{"arxiv_id":"hep-ph/0004004","incoming":{"papers":72,"sentences":104,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":11,"sentences":13,"quotes":[{"arxiv_id":"2501.15224","title":"Investigate the glueball-like particle $X(2370)$ in $B$ meson decays","url":"/paper/2501.15224","section":"Transition form factors","sentence":"As an estimate we will adopt the perturbative QCD (PQCD) approach [ref] based on $k_T$ factorization to compute the transition form factor in which the leading-order Feynman diagram for the $B→G lν̅$ decays is displayed in Fig [ref].","intent_p":1.0,"contests_p":null},{"arxiv_id":"1204.3144","title":"The pure annihilation type decays $B^0\\rightarrow D_{s}^{-}K_{2}^{*+}$ and $B_{s}\\rightarrow \\bar{D}a_{2}$ in perturbative QCD approach","url":"/paper/1204.3144","section":"Introduction","sentence":"In this paper, we shall study the pure annihilation type charmed decays $B^0→D_s^-K_2^*+$ and $B_s→D̅a_2$ in the PQCD approach, which is based on the $k_T$ factorization [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1008.5326","title":"B to tensor meson form factors in the perturbative QCD approach","url":"/paper/1008.5326","section":"Introduction","sentence":"The motif of this work is to handle the first sector with the computation of the $B→T$ form factors, and in particular we will use the perturbative QCD (PQCD) approach [ref] which is based on the $k_T$ factorization.","intent_p":0.98,"contests_p":null},{"arxiv_id":"0711.3282","title":"Study of Pure Annihilation Decays B_{d,s} \\to D^{0} \\bar D^{0}","url":"/paper/0711.3282","section":"Analytic formulas","sentence":"In PQCD, we factorize the decay amplitude into soft($Φ$), hard($H$), and harder ($C$) dynamics characterized by different scales, [ref] [equation] In above equation, $b_i$ is the conjugate space coordinate of the transverse momentum $k_iT$, and $t$ is the largest energy scale. $C$ is Wilson coefficient, and $Φ$ is the wave function.","intent_p":0.87,"contests_p":null},{"arxiv_id":"1807.05350","title":"New Physics Search in the Doubly Weak Decay $\\overline B^0 \\to K^+ \\pi^- $","url":"/paper/1807.05350","section":"$B^0 →K^+ π^-$ decay in the standard model","sentence":"In PQCD [ref] , the decay amplitude is factorized into soft ($Φ$), hard ($H$) and harder ($C$) dynamics characterized by different scales [equation] where $Tr$ denotes the trace over Dirac and color indices, and the $b_i$ are the conjugate variables of $k_i T$ of the valence quarks.","intent_p":0.99,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":6,"sentences":6,"quotes":[{"arxiv_id":"2108.06942","title":"Effects from Hadronic Structure of Photon on $B\\to\\phi\\gamma$ and $B_s\\to(\\rho^0,\\omega)\\gamma$ Decays","url":"/paper/2108.06942","section":"Framework and Inputs","sentence":"Noted that $ϕ_B$ is normalized by the decay constant $f_B$, [equation] As aforementioned, the parameters $ω_b=0.40±0.08$ for $B^0$ meson and $ω_b=0.50±0.10$ for $B^0_s$ meson are almost best fits from the well measured results of the $B_d,s→Kπ$, $ππ$ decays [ref] , including the branching fractions and the $CP$ asymmetries.","intent_p":0.84,"contests_p":null},{"arxiv_id":"1205.2971","title":"The $B(B_{s})\\rightarrow D_{(s)}(\\bar{D}_{(s)}) T$ and $D_{(s)}^{*}(\\bar{D}_{(s)}^{*})T$ decays in perturbative QCD approach","url":"/paper/1205.2971","section":"FORMALISM AND WAVE FUNCTION","sentence":"We will take $ω_B=(0.4 ± 0.04)$ GeV and $f_B=(0.21 ± 0.02)$ GeV for B meson [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2501.15224","title":"Investigate the glueball-like particle $X(2370)$ in $B$ meson decays","url":"/paper/2501.15224","section":"Transition form factors","sentence":"The sources of the first two errors are from those for the $B$ meson wave function: $ω_B=(0.40±0.05)$ and $f_B=(0.19±0.02)GeV$ for $B$ mesons [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1008.5326","title":"B to tensor meson form factors in the perturbative QCD approach","url":"/paper/1008.5326","section":"Wave functions","sentence":"In recent years, a number of studies of $B^±$ and $B_d^0$ decays have been performed in the PQCD approach, from which the $ω_b$ is found around $0.40$ [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"2501.15150","title":"Improved global determination of two-meson distribution amplitudes from multi-body $B$ decays","url":"/paper/2501.15150","section":"Distribution Amplitudes","sentence":"The shape parameter takes the values $ω_B = 0.40$ GeV for $B^+,B^0$ mesons and $ω_B_s=0.48$ GeV [ref] for a $B^0_s$ meson with 10% variation in the numerical study below.","intent_p":0.84,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1007.2943","title":"Studying of Bs --> K(*)-pi+, K(*)-rho+ decays within supersymmetry","url":"/paper/1007.2943","section":"Introduction","sentence":"Compared with the