Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach

Abstract

We calculate the branching ratios and CP asymmetries for B^0 to pi^+pi^-, B^+ to pi^+pi^0 and B^0 to pi^0pi^0 decays, in a perturbative QCD approach. In this approach, we calculate non-factorizable and annihilation type contributions, in addition to the usual factorizable contributions. We found that the annihilation diagram contributions are not very small as previous argument. Our result is in agreement with the measured branching ratio of B to pi^+pi^- by CLEO collaboration. With a non-negligible contribution from annihilation diagrams and a large strong phase, we predict a large direct CP asymmetry in B^0 to pi^+pi^-, and pi^0pi^0, which can be tested by the current running B factories.

Latex, 28 pages including 11 figures; added contents and figures, corrected typos

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• Study of B_{c}\to J/ψK decays in the perturbative QCD approach
• The PQCD approach towards to next-to-leading order: a short review
• Large Strong Phases and CP Violation in the Annihilation Processes ${\bar{B}}^0\to K^{+}{K}^{-}$, $K^{\ast \pm }{K}^{\mp }$, $K^{\ast +}{K}^{\ast -}$
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• Direct $CP$ violation for ${\bar{B}}_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• Study of $B_s$ $\to$ ${\eta }_c(J/\psi )D$ decay with perturbative QCD approach
• Complete Analysis on the Short Distance Contribution of $B_s\to {\ell }^{+}{\ell }^{-}\gamma$ in Standard Model
• 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
• CP violation in non-leptonic $B_c$ decays to excited final states
• Charmless $B_s\to VS$ Decays in PQCD Approach
• Analysis of CKM-Favored Quasi-Two-Body $B\to D(R\to )K\pi$ Decays in PQCD Approach
• Calculation of the Branching Ratio of $B^{-}\to h_c+K^{-}$ in PQCD
• Probing heavy meson lightcone distribution amplitudes with heavy quark spin symmetry
• Study of the four-body decays $B_S^0\to \pi \pi \pi \pi$ in the perturbative QCD approach
• $CP$ violation for $B_c^{+}\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• Penguin-dominated $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays in the perturbative QCD approach
• Sudakov effects in BBNS approach
• A study on the radiative dileptonic decays $B^0(B_s)\to \gamma {\ell }^{+}{\ell }^{-}$
• Renormalization-Group Evolution of the None-local Matrix Element of $B$-meson In QCD and $B\to \pi$ transition form factor
• Studying of Bs --> K(*)-pi+, K(*)-rho+ decays within supersymmetry
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• Possible solution of the puzzle for the branching ratio and $CP$ violation in $B\to \pi \pi$ decays with a modified perturbative QCD approach
• Measurement of the branching fractions of $D_s^{+}\to {\eta }^{\prime }X$ and $D_s^{+}\to {\eta }^{\prime }{\rho }^{+}$ in $e^{+}{e}^{-}\to D_s^{+}{D}_s^{-}$
• Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$
• Measurement of the branching fraction and $CP$ asymmetry of $B^0\to {\pi }^0{\pi }^0$ decays using $198\times 10^6$ $B\overline{B}$ pairs in Belle II data
• Large non-factorizable contributions in $B\to a_0{a}_0$ decays
• Probing new physics in $B\to J/\Psi {\pi }^0$ decay
• Branching ratios of $B^{+}\to D^{(\ast )+}{K}^{(\ast )0}$ decays in perturbative QCD approach
• Inclusive weak-annihilation decays and lifetimes of beauty-charmed baryons
• Reinvestigating the $B$ $\to$ $PV$ decays by including the contributions from ${\varphi }_{B2}$ with the perturbative QCD approach
• Probing new physics in class-I $B$-meson decays into heavy-light final states
• 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
• Bd \to π^- K^{(*)+} and Bs \to π^+(ρ^+) K^- decays with QCD factorization and flavor symmetry
• 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
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Non-leptonic annihilation decays of B mesons with a natural infrared cutoff
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• 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?
• Branching ratio and $CP$ violation of $B\to K\pi$ decays in a modified 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
• Investigating $B_s$ three-body decays to scalar mesons in perturbative QCD approach
• Study of W-exchange Mode $D^0\to \varphi {\bar{K}}^0$
• Study of $B\to PP$ decays in the modified perturbative QCD approach
• Double-mixing CP violation in $B$ decays
• Semileptonic baryon decays ${\Xi }_b\to {\Xi }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ in perturbative QCD
• New Physics in b --> s bar(s) s Decay
• Analysis of the electromagnetic form factors and the radiative decays of the vector heavy-light mesons
• Family Non-universal $Z^{\prime }$ Effects on $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ Decays in Perturbative QCD Approach
