Charmless hadronic $B$ and $B_s$ decays in perturbative QCD approach
Cai-Dian Lu
备注：
5 pages, talk given at Flavor Physics & CP Violation Conference, Taipei, 2008 and The 4th International Conference on Flavor Physics Sep. 24, 2007, Beijing
We review the perturbative QCD approach study of hadronic B decays. Utilizing the constrained parameters in these well measured decay channels, we study most of the possible charmless $B_s \to PP$, $PV$ and $VV$ decay channels in the perturbative QCD approach. In addition to the branching ratios and CP asymmetries, we also give predictions to the polarization fractions of the vector meson final states. The size of SU(3) breaking effect is also discussed. These predictions can be tested by the future LHCb experiment.
We give the first estimate of charmless scalar meson emitting weak hadronic decays of 0 $\Lembda_{b}^{0}$, $Ξ_{b}^{0}$ and $Ξ_{b}^{-}$ bottom baryons employing the pole model and consequently predict their branching ratios.
We report on the status of the perturbative calculation in the QCD factorization framework to charmless hadronic B meson decays and present a compilation of available NNLO results.
We make an analysis of the hadronic invariant mass spectrum in inclusive charmless semileptonic B meson decays in a QCD-based approach. The decay width is studied as a function of the invariant mass cut. We examine their sensitivities to the parameters of the theory. The theoretical uncertainties in the determination of $|V_{ub}|$ from the hadronic invariant mass spectrum are investigated. A strategy for improving the theoretical accuracy in the value of $|V_{ub}|$ is described.
Using the next-to-leading order QCD-corrected effective Hamiltonian, charmless exclusive nonleptonic decays of the $B_s$ meson into $η$ or $η'$ are calculated within the generalized factorization approach. Nonfactorizable contributions are included with two different treatments. Some subtleties involved are discussed.
We report OPE predictions for hadronic mass and q^2 moments in inclusive semileptonic B decays without charm, taking into account experimental cuts on the charged lepton energy and on the hadronic invariant mass, and address the related theoretical uncertainty.
By choosing two typical input parameter points in the minimal supergravity (mSUGRA) model and using the QCD factorization (QCDF) approach, we studied the supersymmetric effects to the CP violation of the two-body charmless hadronic $B$ meson decays. We found that though the SUSY contributions can give large corrections to the CP asymmetries for some decay channels, they could not be distinguished experimentally from the SM values because of the large theoretical errors dominated by calculating the annihilation contributions in the QCDF approach.
Charmless hadronic decays of B mesons to a vector meson (V) and a tensor meson (T) are analyzed in the frameworks of both flavor SU(3) symmetry and generalized factorization. We also make comments on B decays to two tensor mesons in the final states. Certain ways to test validity of the generalized factorization are proposed, using $B \to VT$ decays. We calculate the branching ratios and CP asymmetries using the full effective Hamiltonian including all the penguin operators and the form factors obtained in the non-relativistic quark model of Isgur, Scora, Grinstein and Wise.
We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced a…
The perturbative QCD approach has achieved great success in the study of hadronic B decays. Utilizing the constrained parameters in these well measured decay channels, we study most of the possible charmless $B_s \to PP$, $PV$ and $VV$ decay channels in the perturbative QCD approach. In addition to the branching ratios and CP asymmetries, we also give predictions to the polarization fractions of the vector meson final states. The size of SU(3) breaking effect is also discussed. All of these predictions can be tested by the future LHCb experiment.
The decays of $B$ mesons to a pair of charmless pseudoscalar mesons ($PP$ decays) or to a vector and pseudoscalar meson ($VP$ decays) have been analyzed within the framework of flavor SU(3) symmetry and the Kobayashi-Maskawa mechanism of CP violation. Separate $PP$ and $VP$ fits proved to be successful in describing the experimental data (branching ratios, CP asymmetries and time-dependent parameters). Decay magnitudes and relative weak and strong phases have been extracted from the fits. Values of the weak phase $γ$ were found to be consistent with the current indirect bounds from other analy…
We compare the factorization approach, the perturbative QCD approach and the Beneke-Buchalla-Neubert-Sachrajda approach to nonleptonic charmless $B$ meson decays. We discuss their treatments of factorizable, nonfactorizable, and annihilation contributions, infrared-cutoff and scale dependences, and strong phases. It is proposed that measurement of CP asymmetries in two-body $B$ meson decays provides an appropriate test of the these approaches.