theoretical predictions for these quantities in Refs. [ref] , based on the QCD factorization (QCDF) [ref] , the perturbative QCD (PQCD) [ref] , and the soft-collinear effective theory (SCET) [ref] , respectively, one would find the experimental measurement of this branching ratio agrees with the SM predictions with SCET [ref] , but lower than the predictions with QCDF and PQCD [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"0903.0256","title":"B_s\\to K^{(*)-}K^{(*)+}, K^{(*)-}\\pi^{+}, K^{(*)-}\\rho^{+} decays in R-parity violating supersymmetry","url":"/paper/0903.0256","section":"Introduction","sentence":"Compared with the theoretical predictions for these quantities in Refs. [ref] , [ref] and [ref] , based on the QCD factorization approach (QCDF) [ref] , the perturbative QCD (PQCD) [ref] , and the soft-collinear effective theory (SCET) [ref] , respectively, one would find the experimental measurements of branching ratios agree with the SM predictions within their large theoretical uncertainties.","intent_p":0.9,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1112.1257","title":"The two-body B_c {\\to} D^{(*)}_{(s)}P, D^{(*)}_{(s)}V decays in the Perturbative QCD Approach","url":"/paper/1112.1257","section":"Introduction","sentence":"It has been tested in the study of charmless $B$ meson decays successfully [ref] , especially for the direct CP asymmetries [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"0711.0432","title":"Radiative charmless B_{(s)}\\to V \\gamma and B_{(s)}\\to A \\gamma decays in pQCD approach","url":"/paper/0711.0432","section":"Introduction","sentence":"The importance of annihilation diagrams are already tested in the predictions of direct CP asymmetries in $B^0 →π^+π^-$, $K^+π^-$ decays [ref] and in the explanation of $B→ϕK^*$ polarization problem [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1409.1322","title":"Spectator Scattering and Annihilation Contributions as a Solution to the ${\\pi}K$ and ${\\pi}{\\pi}$ Puzzles within QCD Factorization Approach","url":"/paper/1409.1322","section":"Scenario I","sentence":"The large value of $ϕ_A^i$, corresponding to a large imaginary part of the enhanced complex corrections, also lends some support to the pQCD claim that the annihilation amplitudes can provide a large strong phase [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":28,"sentences":28,"quotes":[{"arxiv_id":"1007.2291","title":"Comments on $\\left|\\frac{V_{ub}}{V_{cb}}\\right|$ and $|V_{ub}|$ from Non-leptonic $B$ Decays within the Perturbative QCD Approach","url":"/paper/1007.2291","section":"Introduction","sentence":"In the past ten years, many efforts have been promoted to estimate the non-factorizabale contributions quantitatively, such as the QCD fatorization approach (QCDF) [ref] , the perturbative QCD approach (PQCD) [ref] and the soft collinear effective theory (SCET) [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1802.00155","title":"Revisiting Final State Interaction in Charmless $B_q\\to P P$ Decays","url":"/paper/1802.00155","section":"Introduction","sentence":"Indeed, several quantum chromodynamics (QCD)-based factorization approaches, such as pQCD [ref] , QCD factorization (QCDF) [ref] and soft collinear effective theory (SCET) [ref] make use of the large $B$ mass and give predictions on the facrorization amplitudes, $A^fac$.","intent_p":0.81,"contests_p":null},{"arxiv_id":"0711.0432","title":"Radiative charmless B_{(s)}\\to V \\gamma and B_{(s)}\\to A \\gamma decays in pQCD approach","url":"/paper/0711.0432","section":"Introduction","sentence":"Recently three commonly-accepted approaches are developed to study exclusive $B$ decays: QCD factorization (QCDF) [ref] , soft collinear effective theory (SCET) [ref] and perturbative QCD approach [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"0801.3123","title":"Charmless Two-body $B(B_s)\\to VP$ decays In Soft-Collinear-Effective-Theory","url":"/paper/0801.3123","section":"Introduction","sentence":"At present, there are three commonly-accepted theoretical approaches to investigate the dynamics of these decays, the QCD factorization (QCDF) [ref] , the perturbative QCD (PQCD) [ref] , and the soft-collinear effective theory (SCET) [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1002.4518","title":"Bd \\to \\pi^- K^{(*)+} and Bs \\to \\pi^+(\\rho^+) K^- decays with QCD factorization and flavor symmetry","url":"/paper/1002.4518","section":"Introduction","sentence":"For charmless B decays, there are three factorization approaches available in the market: QCDF [ref] , the perturbative QCD method (PQCD) [ref] and soft collinear effective theory (SCET) [ref] .","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":52},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. 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