Guido Bell, Martin Beneke, Tobias Huber, Xin-Qiang Li
We complete the calculation of the QCD penguin amplitude at next-to-next-to-leading order in the QCD factorization approach to non-leptonic B-meson decays. This provides the last missing piece in the computation of the QCD correction to direct CP asymmetries at leading power in the heavy-quark expansion.
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The computation of direct CP asymmetries in charmless B decays at next-to-next-to-leading order (NNLO) in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current-current operators Q_{1,2} and provide a first estimate of NNLO CP asymmetries in penguin-dominated b -> s transitions.
We present a study of non-leptonic B-meson decays, partial widths and CP asymmetries, and discuss the possibilities of determining the penguin contributions through less model-dependent phenomenological analyses. In the last section we employ a specific model to give more definite numerical predictions.
We compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results for all master integrals in terms of iterated integrals with rational weight functions. It is the first application of this method to the case of two different internal masses.
We show that the factorization formula for non-leptonic B decays to two light flavor non-singlet mesons derived by Bauer et al. in the context of soft-collinear effective theory is equivalent to the corresponding formula in the QCD factorization approach. The apparent numerical differences in the analysis of B->pi+pi data performed by these authors, as compared to previous QCD factorization analyses, can largely be attributed to the neglect of known perturbative and power corrections.
We introduce the Working Group 2 proceedings contributions from the 2nd workshop on the CKM Unitarity Triangle and note their connection to the proceedings of the first workshop. The topic of WG2 was the determination of the CKM matrix elements Vtd and Vts from B-Bbar mixing, radiative penguin B to X{s/d} gamma decays and rare (semi)leptonic decays such as B to Xs l+ l-.
We complete the computation of the 1-loop (alpha_s^2) corrections to hard spectator scattering in non-leptonic B decays at leading power in Lambda/m_b by evaluating the penguin amplitudes. This extends the knowledge of these next-to-next-to-leading-order contributions in the QCD factorization formula for B decays to a much wider class of final states, including all pseudoscalar-pseudoscalar, pseudoscalar-vector, and longitudinally polarized vector-vector final states, except final states with eta or eta' mesons. The new 1-loop correction is significant for the colour-suppressed amplitudes, but…
We calculate the O(alpha_s) corrections to the Z^0-penguin and electroweak box diagrams relevant for non-leptonic Delta F = 1 decays with F = S, B. This calculation provides the complete O(alpha_w alpha_s) and O(alpha_w alpha_s sin^2 theta_w m_t^2) corrections (alpha_w = alpha/sin^2 theta_w) to the Wilson coefficients of the electroweak penguin four quark operators relevant for non-leptonic K- and B-decays. We argue that this is the dominant part of the next-next-to-leading (NNLO) contributions to these coefficients. Our results allow to reduce considerably the uncertainty due to the definitio…
Using the soft-collinear effective theory we derive the factorization theorem for the decays B-> M1 M2 with M{1,2}= pi,K, rho,K*, at leading order in Lambda/E_M and Lambda/mb. The results derived here apply even if alpha_s(E_M Lambda) is not perturbative, and we prove that the physics sensitive to the E*Lambda scale is the same in B-> M1 M2 and B-> M form factors. We argue that c-cbar penguins could give long-distance effects at leading order. Decays to two transversely polarized vector mesons are discussed. Analyzing B-> pi pi we find predictions for B^0 -> pi^0 pi^0 and |V_{ub}| f_+(0) as a …
The phenomenon of CP violation in the B system and strategies for extracting CKM phases are reviewed. We focus both on general aspects and on some recent developments including CP-violating asymmetries in B_d decays, the B_s system in light of a possible width difference $ΔΓ_s$, charged B decays, and SU(3) relations among certain transition amplitudes. In order to describe the relevant non-leptonic B decays, low energy effective Hamiltonians calculated beyond the leading logarithmic approximation are used. Special emphasis is given to the role of electroweak penguin operators in such transitio…
Inclusive Charmless Non-Leptonic B Decays at NLO within and beyond the Standard Model
研究含粲无轻子 B 衰变的 BSM 贡献，通过计算切割图和相空间积分，在弱有效理论框架内达 NLO，可用于约束与衰变异常相关的新物理情景。
Using a theoretical framework based on the next-to-leading order QCD-improved effective Hamiltonian and a factorization Ansatz for the hadronic matrix elements of the four-quark operators, we reassess branching fractions in two-body non-leptonic decays $B \to PP, PV, VV$, involving the lowest lying light pseudoscalar $(P)$ and vector $(V)$ mesons in the standard model. Using the sensitivity of the decay rates on the effective number of colors, $N_c$, as a criterion of theoretical predictivity, we classify all the current-current (tree) and penguin transitions in five different classes. The rec…
We discuss few selected topics related to the calculation of hadronic amplitudes relevant for two-body non-leptonic B decays.