A way of circumventing the gauge and infrared problems with effective Wilson coefficients is shown. Implications of experimentally measured charmless $B$ decays are discussed.
With the generalized factorization approximation, we calculate the branching ratios and CP asymmetries in B meson decays into two charmless pseudoscalar mesons. We give a new estimation of the matrix elements of (S+P)(S-P) current products with the PQCD method instead of equation of motion. We find that our results are comparatively smaller than those in the literature.
We study two-body charmless hadronic decays of $B$ mesons to a pseudoscalar meson ($P$) and a tensor meson ($T$) in the frameworks of both flavor SU(3) symmetry and generalized factorization. Certain ways to test validity of the generalized factorization are proposed, based on the flavor SU(3) analysis. We present a set of relations between a flavor SU(3) amplitude and a corresponding amplitude in the generalized factorization which bridge both approaches in $B \to PT$ decays. The branching ratios and CP asymmetries are calculated using the \emph{full} effective Hamiltonian including all the \…
We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B -> pi pi. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quar…
The problem of hadronic input in charmless nonleptonic B decays is discussed. QCD sum rules and their light-cone versions (LCSR) provide an important part of this input, such as the decay constant $f_B$ and $B\to π$ form factor. Employing the LCSR technique, the $B\to ππ$ hadronic matrix elements with emission, penguin and annihilation topologies are calculated, with no evidence for large nonfactorizable effects and/or strong phases.
I summarize results and performance of the dynamical theory of charmless hadronic B decays, based on QCD factorization in the heavy quark limit. On the theoretical side, a number of NNLO (alpha_s^2) amplitudes are now available, all showing a well-behaved perturbative expansion. The large observed branching fraction in B0 -> pi0 pi0 remains a challenge, implying either a large inverse moment of the B-meson wave function or a sizable power correction (or unexpected new physics). B-factory/Belle2 analyses of B -> gamma l nu may shed light on this. On the other hand, the new Belle and LHCb measur…
Using a theoretical framework based on the next-to-leading order QCD improved effective Hamiltonian, we have estimated the branching ratios and asymmetry parameters for the two body charmless nonleptonic decay modes of $Λ_b$ baryon i.e. $Λ_b \to p (π/ρ),~p(K/K^*)$ and $Λ(π/ρ)$, within the framework of generalized factorization. The nonfactorizable contributions are parametrized in terms of the effective number of colors, $N_c^{eff}$. So in addition to the naive factorization approach ($N_c^{eff}=3 $), here we have taken two more values for $N_c^{eff}$ i.e., $N_c^{eff}=2 $ and $\infty $. The ba…
We perform a model dependent fit to recent data on charmless hadronic B decays and determine $γ$, the phase of $V^*_{ub}$. We find $γ= 114^{+25}_{-21}$ degrees, which disfavors the often quoted $γ\sim 60^\circ$ at the two standard deviation level. We also fit for the form factors $F_0^{Bπ}$ and $A_0^{Bρ}$, and the strange-quark mass. They are consistent with theoretical expectations, although $m_s$ is somewhat low. Such agreement and the good $χ^2$ for the fit may be interpreted as a confirmation of the adequacy of our model assumptions.
