K pi form factors, final state interactions and D+ -> K- pi+ pi+ decays
D. R. Boito, R. Escribano
备注：
5 pages, uses aipproc style. Talk presented by R. Escribano at the XIII International Conference on Hadron Spectroscopy (HADRON09), Florida State University (Tallahassee), USA, 29.11-4.12.2009
We present a model for the decay $D^+\to K^-π^+π^+$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the $Kπ$ scalar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. Allowing for a global phase difference between the $S$ and $P$ waves of $-65^\circ$, the Dalitz plot of the $D^+\to K^-π^+π^+$ decay, the $Kπ$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.
We evaluate $B_{s}\rightarrow K^{\ast 0}$ transition form factors in the full kinematical region within the covariant confined quark model. The calculated form factors can be used to calculate the $B_{s}\rightarrow K^{\ast 0}μ^+ μ^-$ rare decay branching ratio, which was recently measured by LHCb collaboration.
Based on Bbar to D{(*)}K-K{*0} decay data, which supports factorization, we propose to extract the kaon axial form factor in the factorization framework. Experiment indicates that the K-K{*0} pair is produced by an axial current where only one out of three axial form factors is dominant. The axial form factor can be extracted by fitting the K-K{*0} mass spectrum with an a_1(1260)-resonance plus QCD-motivated non-resonant contributions, which can be improved as data improves.
Recently, the tau --> K pi nu_tau decay spectrum has been measured by the Belle and BaBar collaborations. In this work, we present an analysis of such decays introducing a dispersive parametrization for the vector and scalar Kpi form factors. This allows for precise tests of the Standard Model. For instance, the determination of f_+(0)|V_{us}| from these decays is discussed. A comparison and a combination of these results with the analyses of the K_{l3} decays is also considered.
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.
A sample of more than one million Ke4 decay candidates with less than one percent background contamination has been collected by the NA48/2 experiment at the CERN SPS in 2003-2004, allowing a detailed study of the decay properties. The branching ratio, inclusive of radiative Ke4gamma decays, is measured to be BR(Ke4) = (4.257 +/- 0.016_exp +/- 0.031_ext) x 10-5 with a total relative error of 0.8%. This measurement complements the study of S- and P-wave hadronic form factors by assigning absolute values to the relative hadronic form factors obtained earlier in a simultaneous analysis of the pio…
We investigate transition form factors of $B$ meson decays into a scalar glueball in the light-cone formalism. Compared with form factors of $B$ to ordinary scalar mesons, the $B$-to-glueball form factors have the same power in the expansion of $1/m_B$. Taking into account the leading twist light-cone distribution amplitude, we find that they are numerically smaller than those form factors of $B$ to ordinary scalar mesons. Semileptonic $B\to Gl\barν$, $B\to Gl^+l^-$ and $B_s\to Gl^+l^-$ decays are subsequently investigated. We also analyze the production rates of scalar mesons in semileptonic …
$B_s^0\rightarrow D_s^{-}$ and $B_s^0\rightarrow D_s^{*-}$ weak transition form factors are estimated for the whole physical region with a method based on an instantaneous approximated Mandelstam formulation of transition matrix elements and the instantaneous Bethe-Salpeter equation. We apply the estimated form factors to branching ratios, CP asymmetries and polarization fractions of non-leptonic decays within the factorization approximation. And we study the non-factorizable effects and annihilation contributions with the perturbative QCD approach. The branching ratios of semi-leptonic $B_s^0…
Using data from the B factories and the Tevatron, we perform tests of how well non-leptonic B decays of the kind B -> D^{(*)}_{(s)} P, where P is a pion or kaon, are described within the factorization framework. We find that factorization works well - as is theoretically expected - for color-allowed, tree-diagram-like topologies. Moreover, also exchange topologies, which have a non-factorizable character, do not show any anomalous behavior. We discuss also isospin triangles between the B -> D^{(*)} pi decay amplitudes, and determine the corresponding amplitudes in the complex plane, which show…
We report lattice results of $D_s$ meson semi-leptonic decay form factors to $η$ and $η'$ mesons. This decay process contains disconnected fermion loops, which are challenging in lattice calculations. Our result shows that the disconnected loops give significant contributions to the form factors.
Rare exclusive $B_c^\ast \rightarrow D_{s}~l^+ l^-$ decays are analyzed in the framework of the three--point QCD sum rules approach. The two gluon condensate corrections to the correlation function are included and the form factors of this transition are evaluated. Using the form factors, the decay width and integrated decay rate for these decays are also calculated.