We study Lambda_{QCD}/m_B corrections to factorization in B -> K pi decays. First, we analyze these decay channels within factorization, showing that, irrespectively of the value of gamma, it is not possible to reproduce the experimental data. Then, we discuss Lambda_{QCD}/m_B corrections to these processes, and argue that there is a class of doubly Cabibbo enhanced non-factorizable contributions, usually called charming penguins, that cannot be neglected. Including these corrections, we obtain an excellent agreement with experimental data. Furthermore, contrary to what is obtained with factor…
In the study of two-body charmless B decays as a mean of looking for direct CP-violation and measuring the CKM mixing parameters in the Standard Model, the short-distance penguin contribution with its absorptive part generated by charm quark loop seems capable of producing sufficient $B \to Kπ$ decays rates, as obtained in factorization and QCD-improved factorization models. However there are also long-distance charming penguin contributions which could give rise to a strong phase due to the rescattering $D^{*}D^{*}_{s} \to Kπ$ etc. In this talk, I would like to discuss recent works on the cha…
We calculate branching ratios for pure penguin decay modes, $B\to ϕK$ decays using perturbative QCD approach. Our results of branching ratios are consistent with the experimental data and larger than those obtained from the naive factorization assumption and the QCD-improved factorization approach. This is due to a dynamical penguin enhancement in perturbative QCD approach.
Within the framework of QCD factorization (QCDF), we consider two different types of power correction effects in order to resolve the CP puzzles and rate deficit problems with penguin-dominated two-body decays of B mesons and color-suppressed tree-dominated $π^0π^0$ and $ρ^0π^0$ modes: penguin annihilation and soft corrections to the color-suppressed tree amplitude. We emphasize that the electroweak penguin solution to the $B\to Kπ$ CP puzzle via New Physics is irrelevant for solving the CP and rate puzzles related to tree-dominated decays. While some channels e.g. $K^-π^+,K^-ρ^0,π^+π^-,ρ^\pmπ…
We present results on the NLO (alpha_s^2) spectator-scattering corrections to the topological penguin amplitudes for charmless hadronic two-body B-decays in QCD factorization. The corrections can be sizable for the colour-suppressed electroweak penguin amplitudes alpha_{4,EW}^p but otherwise are numerically small. Our results explicitly demonstrate factorization at this order. To assess the phenomenological viability of the framework, we consider penguin-to-tree ratios in the penguin-dominated pi K system and find agreement to the expected precision (i.e., a power correction).