In the light of recent experimental data from the CLEO Collaboration we study, the decays of B mesons to a pair of pseudoscalar (P) mesons, and a vector (V) meson and a pseudoscalar meson, in the framework of factorization. In order to obtain the best fit for the recent CLEO data, we critically examine the values of several input parameters to which the predictions are sensitive. These input parameters are the form factors, the strange quark mass, $ξ\equiv 1/ N_c$ (N_c is the effective number of color), the CKM matrix elements and in particular, the weak phase $γ$. It is possible to give a sat…
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 …
Based on the effective Hamiltonian with the generalized factorization approach, we calculate the branching ratios and CP asymmetries of $B \to VV$ decays in the Topcolor-assisted Technicolor (TC2) model. Within the considered parameter space we find that: (a) for the penguin-dominated $B \to K^{*+}ϕ$ and $K^{*0}ϕ$ decays, the new physics enhancements to the branching ratios are around 40%; (b) the measured branching ratios of $B \to K^{*+} ϕ$ and $ K^{*0} ϕ$ decays prefer the range of $3 \lesssim \nceff \lesssim 5$; (c) the SM and TC2 model predictions for the branching ratio ${\cal B}(B^+ \to…
The charmless bottom meson decays are systematically investigated based on an approximate six quark operator effective Hamiltonian from perturbative QCD. It is shown that within this framework the naive QCD factorization method provides a simple way to evaluate the hadronic matrix elements of two body mesonic decays. The singularities caused by on mass-shell quark propagator and gluon exchanging interaction are appropriately treated. Such a simple framework allows us to make theoretical predictions for the decay amplitudes with reasonable input parameters. The resulting theoretical predictions…
We give an overview of the experimental measurements and the theoretical understanding of the branching fractions and CP-violating asymmetries of charmless B-meson decays. Most experimetal results are from the BABAR and Belle experiments during the past decade. The global features of these experimental results are typically well described by the QCD-motivated theories such as QCD factorization, pQCD and soft-collinear effective theory. The agreement between theory and experiment is generally satisfactory, though there remain some unsolved puzzles that pose a great challenge to both theorists a…
Flavor SU(3) analysis of heavy meson ($B$ and $D$) hadronic charmless decays can be formulated in two different ways. One is to construct the SU(3) irreducible representation amplitude (IRA) by decomposing effective Hamiltonian according to the SU(3) transformation properties. The other is to use the topological diagrams (TDA). These two methods should give equivalent physical results in the SU(3) limit. Using $B \to PP$ decays as an example, we point out that previous analyses in the literature using these two methods do not match consistently in several ways, in particular a few SU(3) indepe…
The branching fraction of the psi(3770) decays into charmless final states is estimated in the S- and D-wave charmonia mixing scheme. With the information of the hadronic decays of J/psi and psi(3686), it is found that a large branching fraction, up to 13% of the total psi(3770) decays may go to charmless final states. The experimental search for these decays is also discussed.
Nonleptonic charmless B decays into a pseudoscalar (P) or a vector (V) meson accompanying a tensor (T) meson are re-analyzed. We scrutinize the hadronic uncertainties and ambiguities of the form factors which appear in the literature. The Isgur-Scora-Grinstein-Wise updated model (ISGW2) is adopted to evaluate the relevant hadronic matrix elements. We calculate the branching ratios and CP asymmetries for various $B\to P(V)T$ decay processes. With the ISGW2 model, the branching ratios are enhanced by about an order of magnitude compared to the previous estimates. We show that the ratios $\calB(B…
A leading-power factorization formula for weight functions relating the B to Xs gamma photon spectrum to arbitrary partial decay rates in B to Xu l nu is derived. These weight functions are independent of the hadronic shape function and allow for the determination of V_{ub} in a model-independent way. We calculate the weight function in renormalization-group improved perturbation theory to complete next-to-next-to leading order at the jet scale mu_i^2 ~ m_b Lambda_{QCD} and to next-to leading order at the hard scale mu_h ~ m_b. First-order power corrections are also included, where a model-dep…
We present fits to charmless strangeless hadronic B decay data for mean branching ratios and CP-violating asymmetries using the QCD factorization model of Beneke et al. Apart from one CP-violating parameter, the model gives a very good representation of 26 measured data. We find the CKM angle alpha = (93.5 +/- 8.4 -1.3) degrees and to be quite stable to plausible "charming penguin" corrections.
