s)}^{\ast }\to M_1{M}_2$ $(M=D$, $D_s$, $\pi$, $K)$ Weak Decays with Factorization Approach
• Resonances $\rho (1450{)}^{+}$ and $\rho (1700{)}^{+}$ in $B\to DKK$ decays
• Double Lepton Polarization Forward--Backward Asymmetries in B \rar K^\ast \ell^+ \ell^- Decay in the SM4
• Study of nonleptonic $B_q^{\ast }$ $\to$ $D_{q}V$ and $P_q{D}^{\ast }$ weak decays
• Perturbative QCD Analysis of Exclusive Processes $e^{+}{e}^{-}\to VP$ and $e^{+}{e}^{-}\to TP$
• Study of $CP$ Violations in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}{f}_0(500)$ decays in the QCD factorization approach
• Power Corrections in Charmless B Decays
• Charming penguins in B -> PP decays and the extraction of gamma
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• Study of the $B_c$ $\to$ $B_s\pi$ decay with the perturbative QCD approach
• Light-Cone HQET Sum Rules for the B --> pi Transition with 1/m_Q Corrections
• B_s\to K^{(*)-}K^{(*)+}, K^{(*)-}π^{+}, K^{(*)-}ρ^{+} decays in R-parity violating supersymmetry
• CP violation in beauty decays
• Probing heavy meson lightcone distribution amplitudes with heavy quark spin symmetry
• Semi-Inclusive B\to K(K^*) X Decays with Initial Bound State Effects
• A study on the radiative dileptonic decays $B^0(B_s)\to \gamma {\ell }^{+}{\ell }^{-}$
• Penguin-dominated $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays in the perturbative QCD approach
• $CP$ violation for $B_c^{+}\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• Sudakov effects in BBNS approach
• Direct $CP$ violation for ${\bar{B}}_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• Charmless $B_s\to VS$ Decays in PQCD Approach
• Revisiting Final State Interaction in Charmless $B_q\to PP$ Decays
• Calculation of the Branching Ratio of $B^{-}\to h_c+K^{-}$ in PQCD
• Study of $B_s$ $\to$ ${\eta }_c(J/\psi )D$ decay with 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
• Factorization and hadronic B decays in the heavy quark limit
• Complete Analysis on the Short Distance Contribution of $B_s\to {\ell }^{+}{\ell }^{-}\gamma$ in Standard Model
• CP Asymmetry in ${\bar{B}}^0\to K^{-}{\pi }^{+}$ from SUSY Flavor Changing Interactions
• Isospin of new physics in $|\Delta S|=1$ charmless B decays
• Renormalization-Group Evolution of the None-local Matrix Element of $B$-meson In QCD and $B\to \pi$ transition form factor
• Probing new physics in class-I $B$-meson decays into heavy-light final states
• Possible solution of the puzzle for the branching ratio and $CP$ violation in $B\to \pi \pi$ decays with a modified perturbative QCD approach
• Studying of Bs --> K(*)-pi+, K(*)-rho+ decays within supersymmetry
• Branching ratios of $B^{+}\to D^{(\ast )+}{K}^{(\ast )0}$ decays in perturbative QCD approach
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$
• Reinvestigating the $B$ $\to$ $PV$ decays by including the contributions from ${\varphi }_{B2}$ with the perturbative QCD approach
• Rare B-Meson Decays at the Crossroads
• Search for new physics from $B\to \pi \varphi$
• Test of Factorization Hypothesis from Exclusive Non-leptonic B decays
• Probing new physics in $B\to J/\Psi {\pi }^0$ decay
• Tests for CPT sum rule and U-spin violation in Time-dependent CP violation of $B_s^0\to K^{+}{K}^{-}$ and $B_d^0\to {\pi }^{+}{\pi }^{-}$
• Measurement of the branching fractions of $D_s^{+}\to {\eta }^{\prime }X$ and $D_s^{+}\to {\eta }^{\prime }{\rho }^{+}$ in $e^{+}{e}^{-}\to D_s^{+}{D}_s^{-}$
• Large non-factorizable contributions in $B\to a_0{a}_0$ decays
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Non-leptonic annihilation decays of B mesons with a natural infrared cutoff
• Bd \to π^- K^{(*)+} and Bs \to π^+(ρ^+) K^- decays with QCD factorization and flavor symmetry
• Branching ratio and $CP$ violation of $B\to K\pi$ decays in a modified perturbative QCD approach
• Revisiting $B\to K^{\ast }\pi$ and $B\to K\rho$ decays using the modified perturbative QCD approach
• ${\bar{B}}^0\to {\pi }^{+}X$ in the Standard Model
• Searching for the squark flavor mixing in CP violations of Bs -> K+ K- and K0bar K0 decays
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• What can we learn from $B^{+}\to D_s^{(\ast )-}{K}^{+}{\pi }^{+}$, $B_d\to D_s^{(\ast )-}{K}^0{\pi }^{+}$ and $B_d\to D_s^{(\ast )-}{K}^{\ast +}$ decays?