We calculate the two-loop $10 \times 10$ anomalous dimension matrix ${\cal O}(α_s^{2})$ involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for $ΔS=1$ weak non-leptonic decays, but also important for $ΔB=1$ decays. The calculation is performed in two schemes for $γ_{5}$: the dimensional regularization scheme with anticommuting $γ_{5}$ (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving $γ_{5}$ in closed fermion loops can be avoided thus allowing a consistent calculation in the NDR…
We compute the order alpha_s^2 correction to the matrix element of magnetic penguin operator for B meson decaying to light mesons within the QCD factorization framework. We explicitly show that the soft and collinear divergences are canceled out, so that the validity of QCD factorization is confirmed. We present the result of the calculation in complete analytic forms. The result is also applied to B -> K pi decays, and we find that the order alpha_s^2 correction of magnetic penguin operator can considerably reduce the coefficient of penguin amplitude a^c_{4,I}. The reduction is stronger for t…
Using a modified perturbative approach that includes the Sudakov resummation and transverse degrees of freedom we analyze the penguin-induced $B^{-} \to π^{-}ϕ$ decay by applying the next-to-leading order effective weak Hamiltonian. The modified perturbative method enables us to include nonfactorizable contributions and to control virtual momenta appearing in the process. Besides, we apply the three-scale factorization theorem for nonleptonic processes that offers the possibility of having the scale-independent product of short- and long-distance parts in the amplitude of the weak Hamiltonian.…
We present an analysis of two-body B decays with a pseudoscalar (P) and an axial-vector meson (A) in the final state using naive factorization. We employ as inputs a limited number of experimental data, i.e. results for the B -> K1 gamma and B -> K* gamma radiative decays and the branching ratios for B -> pion+rho, pion+K*, K+rho, K+pion non leptonic decays. In this way we are able to make predictions on several B -> P A decays that might be used as a guide for experimental researches of these decays and as tests of factorization.
Non-leptonic $B$ decays into charmless final states offer an important laboratory to study CP violation and the dynamics of strong interactions. Particularly interesting are $B^0_s\to K^-K^+$ and $B^0_d\toπ^-π^+$ decays, which are related by the $U$-spin symmetry of strong interactions, and allow for the extraction of CP-violating phases and tests of the Standard Model. The theoretical precision is limited by $U$-spin-breaking corrections and innovative methods are needed in view of the impressive future experimental precision expected in the era of Belle II and the LHCb upgrade. We have recen…
We evaluate $B\to Kπ$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to Kπ$ decays for a representative parameter set are consistent with data. We evaluate $B\to Kπ$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the facto…
Within the framework of QCD factorization (QCDF), power corrections due to penguin annihilation can account for theobserved rates of penguin-dominated two-body decays of $B$ mesons and direct CP asymmetries $A_{CP}(K^-π^+)$, $A_{CP}((K^{*-}π^+)$, $A_{CP}((K^-ρ^0)$ and $A_{CP}((π^+π^-)$. However, the predicted direct CP-violating effects in QCDF for $B^-\to K^-π^0,K^-η,π^-η$ and $\bar B^0\toπ^0π^0$ are wrong in signs when confronted with experiment. We consider two different types of power correction effects in order to resolve the CP puzzles and rate deficit problems with penguin-dominated two…
Using a modified perturbative approach that includes the Sudakov resummation and transverse degrees of freedom we analyze the penguin-induced B -> pi phi decay. The perturbative method enables us to include nonfactorizable contributions and to control virtual momenta appearing in the process. The calculation supports the results obtained in the standard BSW factorization approach, illustrating the electroweak penguin dominance and the branching ratio of order O(10^{-8}). However, the estimated prediction of 16% for CP asymmetry is much larger than that obtained in the factorization approach.