We compare a non-factorizable charming-loop correction to an exclusive FCNC $B$-decay given in terms of the 3-particle Bethe-Salpeter amplitude (3BS) of the $B$-meson, $\langle 0|\bar q(x)G_{μν}(z)b(0)|B(p)\rangle$, with the corresponding correction to the $B$-meson semileptonic form factor. In spite of certain similarities, these two corrections are shown to have substantial differences: The form factor correction is dominated by the collinear light-cone configuration of 3BS: $z_μ= u x_μ$, $0 < u < 1$, $x^2=0$. In contrast, the FCNC amplitude is dominated by a different configuration with non…
QCD sum rules for the determination of form factors of $Λ_b$ and $Λ_c$ semileptonic decays are investigated. With a form for the baryonic current appropriate for the limits of the heavy quark symmetries, the different tensor structures occurring in the two- and three-point functions are separately studied, and in each case general relations are written for the form factors. Particular attention is given to the treatment of the kinematical region ascribed to the continuum. The $t$-dependence of the form factors and the decay rates are numerically evaluated and compared to experimental informati…
According to the heavy-quark flavour symmetry, the $B\to π, K$ transition form factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays $D \to π\ell ν$ and $D\to K \ell ν$, we perform a phenomenological study of $B \to π, K$ transition form factors based on this symmetry. Using BK, BZ and Series Expansion parameterizations of the form factor slope, we extrapolate $B \to π, K$ transition form factors from $q^{2}_{max}$ to $q^{2}=0$. It is found that, although being consistent with each other…
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 study the vector and axial-vector form factors of radiative kaon decay within the framework of the gauged nonlocal effective chiral action from the instanton vacuum, focusing on the effects of flavor SU(3) symmetry breaking. The general tendency of the results are rather similar to those of radiative pion decays: The nonlocal contributions make the results of the vector form factor increased by about $20\,\%$, whereas they reduce those of the axial-vector form factor by almost $30\,\%$. Suppressing the prefactors consisting of the kaon mass and the pion decay constant, we scrutinize how the…
We study the vector and axial vector form factors in the heavy to light transitions in charmed baryon decays using HQET. We calculate the 1/m_c corrections to the form factors and show that these corrections can be significant. We also consider applications to semi-leptonic and hadronic decays of charmed baryons.
It is shown that the existing data on two-body B decays, some of them only upper limits, are precise enough to perform an isospin analysis to extract the phase shifts due to final state interaction. Unlike charm decays, no significant final state interaction is observed in decays $B\to Dπ, Dρ$, and $D^*π$ supporting the factorization hypothesis in these decays. By fitting directly the isospin amplitudes obtained, we extract the ratio $a_2/a_1$, where $a_1$ and $a_2$ are the coefficients in the factorized effective Hamiltonian.
We perform an analysis of the form factors that rule the structure-dependent amplitude in the radiative pion decay. The resonance contributions to pion -> e nu_e gamma decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions VVP and VAP, and by demanding the smoothing of the form factors at high transfer of momentum. A comparison between theoretical and experimental determinations of the form factors is also carried out. We also consider and evaluate the role played by a no…
We present a complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p^4) in covariant baryon chiral perturbation theory. Partial higher-order contributions are obtained, and we discuss chiral extrapolations of the vector form factor at zero momentum transfer. In addition we derive low-energy theorems for the subleading moments in hyperon decays, the weak Dirac radii and the weak anomalous magnetic moments, up to O(p^4).
We study the semileptonic decays of heavy mesons into light pseudoscalars by making use of dispersion relations. Constraints from heavy quark symmetry, chiral symmetry and perturbative QCD are implemented into a dispersive model for the form-factors. Large deviations from $B^*$-pole dominance are observed in $B\toπ\ellν$. We discuss the model prediction for this mode and its possible impact on the extraction of $|V_{ub}|$.
We discuss the general properties of the $B$-meson decay form factors $F(q^2,q'^2)$, describing $B$-meson decays induced by two currents, e.g., $B$-decays into four leptons in the final state. We study the analytic properties of these complicated objects and identify those regions of $q^2$ and $q'^2$, where perturbative QCD can be applied for obtaining predictions for the physical form factors.