• Transition to perturbative QCD in two-photon collisions
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• The pure annihilation type decays $B^0\to D_s^{-}{K}_2^{\ast +}$ and $B_s\to \bar{D}{a}_2$ in perturbative QCD approach
• Complete analysis of all $B\to \pi K$ decays
• Three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ in the PQCD approach
• B Physics Theory for Hadron Colliders
• 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
• Model independent investigation of rare semileptonic b \to u l \barν_l decay processes
• Analysis of the electromagnetic form factors and the radiative decays of the vector heavy-light mesons
• Study of W-exchange Mode $D^0\to \varphi {\bar{K}}^0$
• Family Non-universal $Z^{\prime }$ Effects on $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ Decays in Perturbative QCD Approach
• Exclusive production of $B_c$ mesons in $e^{+}{e}^{-}$ colliders
• Extraction of the CKM angle $\gamma$ from the new "mixed " system of $B^{+}\to {\pi }^{+}{K}^0$ and $B_d^0\to {\pi }^0{K}^0$ decays
• Semi-inclusive Decay $B\to \varphi X_s$: Rate and Momentum Spectrum of $\varphi$
• Baryon helicity in B decay
• Investigating $B_s$ three-body decays to scalar mesons in perturbative QCD approach
• Branching ratios and $CP$ asymmetries of $B\to {\chi }_{c1}K(\pi )$ decays
• Double-mixing CP violation in $B$ decays
• Study of $B\to PP$ decays in the 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
• New Physics in b --> s bar(s) s Decay
• Leading SU(3) breaking in lightcone distribution amplitudes
• Semileptonic baryon decays ${\Xi }_b\to {\Xi }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ in perturbative QCD
• QCD Approach to B->D πDecays and CP Violation
• Elastic and inelastic SU(3)-breaking final-state interactions in B decays to pseudoscalar mesons
• Revisiting $B_s\to PP$ and $PV$ Decays with Contributions from ${\varphi }_{B2}$ with perturbativen QCD approach
• Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays
• Study of $B_c\to \psi (2S)K$, ${\eta }_c(2S)K$, $\psi (3770)K$ decays with perturbative QCD approach
• Study of the quasi-two-body decays B^{0}_{s} \rightarrow ψ(3770)(ψ(3686))π^+π^- with perturbative QCD approach
• Study of ${\bar{B}}^0\to D^0{\mu }^{+}{\mu }^{-}$ Decay in Perturbative QCD Approach
• Comments on $\left|\frac{V_{ub}}{V_{cb}}\right|$ and $|V_{ub}|$ from Non-leptonic $B$ Decays within the Perturbative QCD Approach
• $B_u$ $\to$ $\psi M$ decays and $S$-$D$ wave mixing effects
• The B ---> π K puzzle and the Bulk Randall-Sundurm model
• Hadron Spin Dynamics
• Soft-collinear factorization in B decays
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• Hadronic B Decays: A General Approach
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• Right-handed current contributions in B -> K pi decays
• Study the contributions of S, P, and D-wave resonances to the quasi-two-body decays $B_s^0\to \psi (3686,3770)K\pi$ in perturbative QCD approach
• $B\to K\pi$ Decays with $1/m_b$ Corrections in $QCD$ Factorization
• The B\to D_s^{(*)}η^{(\prime)} decays in the perturbative QCD
• Possibility of experimental study on nonleptonic $B_c^{\ast }$ weak decays
• Next-to-Leading-logarithm threshold resummation for exclusive $B$ meson decays
• Quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ in the perturbative QCD approach
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• W-exchange/Annihilation amplitudes in LCSR - $B_d^0\to D_s^{-}{K}^{+}$ as an example
• Study of the ${\bar{B}}_q^{\ast }$ $\to$ $DM$ decays with perturbative QCD approach
• B\to K_1π(K) decays in the perturbative QCD approach
• Study of Pure Annihilation Decays B_{d,s} \to D^{0} \bar D^{0}
• Analysis of the decay $B^0\to {\chi }_{c1}{\pi }^0$ with light-cone QCD sum rules
• Study of f_0(980) and f_0(1500) from B_s \to f_0(980)π, f_0(1500)πDecays
• The B-CP Puzzles in QCD Factorization
• QCD Factorization Based on Six-Quark Operator Effective Hamiltonian from Perturbative QCD and Charmless Bottom Meson Decays $B_{(s)}\to \pi \pi ,\pi K,KK$
• CP violation of the two-body charmless hadronic B decays in the minimal supergravity Model
• Pure Annihilation Type $B\to K_0^{\ast \pm }(1430)K^{(\ast )\mp }$ Decays in the Family Non-universal $Z^{\prime }$ Model
• The B\to D_s^{(*)}πdecays in the perturbative QCD
• Hadronic decays of $B\to a_1(1260)b_1(1235)$ in the perturbative QCD approach
• PQCD approach to exclusive B decays
• Contributions from ${\Phi }_{B2}$ to the $B$ $\to$ $PP$ decays within the QCD factorization
• Study of the ${\rm Y}(1S)$ $\to$ $DP$ decays
• Two-body modes of B mesons and the CP-b triangle
• Can contribution from magnetic-penguin operator with real photon to $B_s\to {\ell }^{+}{\ell }^{-}\gamma$ in the standard model be neglected?
• Annihilation Contributions and CP Asymmetries in $B^{+}\to {\pi }^{+}{K}^0,K^{+}{K}^0$ and $B^0\to K^0{\bar{K}}^0$
• Study of B^{0}_{s} \rightarrow \ TT(a_{2}(1320),K^{*}_{2}(1430),f_{2}(1270),f^{'}_{2}(1525)) in the perturbative QCD approach
• The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review
• Theory of hadronic B decays
• Semi-inclusive nonleptonic decays B\to D_s^{(*)} X
• General non-leptonic $\Delta F=1$ WET at the NLO in QCD
• CP-Violation in the decay B^0, (B^0)bar -> pi^+ pi^- gamma
• New Physics Search in the Doubly Weak Decay ${\overline{B}}^0\to K^{+}{\pi }^{-}$
• Study of $C$ parity violating and strangeness changing $J/\psi$ $\to$ $PP$ weak decays
• Model-Independent Analysis of CP Violation in Charmed Meson Decays
• CP violation in quasi-two-body $D\to VP$ decays and three-body $D$ decays mediated by vector resonances
• Analysis of $B\to a_1(1260)(b_1(1235))K^{\ast }$ decays in the perturbative QCD approach
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays
• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach
• Soft end-point and mass corrections to the eta' g*g* vertex function
• Study of the two-body nonleptonic $B_c(2S)$ weak decays with the QCD factorization approach
• $B$ to light meson form factors with end-point cutoff
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach
• Study of quasi-two-body B^{0}\rightarrow T(ππ, K\bar{K},πη) decays in perturbative QCD approach
• Highlights from Five Years at the B Factories
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays
• Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson
• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the charmed three-body $B$ meson decays