Within the framework of QCD factorization (QCDF), power corrections due to penguin annihilation can account for the observed rates of penguin-dominated two-body decays of $B$ mesons and direct CP asymmetries $A_{CP}(K^-π^+)$, $A_{CP}(K^{*-}π^+)$, $A_{CP}(K^-ρ^0)$ and $A_{CP}(π^+π^-)$. However, the predicted direct CP-violating effects in QCDF for $B^-\to K^-π^0,K^-η,π^-η$ and $\bar B^0\toπ^0π^0$ are wrong in signs when confronted with experiment. We show that subleading $1/m_b$ power corrections to the color-suppressed tree amplitude due to spectator scattering or final-state interactions will…
We make a further study of $CP$ asymmetries in the pure penguin-induced decay modes $B^{-}_{u}\rightarrow K^{(*)0} + K^{(*)-}$ and $B^{-}_{u} \rightarrow \bar{K}^{(*)0} + (π^{-}, ρ^{-}, a^{-}_{1})$ by using the two-loop renormalization-group-improved effective Hamiltonian and factorization approximation. Different from the previous results obtained without QCD corrections, the $CP$ asymmetries in each of the two groups are enhanced and classified with their respective factorization coefficients. A sum over the pure penguin modes of each group is proposed to obtain an effective branching ratio …
Motivated by the recent experimental data, we have revisited the $B\to πK,ππ$ decays in the framework of QCD factorization, with inclusion of the important strong penguin corrections of order $α_s^2$ induced by $b\to D g^\ast g^\ast$ ($D=d$ or $s$ and $g^\ast$ denotes an off-shell gluon) transitions. We find that these higher order strong penguin contributions can provide $\sim 30%$ enhancement to the penguin-dominated $B\to πK$ decay rates, and such an enhancement can improve the consistency between the theoretical predictions and the experimental data significantly, while for the tree-domina…
We calculate the $10\times 10$ two--loop anomalous dimension matrix to order $\ord(α_e α_s)$ in the dimensional regularization scheme with anticommuting $γ_5$ (NDR) which is necessary for the extension of the $ΔS=1$ weak Hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate, how a direct calculation of penguin diagrams involving $γ_5$ in closed fermion loops can be avoided thus allowing a consistent calculation of two--loop anomalous dimensions in the simplest renormalization scheme with anticommuting $γ_5$ in $D$ dimensions. We give the necess…
We extend the framework of QCD factorization to non-leptonic $B$ decays into three light mesons, taking as an example the decay $B^+ \to π^+ π^+ π^-$. We discuss the factorization properties of this decay in different regions of phase space. We argue that, in the limit of very large $b$-quark mass, the central region of the Dalitz plot can be described in terms of the $B \to π$ form factor and the $B$ and $π$ light-cone distribution amplitudes. The edges of the Dalitz plot, on the other hand, require different non-perturbative input: the $B \to ππ$ form factor and the two-pion distribution amp…
The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays. The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are conventionally defined, not from the topology of the dominant diagrams, but through their associated CKM factors V_{ub}^* V_{uq} and V_{tb}^* V_{tq}, respectively, with q=d,s. We find that for B_{d,s} \to π^+ K^- decays, the "tree" amplitude can be well estimated in QCDF with small errors, as the endpoint singularities have been canceled to a lar…
Long-distance contributions of operators of the effective non-leptonic weak Hamiltonian containing charmed currents have been recently studied. Penguin-like contractions of these operators, denoted as charming penguins, have been shown to be relevant for several B decays into two pseudoscalar mesons. In particular, they are expected to give large enhancements to processes which would be otherwise Cabibbo suppressed. Their contributions easily lead to values of BR(B^+ \to K^0 π^+) and BR(B_d \to K^+ π^-) of about 1 \times 10^{-5}, as recently found by the CLEO collaboration. In this paper, we s…
We present fits to charmless hadronic B decay data from the BaBar, Belle and Cleo experiments using two theoretical models: (i) the QCD factorization model of Beneke et al. and (ii) QCD factorization complemented with the so-called charming penguins of Ciuchini et al. When we include the data from pseudoscalar-vector decays the results favor the incorporation of the charming penguin terms. We also fit results for the unitarity triangle parameters and the CP-violating asymmetries.
In various extensions of the Standard Model (SM) tree level non-leptonic decays of hadrons receive contributions from new heavy gauge bosons and scalars. Prominent examples are the right-handed W' bosons in left-right symmetric models and charged Higgs (H^\pm) particles in models with extended scalar sector like two Higgs doublet models and supersymmetric models. Even in the case of decays with four different quark flavours involved, to which penguin operators cannot contribute, twenty linearly independent operators, instead of two in the SM, have to be considered. Anticipating the important r…
We propose a QCD-based model for calculation of the non-perturbative corrections to the factorization approximation in the decays of heavy mesons. In the framework of the model, factorization in pseudoscalar transitions holds exactly at the leading order leaving the opportunity to calculate non-leading corrections consistently.