Motivated by the experimental data, we study charmless $B_{u,d,s}\to VT$ ($V$ and $T$ denote light vector and tensor mesons respectively) decays in the perturbative QCD approach. The predictions of branching ratios, polarization fractions and direct CP violations are given in detail. Specifically, within this approach we have calculated the polarization fractions and the branching ratios of $B\to ϕ(K_2^{*-}, \bar K_2^{*0})$ which agree well with the observed experimental data, however the branching ratios of $B\to ω(K_2^{*-}, \bar K_2^{*0})$ are hard to be explained, where the polarization fra…
Two-body charmless hadronic B decays involving a light tensor meson in the final states are studied in the perturbative QCD approach based on $k_T$ factorization. From our calculations, we find that the decay branching ratios for color allowed tree-dominated decays $B\to a_{2}^{0}π^{+}$ and $B\to a_{2}^{-}π^{+}$ modes are of order $10^{-6}$ and $10^{-5}$, respectively. While other color suppressed tree-dominated decays have very small branching ratios. In general, the branching ratios of most decays are in the range of $10^{-5}$ to $10^{-8}$, which are bigger by one or two orders of magnitude …
We calculated the CP averaged branching ratios and CP-violating asymmetries of two-body charmless hadronic Bs->PP,PV decays with the QCDF approach, including the contributions from the chirally enhanced power corrections and weak annihilations. Only several decay modes, such as Bs -> K^(*)K, K^(*{\pm})π^{\mp}, K^{\pm}ρ^{\mp}, η^(')η^('), have large branching ratios, which may be observed in the near future. The penguin-to-tree ratio P_{ππ}/T_{ππ} and a bound on angle $γ$ are given.
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.
We analyze the charmless two-body $B\to VP$ decays in the soft-collinear-effective-theory (SCET), where $V(P)$ denotes a light vector (pseudoscalar) meson. Using the current experimental data, we find two solutions in $χ^2$ fit for the 16 non-perturbative inputs responsible for the 87 $B\to PP$ and $B\to VP$ decay channels in SU(3) symmetry. Chirally enhanced penguins can only change several charming penguins sizably, since they share the same topology. The (S-P)(S+P) annihilation penguins in the perturbative QCD approach have the same topology with charming penguins in SCET, which play an imp…
We study the hadronic charmless two-body B decays to final states involving pseudoscalar and vector mesons with QCD factorization approach, including the contributions from the chirally enhanced power corrections and weak annihilations. The CP-averaged branching ratios and CP-violating asymmetries are given. Most of our results are in agreement with the present measurements, but the branching ratios of some decay channels are only marginally consistent with the experimental observations. Considering the large uncertainties, great advances in both experiment and theory in the near future are st…
The perturbative QCD (PQCD) approach based on $k_T$ factorization has made a great achievement for the QCD calculation of the hadronic B decays. Regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can do the perturbation calculation for kinds of diagrams including the annihilation type diagrams. In this paper, we review the current status of PQCD factorization calculation of two-body charmless $B\to PP, PV, VV$ decays up to the next-to-leading order (NLO) QCD corrections. two new power suppressed terms in decaying amplitudes are also taken into accou…
We discuss exclusive charmless B decays within the Standard Model of particle physics. In particular, we consider hadronic two-body decays as B -> pi pi and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B -> pi l nu. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. We present results for the imaginary part of the topological tree amplitudes and a partial calculation of the real part of the…
Our analysis suggests that the charmless yield in B decays is enhanced over traditional estimates. The c c.bar pair produced in b to c c.bar transitions may be seen significantly as light hadrons due to non-perturbative effects. Existing data samples at Upsilon(4S) and Z^0 factories allow key measurements which are outlined.