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…
We calculate the decay constants of $D_s$ and $D_s^{*}$ with $\bar{B}^0 \ra D^{+}\ell^{-}ν$ and $\bar{B}^0 \ra D^{+}D_s^{-(*)}$ decays. In our analysis we take the factorization method including non-factorizable term contributions and used two different form factor behaviours (constant and monopole-type) for $F_0(q^2)$. We also consider the QCD-penguin and Electroweak-penguin contributions in hadronic decays within the NDR renormalization scheme at NLO calculation. We estimate the decay constant of the $D_s$ meson to be $233\pm49$ ${\rm MeV}$ for (pole/pole)-type form factor and $255\pm54$ ${\…
We have calculated the parameter Ksi(0)=f-(0)/f+(0) of the Kmu3 decay in the spectator approximation of the Standard Model. It was obtained that Ksi(0) ~ -0.02.
We evaluate $B \rightarrow ρ$ transition form factors in the full kinematical region within the covariant confined quark model. We compare the obtained results with the results from light-cone sum rules. The calculated form factors can be used to calculate the $B^+ \rightarrow ρ^+ μ^+ μ^-$ rare decay branching ratio.
I consider nonleptonic decays of B mesons into two light mesons using the light-cone wave functions for the mesons. In the heavy quark limit, nonfactorizable contributions are calculable from first principles in some decay modes. I review the idea of the QCD-improved factorization method and discuss the implications in phenomenology.
We review recent advances in the theory of strong-interaction effects and final-state interactions in hadronic weak decays of heavy mesons. In the heavy-quark limit, the amplitudes for most nonleptonic, two-body B decays can be calculated from first principles and expressed in terms of semileptonic form factors and light-cone distribution amplitudes. We summarize the main features of this novel QCD factorization and discuss its phenomenological applications to B -> D^(*) L decays (with L a light meson), and to the rare charmless decays B -> pi K and B -> pi pi.
Meson decays are considered within the constituent quark model, making use of the dispersion formulation of the model: Starting with spacelike momentum transfers $q$, meson transition form factors are expressed as relativistic invariant double spectral representations over the invariant masses of the initial and final $Q\bar Q$ pairs. The form factors at timelike momentum transfers are obtained by performing the analytical continuation in $q^2$. As a result, the form factors both in the scattering and decay regions are expressed through the light--cone wave functions of the initial and final h…
We investigate the role of R-parity violating interaction in the non-leptonic decays of B mesons into two light mesons B --> PP. The decay amplitudes are calculated using the QCD improved factorization method. Using the combined data on B decays from BaBar, Belle and CLEO, we obtain strong constraints on the various products of R-parity violating couplings. Many of these new constraints are stronger than the existing bounds.
We analyze the semileptonic $D_{q}\to K_1 \ellν$ transition with $q=u, d, s$, in the framework of the three--point QCD sum rules and the nonleptonic $D\to K_1 π$ decay within the QCD factorization approach. We study $D_{q}$ to $K_1(1270)$ and $K_1(1400)$ transition form factors by separating the mixture of the $K_1(1270)$ and $K_1(1400)$ states. Using the transition form factors of the $D\to K_1 $, we analyze the nonleptonic $D\to K_1 π$ decay. We also present the decay amplitude and decay width of these decays in terms of the transition form factors. The branching ratios of these channel mode…
We review recent advances in the theory of strong-interaction effects and final-state interactions in hadronic weak decays of heavy mesons. In the heavy-quark limit, the amplitudes for most nonleptonic, two-body B decays can be calculated from first principles and expressed in terms of semileptonic form factors and light-cone distribution amplitudes. We summarize the main features of this novel QCD factorization and discuss its phenomenological applications to B->D^(*)+L decays (with L a light meson), and to the rare charmless decays B->pi+K and B->pi+pi.
We calculate the QCD factors $a_1$ and $a_2$, entering the tests of factorization in non-leptonic heavy meson decays, beyond the leading logarithmic approximation in three renormalization schemes (NDR, HV, DRED). We investigate their $μ$--dependence and the renormalization scheme dependence. We point out that $a_1$ for B-decays depends very weakly on $\Lms$, $μ$ and the choice of the renormalization scheme. For $\Lms^{(5)}=225\pm85~MeV$ and $4~GeV\leqμ\leq 8~GeV$ we find $a_1=1.01\pm0.02$ in accordance with phenomenology. The $\Lms$, $μ$ and scheme dependences of $a_2$ are on the other hand si…
We calculate $\bar{B}_s^0\to ϕ$ translation form factors $V$, $A_0$, $A_1$, $A_2$ based on QCD sum rule and study the nonleptonic two-body decay of $\bar{B}_s^0\to J/ψϕ$ with the form factors obtained. We calculate the time-integrated branching ratio of $\bar{B}_s^0\to J/ψϕ$ decay. The results for both the total branching ratio and the cases for the final vectors in longitudinal and transverse polarizations are consistent with experimental data.