In the study of two-body charmless B decays as a mean of looking for direct CP-violation and measuring the CKM mixing parameters in the Standard Model, the short-distance penguin contribution with its absorptive part generated by charm quark loop seems capable of producing sufficient $B \to Kπ$ decays rates, as obtained in factorization and QCD-improved factorization models. However there are also long-distance charming penguin contributions which also give rise to a strong phase due to the rescattering $D^{*}D^{*} \to Kπ$ . In this talk, I would like to discuss \cite{Isola} a recent work on t…
The Bc -> BP,BV decays are studied with the QCD factorization approach (where P and V denote pseudoscalar and vector mesons, respectively). Considering the contributions of both current-current and penguin operators, the amplitudes of branching ratios are estimated at the leading approximation. We find that the contributions of the penguin operators are very small due to the serious suppression by the CKM elements. The most promising decay modes are Bc -> Bs Pi, Bs rho, which might be easily detected at hadron colliders.
The QCD$\times$QED factorization is studied for two-body non-leptonic and semi-leptonic $B$ decays with heavy-light final states. These non-leptonic decays, like $\bar{B}^0_{(s)}\to D^+_{(s)} π^-$ and $\bar{B}_d^0 \to D^+ K^-$, are among the theoretically cleanest non-leptonic decays as penguin loops do not contribute and colour-suppressed tree amplitudes are suppressed in the heavy-quark limit or even completely absent. Advancing the theoretical calculations of such decays requires therefore also a careful analysis of QED effects. Including QED effects does not alter the general structure of …
We address a number of theoretical and phenomenological issues in two-body charmless non-leptonic B decays in the context of a factorization model. A classification of the exclusive decays involving tree and penguin amplitudes is reviewed. The role of QCD anomaly in exclusive decays involving an $η$ or $η'$ is elucidated and comparison is made with the existing data. We argue that the factorization approach accounts for most of the observed two-body B decays.
By using the recent experimental measurements of B to pi pi and B to K pi branching ratios, we find that factorization is unable to reproduce the observed BRs even taking into account the uncertainties of the input parameters. Charming and GIM penguins allow to reconcile the theoretical predictions with the data. Because of these large effects, we conclude, however, that it is not possible, with the present theoretical and experimental accuracy, to determine the CP violation angle gamma from these decays. Contrary to factorization, we predict large asymmetries for several of the particle-antip…
We study the rates and direct CP violations of two-body baryonic $\bar B_{u,d,s}\to {{\rm\bf B}\overline{\rm\bf B}}'$ and $B^-_c\to{{\rm\bf B}\overline{\rm\bf B}}'$ decays, where the final state baryons include low-lying octet and decuplet baryons. We incorporate topological amplitude formalism and the factorization approach. Asymptotic relations at large $m_b$ are used to simplify decay amplitudes. Using the most up-to-date data on $\bar B^0\to p\bar p$ and $B^-\toΛ\bar p$ decay rates as inputs, rates and direct CP violations of $\bar B_{u,d,s}\to {{\rm\bf B}\overline{\rm\bf B}}'$ decays are …
The colour-suppressed tree amplitude in non-leptonic B decays is particularly sensitive to perturbative and non-perturbative corrections. We calculate the two-loop (NNLO) vertex corrections to the colour-suppressed and colour-allowed tree amplitudes in QCD factorization. Our results are given completely analytically, including the full dependence on the charm quark mass. We then update theoretical predictions for a range of interesting observables derived from pi pi, pi rho, and rho rho final states that do not depend (significantly) on penguin contributions, and hence are now available with N…
We discuss factorization in exclusive radiative leptonic B->γeνdecays using the soft-collinear effective theory. The form factors describing these decays can be expanded in a power series in Lambda/E_γwith E_γthe photon energy. We write down the most general operators in the effective theory which contribute to the form factors at leading order in Lambda_QCD/E_γ, proving their factorization into hard, jet and soft contributions, to all orders in alpha_s.