Based on the low-energy effective Hamiltonian with the generalized factorization, we calculate the new physics contributions to the branching ratios of the two-body charmless hadronic decays of $B_u$ and $B_d$ mesons induced by the new gluonic and electroweak charged-Higgs penguin diagrams in the general two-Higgs doublet models (models I, II and III). Within the considered parameter space, we find that: (a) the new physics effects from new gluonic penguin diagrams strongly dominate over those from the new $γ$- and $Z^0$- penguin diagrams; (b) in models I and II, new physics contributions to m…
Based on the assumption of two-quark structure of the scalar $K_0^*(1430)$, the CP-averaged branching ratios(BRs) and CP-violating asymmetries of charmless hadronic $B_q(q=u,d,s,c) \to \kst \kstb$ decays are studied in the standard model(SM) by employing the perturbative QCD(pQCD) factorization approach. Our predictions are the following: (1) the CP-averaged BRs for $B_{q} \to \kst \kstb$ decays in both scenarios vary in the range of $10^{-6} \sim 10^{-4}$ in the SM; (2) the magnitudes of $\acp^{\rm dir}(B_u \to {\kst}^+ {\kstb}^0)$ and $\acp^{\rm dir}(B_{d,s} \to {\kst}^+ {\kst}^-)$ in Scenar…
Recently Belle collaboration reported new measurements for the branching fractions with the first observing two processes of $\mathcal{B}(Ξ_c^0\toΛK^0_S)$, $\mathcal{B}(Ξ_c^0\toΣ^0 K^0_S)$ and updating data for $\mathcal{B}(Ξ_c^0\toΣ^+ K^-)$. Combined with other known data on charmless two body decays of anti-triplet charmed baryons, a lot of information can be derived with the assistance of $SU(3)$ flavour symmetry. Using $SU(3)$ relations between different decay modes, we can give some predictions based on the new measurements which can be tested with the high luminosity experiments in the f…
The CLEO collaboration has studied two-body charmless hadronic decays of $B$ mesons into final states containing two pseudo-scalar mesons, or a pseudo-scalar and a vector meson. We summarize and discuss results presented during the winter/spring 1999 conference season, and provide a brief outlook towards future attractions to come. In particular, CLEO presented preliminary results on the decays $B^\pm \to π^\pmρ^0$ ($Br(B^\pm \to π^\pmρ^0) = (1.5 \pm 0.5 \pm 0.4)\times 10^{-5}$), $B\to π^\pmρ^\mp$ ($Br(B\to π^\pmρ^\mp)=(3.5^{+1.1}_{-1.0}\pm 0.5)\times 10^{-5}$), $B\to π^\pm K^{\star\mp}$ ($Br(…
Using the next-to-leading order QCD-corrected effective Hamiltonian, charmless exclusive nonleptonic decays of the $B_s$ meson into $η$ or $η'$ are calculated within the generalized factorization approach. Nonfactorizable contributions, which can be parametrized in terms of the effective number of colors $N_c^{\rm eff}$ for $P P$ and $V P$ decay modes, are studied in two different schemes: (i) the one with the "homogeneous" structure in which $(N_c^{\rm eff})_1 \approx (N_c^{\rm eff})_2 \approx ... \approx (N_c^{\rm eff})_{10}$ is assumed, and (ii) the "heterogeneous" one in which the possibil…
In this work, based on the assumption of two-quark structure of the scalars, the charmless hadronic $B_c \to SP, SV$ decays(here, $S$, $P$, and $V$ denote the light scalar, pseudoscalar, and vector mesons, respectively) are investigated by employing the perturbative QCD(pQCD) factorization approach.From our numerical evaluations and phenomenological analysis, we find that (a) the pQCD predictions for the {\it CP}-averaged branching ratios(BRs) of the considered $B_c$ decays vary in the range of $10^{-5}$ to $10^{-8}$, which will be tested in the ongoing LHCb and forthcoming Super-B experiments…
Within the framework of perturbative QCD factorization, we investigate the nonfactorizable contributions to these factorization-forbidden Quasi-two-body decays $B_{(s)}\rightarrow hχ_{c0}\rightarrow hπ^+π^-(K^+K^-)$ with $ h=π, K$. We compare our predicted branching ratios for the $B_{(s)}\rightarrow Kχ_{c0}\rightarrow Kπ^+π^-(K^+K^-)$ decay with available experiment data as well as predictions by other theoretical studies. The branching ratios of these decays are consistent with data and other theoretical predictions. In the Cabibbo-suppressed decays $B_{(s)}\rightarrow hχ_{c0}\rightarrow hπ^…
We review recent results on hadronic B meson decays including rare as well as non-suppressed decays. The main emphasis is on those channels relevant to measurement of CP violation in the coming B factories. After briefly describing flavor-tagged charm counting, we cover B -> DK(*), B -> charmless 2-body decays, inclusive eta' production, and final-state-interaction phases in B -> Psi K* and B -> D* rho.