• The two-body hadronic decays of $B_c$ meson in the perturbative QCD approach: A short review
• 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 nonfactorizable contributions to factorization-forbidden decays of $B$ mesons to charmonium
• Studies on the $B\to \kappa \bar{\kappa }$ decays 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
• Model independent investigation of rare semileptonic b \to u l \barν_l decay processes
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Exclusive production of $B_c$ mesons in $e^{+}{e}^{-}$ colliders
• Branching ratios and $CP$ asymmetries of $B\to {\chi }_{c1}K(\pi )$ decays
• New Physics contribution to $B\to K\pi$ decays in SCET
• Study of $B_c\to \psi (2S)K$, ${\eta }_c(2S)K$, $\psi (3770)K$ decays with perturbative QCD approach
• Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the 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 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
• Leptophobic dark photon interpretation of the ${\eta }^{\left(\prime \right)}\to {\pi }^0\left(\eta \right)\gamma \gamma$ puzzle
• $B_u$ $\to$ $\psi M$ decays and $S$-$D$ wave mixing effects
• Implications for new physics from ${\bar{B}}^0\to {\pi }^0{\pi }^0$ and ${\bar{B}}^0\to {\bar{K}}^0{K}^0$
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• Analysis of B to J a1(1260)in pertubative QCD approach
• The B ---> π K puzzle and the Bulk Randall-Sundurm model
• $B_s^0\to {\eta }^{(\prime )}{\eta }^{(\prime )}$ decays in the pQCD approach
• Comments on $\left|\frac{V_{ub}}{V_{cb}}\right|$ and $|V_{ub}|$ from Non-leptonic $B$ Decays within the Perturbative QCD Approach
• Soft-collinear factorization in B decays
• Study of ${\bar{B}}^0\to D^0{\mu }^{+}{\mu }^{-}$ Decay in Perturbative QCD Approach
• B\to K_1π(K) decays in the perturbative QCD approach
• Possibility of experimental study on nonleptonic $B_c^{\ast }$ weak decays
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• The B\to D_s^{(*)}πdecays in the perturbative QCD
• Study of f_0(980) and f_0(1500) from B_s \to f_0(980)π, f_0(1500)πDecays
• The B\to D_s^{(*)}η^{(\prime)} decays in the perturbative QCD
• The two-pseudoscalar-meson decay of ${\chi }_{cJ}$ with twist-3 corrections
• Next-to-Leading-logarithm threshold resummation for exclusive $B$ meson decays
• Charmless $B_c\to VV$ decays in the QCD factorization approach
• Study of the ${\bar{B}}_q^{\ast }$ $\to$ $DM$ decays with perturbative QCD approach
• Study of Pure Annihilation Decays B_{d,s} \to D^{0} \bar D^{0}
• Quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ in the perturbative QCD approach
• Estimates of the isospin-violating ${\Lambda }_b\to {\Sigma }^0\varphi ,{\Sigma }^{0}J/\psi$ decays and the $\Sigma -\Lambda$ mixing
• The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review
• SU(3) symmetry and its breaking effects in semileptonic heavy baryon decays
• Study of the ${\rm Y}(1S)$ $\to$ $DP$ decays
• Annihilation Contributions and CP Asymmetries in $B^{+}\to {\pi }^{+}{K}^0,K^{+}{K}^0$ and $B^0\to K^0{\bar{K}}^0$
• Supersymmetric contribution to B to rho K and B to pi K^* decays in SCET
• 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
• Study of B^{0}_{s} \rightarrow \ TT(a_{2}(1320),K^{*}_{2}(1430),f_{2}(1270),f^{'}_{2}(1525)) in the perturbative QCD approach
• Contributions from ${\Phi }_{B2}$ to the $B$ $\to$ $PP$ decays within the QCD factorization
• PQCD approach to exclusive B decays
• Constrain the UT angle $\gamma$ by CP violation parameters in $B^0\to {\pi }^{+}{\pi }^{-}$
• Can contribution from magnetic-penguin operator with real photon to $B_s\to {\ell }^{+}{\ell }^{-}\gamma$ in the standard model be neglected?
• New Physics Search in the Doubly Weak Decay ${\overline{B}}^0\to K^{+}{\pi }^{-}$
• Charmless Quasi-two-body $B$ Decays in Perturbative QCD Approach: Taking $B\to K(\mathcal{R}\to )K^{+}{K}^{-}$ As Examples
• Study of quasi-two-body B^{0}\rightarrow T(ππ, K\bar{K},πη) decays in perturbative QCD approach
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach
• Analysis of $B\to a_1(1260)(b_1(1235))K^{\ast }$ decays in the perturbative QCD approach
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays
• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach
• Non-leptonic B-decays at two loops in QCD Factorization
• Study of $C$ parity violating and strangeness changing $J/\psi$ $\to$ $PP$ weak decays
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays
• A possible solution of $B$ arrow $\pi \pi$ puzzle in Z' model
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• Glauber gluons in annihilation amplitudes for heavy meson decays
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays
• Effects from Hadronic Structure of Photon on $B\to \varphi \gamma$ and $B_s\to ({\rho }^0,\omega )\gamma$ Decays
• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the charmed three-body $B$ meson decays