We make an attempt to clarify the role of the annihilation or "penguin" mode in the description of the $K\rightarrowππ$ decay within the Standard Model. The attention is concentrated on new operators in the effective $ΔS=1$ Hamiltonian and the violation of factorization for mesonic matrix elements of the local four-quark operators. We propose a regular method to evaluate the mesonic matrix elements of $K\rightarrowππ$ transitions based on studying three-point correlators via {\it QCD} sum rules using the chiral effective theory as an underlying low-energy model for strong interaction. Matrix e…
We investigate the possibility of testing factorization hypothesis in non-leptonic exclusive decays of B-meson. In particular, we considered the non factorizable \bar{B^0} -> D^{(*)+} D_s^{(*)-} modes and \bar{B^0} -> D^{(*)+} (π^-, ρ^-) known as well-factorizable modes. By taking the ratios BR(\bar{B^0}-> D^{(*)+}D_s^{(*)-})/BR(\bar{B^0}-> D^{(*)+}(π^-,ρ^-)), we found that under the present theoretical and experimental uncertainties there's no evidence for the breakdown of factorization description to heavy-heavy decays of the B meson.
We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as $B\to Dπ$ and $B\to ππ$. We discuss the factorization formula for a general final state from a general point of view. We then consider factorization for decays into heavy-light final states (such as $B\to Dπ$) in more detai…
Using flavor SU(3) symmetry, we perform a model-independent analysis of charmless $\bar B_{u,d} (\bar B_s) \to PP, ~PV$ decays. All the relevant topological diagrams, including the presumably subleading diagrams, such as the QCD- and EW-penguin exchange diagrams and flavor-singlet weak annihilation ones, are introduced. Indeed, the QCD-penguin exchange diagram turns out to be important in understanding the data for penguin-dominated decay modes. In this work we make efforts to bridge the (model-independent but less quantitative) topological diagram or flavor SU(3) approach and the (quantitativ…
With a consistent definition of transverse-momentum-dependent(TMD) light-cone wave function of $B$-meson, we show that the amplitude of the radiative leptonic B-decay can be factorized at one-loop level as a convolution with the wave function and a perturbative coefficient function, combined with a soft factor. In this TMD factorization, the transverse momenta of partons in the $B$-meson are taken into account and all soft divergences are contained in the wave function and the soft factor. The coefficient function is infrared-safe. The factorization works on a diagram-by-diagram basis and is p…
We report on the calculation of the two-loop penguin amplitudes in non-leptonic B decays in the framework of QCD factorization. We discuss the computation of this genuine two-loop, two-scale problem and provide details on the matching from QCD onto SCET, the evaluation of the master integrals, and the convolution of the hard scattering kernels with the light-cone distribution amplitude of the light meson. Preliminary results on the size of the two-loop correction are given.
Two-body charmless hadronic B decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Due to the G-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and anti-quark in the SU(3) limit. Our main results are: (i) In the naive factorization approach, the decays such as $B^-\to \bar K_2^{*0}π^-$ and $\bar B^0\to K_2^{*-}π^+$ with a tensor meson emitted are prohibited owing to the fact that …
We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\bar{B}_{(s)}\to D_{(s)}^{(\ast)+} \, L^-$ and $Λ_b \to Λ_c^+ \, L^-$, where $L$ is a light meson from the set $\{π,ρ,K^{(\ast)},a_1\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\cal O}(α_s^2)$ correction to the leading-power hard scattering kernels, an…
Exclusive, non-leptonic, two-body decays of B mesons simplify greatly in the heavy quark limit. In this talk I discuss the factorized structure that holds in this limit and some of its consequences: (a) naive factorization is recovered in a certain limit; (b) `non-factorizable' effects are hard and can be calculated; (c) strong interaction phases vanish in the heavy quark limit (and can be calculated as well). As an illustration, I compute the penguin contribution to the decay $B_d\toπ^+π^-$ and its effect on the determination of $\sin 2α$.