This work discusses charmless inclusive B decays and their application to the extraction of $|V_{ub}|$. Starting from first principles we relate the differential decay rate to the hadronic tensor in terms of optimal choice of kinematical variables. We review the traditional methods of calculating the hadronic tensor, expansion in $α_s$ and HQET, and discuss their shortcomings. In the kinematical region relevant for experiment ("shape function" region), the hadronic tensor can be factorized, at each order in $1/m_b$, as a product of calculable hard functions and a convolution of calculable jet …
We discuss the decay of Bc mesons into two light mesons (pi, K^(*), eta', rho, omega, phi). All these decay channels come from a single type of diagram, namely tree annihilation. This allows us to derive extremely simple SU(3) relations among these processes. The size of annihilation contributions is an important issue in B physics, and we provide two different estimates in the case of non-leptonic charmless Bc decays, either a comparison with annihilation decays of heavy-light mesons or a perturbative model inspired by QCD factorisation. We finally discuss a possible search for these channels…
We provide the analysis of charmless two-body $B\to VP$ decays under the framework of the soft-collinear-effective-theory (SCET), where $V(P)$ denotes a light vector (pseudoscalar) meson. Besides the leading power contributions, some power corrections (chiraly enhanced penguins) are also taken into account. Using the current available $B\to PP$ and $B\to VP$ experimental data on branching fractions and CP asymmetry variables, we find two kinds of solutions in $χ^2$ fit for the 16 non-perturbative inputs which are essential in the 87 $B\to PP$ and $B\to VP$ decay channels. Chiraly enhanced peng…
Status of nonfactorizable effects in hadronic charmless B decays is reviewed. Implications of new CLEO measurements on $B^0\toπ^+π^-$ and $B\toη' K$ are discussed. Nonfactorizable effects due to color ocet 4-quark operators are calculated using renormalization group improved QCD sum rules. The resultant B-meson lifetime ratio $τ(B^-)/τ(B_d)$ agrees with experiment.
We derive several relations between CP violating rate differences $Δ(B\to PV) = Γ(B\to PV) - Γ(\bar B \to \bar P \bar V)$ for charmless $B\to P V$ decays in the Standard Model using SU(3) flavor symmetry. It is found that although the relations between branching ratios of $ΔS = 0$ and $ΔS = -1$ processes are complicated, there are simple relations independent of hadronic models between some of the $ΔS =0$ and $ΔS = -1$ rate differences due to the unitarity property of the Kobayashi-Maskawa matrix, such as $ Δ(B\to π^+ ρ^-) = -Δ(B\to π^+ K^{*-})$, $Δ(B\to π^- ρ^+) = - Δ(K^- ρ^+)$. SU(3) breakin…
We present $O(α_s^2)$ QCD corrections to the fully-differential decay rate of a $b$-quark into inclusive semileptonic charmless final states. Our calculation provides genuine two-loop QCD corrections, beyond the Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic observable that can be probed in $b \to X_u e \bar ν$ decays. Kinematic cuts that closely match those used in experiments can be fully accounted for. To illustrate these points, we compute the non-BLM corrections to moments of the hadronic invariant mass and the hadronic energy with cuts on the lepton energy a…
Isospin and flavor SU(3) relations in charmless hadronic B decays $B\to ππ, πK$ are investigated in detail with paying attention to the SU(3) symmetry breaking effects in both amplitudes and strong phases. In general, the isospin and the flavor SU(3) structure of the effective Hamiltonian provide several relations among the amplitudes and strong phases. Whereas a global fit to the latest data shows that some relation seems not to be favorable for a consistent explanation to the current data within the standard model (SM). By considering several patterns of SU(3) breaking, the amplitudes and th…
We study constraints on the CP violating phase $γ$ in the Kobayashi-Maskawa model using available experimental data. We first follow the conventional method to up date the constraint on $γ$ by performing a $χ^2$ analysis using data from $|ε_K|$, $Δm_{B_{d,s}}$ and $|V_{ub}/V_{cb}|$. We also include the recent information on $\sin2β$ in the analysis. We obtain the best fit for $γ$ to be $66^\circ$ and the 95% C.L. allowed range to be $42^\circ \sim 87^\circ$. We then develop a method to carry out a $χ^2$ analysis based on SU(3) symmetry using data from $B\to ππ$ and $B\to K π$. We also discuss …