Toward the goal of extracting the weak angle alpha, the decay B^0/B^0-bar to a_0^{+/-}pi^{-/+} was recently measured. The decay B^0 to a_0^+pi^- is not only forbidden in the factorization limit of the tree interaction, but also strongly suppressed for the penguin interaction if short-distance QCD dominates. This makes extraction of alpha very difficult from a^{+/-}π^{-/+}. We examine the simlar factorization-suppressed decays, in particular, B^0\to b_1^+pi^-. The prospect of obtaining alpha is even less promising with b_1^{+/-}pi^{-/+}. To probe how well the short-distance dominance works, we …
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 study the form factors appearing in the inclusive decay b -> s g^*, in the framework of the noncommutative standard model. Here g^* denotes the virtual gluon. We get additional structures and the corresponding form factors in the noncommutative geometry. We analyse the dependencies of the form factors to the parameter pΘk where p (k) are the four momenta of incoming (outgoing) b quark (virtual gluon g^*, Θis a parameter which measures the noncommutativity of the geometry. We see that the form factors are weakly
We study the weak vector and axial-vector form factors of first- and second-class currents for the semileptonic octet baryon decays in the spirit of the chiral quark model. Our results for the weak magnetism form factors are consistent with the conserved vector current (CVC) results. The induced pseudotensor form factors, which are highly model dependent, are small. The overall performance of the chiral quark model is quite good and in general agreement with existing experimental data.
Within the Standard Model, we investigate the semi-leptonic weak decays of $J/ψ$. The various form factors of $J/ψ$ transiting to a single charmed meson ($D^{(*)}_{(d,s)}$) are studied in the framework of the QCD sum rules. These form factors fully determine the rates of the weak semi-leptonic decays of $J/ψ$ and provide valuable information about the non-perturbative QCD effects. Our results indicate that the decay rate of the semi-leptonic weak decay mode $J/ψ\to D^{(*)-}_{s}+e^{+}+ν_{e}$ is at order of $10^{-10}$.
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…
By means of the universal unitary and analytic model of electromagnetic structure of hadrons the two-photon decay rates of P=pi^0, eta, eta' mesons are determined in an alternative way from data on their transition form factors.
Two body non-leptonic decays: are investigated. Baryon form factors of the heavy quark effective theory are employed. Form factors for renormalization in full QCD are also considered. We find that contributions of the non-factorizable terms are negligible in b-decays. Comparison with calculations in other models shows that form factors for renormalization in full QCD should be more relevant. The asymmetry parameters are negative as in the charmed baryons cases. An experimental measure on the form factors V1 and A1 is accentuated to test the validity of HQET.
We provide upper and lower bounds on the semileptonic weak decay form factors for $B \to D^(*)$ and $Λ_b \to Λ_c$ decays by utilizing inclusive heavy quark effective theory sum rules. These bounds are calculated to second order in $Λ_{QCD}/m_Q$ and first order in $α_s$. The $O(α_s^2 β_0)$ corrections to the bounds at zero recoil are also presented.
The branching ratios for the hadronic B-meson weak decays B -> J/psi K and B -> D pi are used to extract the size of the ``non-factorizable'' terms in the decay amplitudes. It is pointed out that the solutions are not uniquely determined. In the B -> J/psi K case, a 2-fold ambiguity can be removed by analyzing the contribution of this decay to B -> K l+ l-. In the B -> D pi case, a 4-fold ambiguity can only be removed if the ``non-factorizable'' terms are assumed to be a small correction to the vacuum insertion result.