Using the QCD factorization approach, we reexamine the two-body hadronic charmless $B$-meson decays to final states involving a pseudoscalar~($P$) and a vector~($V$) meson, with inclusion of the penguin contractions of spectator-scattering amplitudes induced by the $b\to D g^\ast g^\ast$~(where $D=d$ or $s$, and $g^\ast$ denotes an off-shell gluon) transitions, which are of order $α_s^2$. Their impacts on the CP-averaged branching ratios and CP-violating asymmetries are examined. We find that these higher order penguin contraction contributions have significant impacts on some specific decay m…
Within the factorization-assisted topological-amplitude approach, we studied the 33 charmless $B_{(s)} \to VV$ decays, where $V$ stands for a light vector meson. According to the flavor flows, the amplitude of each process can be decomposed into 8 different topologies. In contrast to the conventional flavor diagrammatic approach, we further factorize each topological amplitude into decay constant, form factors and unknown universal parameters. By $χ^2$ fitting 46 experimental observables, we extracted 10 theoretical parameters with $χ^2$ per degree of freedom around 2. Using the fitted paramet…
We study exclusive non-leptonic two-body $B_c\to(D_{(s)},η_c,B_{(s)})+F$ decays with $F$(pseudoscalar or vector meson) being factored out in QCD factorization approach. The non-leptonic decay amplitudes are related to the product of meson decay constants and the form factors for semileptonic $B_c$ decays. As inputs in obtaining the branching ratios for a large set of non-leptonic $B_c$ decays, we use the weak form factors for the semileptonic $B_c\to(D_{(s)},η_c,B_{(s)})$ decays in the whole kinematical region and the unmeasured meson decay constants obtained from our previous light-front quar…
We compute branching ratios of $B\to Kπ$ 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 comm…
In this work, we study the factorization of the radiative leptonic decays of $B^-$ and $D^-$ mesons, the contributions of the order $O(Λ_{\rm QCD}\left/m_Q\right.)$ are taken into account. The factorization is proved to be valid explicitly at the order $O(α_sΛ_{\rm QCD}\left/m_Q\right.)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O(Λ_{\rm QCD}\left/m_Q\right.)$ contribution is found to be very important, the correction to the decay amplitudes of $B^-\to γe\barν$ is about $20\% - 30\%$. For $D$ mesons…
We give the complete $O(p^2)$ bosonization of the electroweak Penguin operators $Q_{7,8}$ and compare the result with that of the gluon Penguin operators $Q_{5,6}$. We find that, in addition to the usual (constant and current-current) parts, there are three new terms not discussed previously in the literature. Two of these are present in the factorization approximation and should be included in the standard definition of the $B_{7,8}$-factors. The impact of these corrections on the direct $CP$-violating parameter $\varepsilon '/\varepsilon$ is briefly discussed.
Branching fractions and CP-violating asymmetries of charmless $\bar B_s\to PP, VP, VV$ decays (P and V denoting pseudoscalar and vector mesons, respectively) are re-examined in the framework of QCD factorization (QCDF). We take into account subleading power corrections to the penguin annihilation topology and to color-suppressed tree amplitudes that are crucial for resolving the CP puzzles and rate deficit problems with penguin-dominated two-body decays and color-suppressed tree-dominated $π^0π^0$ and $ρ^0π^0$ modes in the $B_{u,d}$ sector. Many of the $B_s\to h_1h_2$ decays can be related to …
These notes provide a pedagogical introduction to the theory of non-leptonic heavy-meson decays recently proposed by Beneke, Buchalla, Sachrajda and myself. We provide a rigorous basis for factorization for a large class of non-leptonic two-body B-meson decays in the heavy-quark limit. The resulting factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, and allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as B->D+pi and B->pi+pi.
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