A formalism for the relativistic description of hadron decays within the constituent quark model is presented. First, hadron amplitudes of the light--cone constituent quark model, in particular the weak transition form factors at spacelike momentum transfers, $q^2\le 0$, are represented in the form of the dispersion integrals over the hadron mass. Second, the form factors at $q^2>0$ are obtained by performing the analytic continuation from the region $q^2<0$. As a result, the transition form factors both in the scattering and the decay regions are expressed through the light--cone wave functio…
We calculate the decay constant of $D_s$ and $D_s^{*}$ with $\bar{B}^0 \ra D^{+}\ell^{-}ν$ and $\bar{B}^0 \ra D^{+}D_s^{-(*)}$ decays. In our analysis we assume that factorization ansatz works and used two different form factor behaviours (constant and monopole-type) for $F_0(q^2)$. We also consider the QCD-penguin contributions in hadronic decays within the NDR renormalization scheme at NLO calculation. We estimate the decay constant of the $D_s$ meson to be $219\pm46 MeV$ for (pole/pole)-type form factor and $239\pm50$ $MeV$ for (pole/constant)-type form factor. For $D_s^{*}$ meson, we predi…
Form factors of the rare $Λ_{b}(Λ_{b}^*)\to N\ell^{+}\ell^{-}$ decays are calculated in the framework of the light cone QCD sum rules by taking into account of the contributions from the negative parity baryons. Using the obtained results on the form factors, the branching ratios of the considered decays are estimated. The numerical survey for the branching ratios of the $Λ_b \rar N\ell^+\ell^- $ and $Λ_b^\ast \rar N\ell^+\ell^- $ decays indicate that these transitions could be measurable in LHCb in near future. Comparison of our predictions on the form factors and branching ratios with those …
We analyze the semileptonic $B \to a_1 \ell^+\ell^-$, $\ell=τ, μ, e$ transitions in the frame work of the three-point QCD sum rules in the standard model. These rare decays governed by flavor-changing neutral current transition of $b \to d$. Considering the quark condensate contributions, the relevant form factors as well as the branching fractions of these transitions are calculated.
A pole model for the form factors describing heavy to light meson transitions is constructed, and the results compared with the predictions of the heavy quark effective theory (HQET). While most of the HQET-predicted relationships among form factors hold at the maximum value of $q^2$, many are violated, suggesting that the simplest version of the pole model of meson form factors should be used with caution, especially when combined with HQET.
A relativistic constituent quark model is adopted to give an unified description of the leptonic and semileptonic decays of pseudoscalar mesons (π, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and the results of other approaches. Eventually, the model is found to reproduce the scaling behaviours of spin-flavor symmetry in the heavy-quark limit.
Two body decays of charm mesons are studied by describing their amplitude in terms of a sum of factorizable and non-factorizable ones. The former is estimated by using a naive factorization while the latter is calculated by using a hard pseudo-scalar-meson approximation. The hard pseudo-scalar-meson amplitude is given by a sum of the so-called equal-time commutator term and surface term which contains all possible pole contributions of various mesons, not only the ordinary $\{q\bar q\}$ but also four-quark $\{qq\bar q\bar q\}$, hybrid $\{q\bar qg\}$ and glue-balls. Naively factorized amplitude…
Two body non-leptonic decays:Lambda_b-->Lambda_c P(V) are investigated. Baryon form factors of the heavy quark effective theory are employed. Form factors for renormalization in full QCD are also considered. We find that contributions of the non-factorizable terms are negligible in b-decays. Comparison with calculations in other models shows that form factors for renormalization in full QCD should be more relevant. The asymmetry parameters are negative as in the charmed baryons cases. An experimental measure on the form factors V1 and A1 is accentuated to test the validity of HQET.
In the framework of QCD factorization, we study the $B$ meson exclusive decays $B\to χ_{cJ}K$ where the spin-triplet P-wave charmonium states $χ_{cJ}(J=0,1,2)$ are described by the color-singlet non-relativistic wave functions. We find that for these decays (except $χ_{c1}$) there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet m…
We present a proposal for detecting new physics at a B-factory running at the $Υ(3S)$ resonance by testing lepton universality to the few percent level in the leptonic decays of the $Υ(1S)$ and $Υ(2S)$ resonances tagged by the dipion in the chain decay: $Υ(3S) \to pi^+π^-Υ(1S,2S)$; $Υ(1S,2S) \to \ell^+\ell^-$, $\ell=e,μ,τ$.
Model-independent bounds are presented for the form-factors describing the semileptonic decay $Λ_b\toΛ_ce\barν_e$ at the end-point of the lepton energy spectrum. For the axial-vector form-factor $f_1^A(1)$ we obtain $f_1^A(1)\leq 0.960÷0.935$, where the uncertainty arises from the value of $μ_π^2$, the average kinetic energy of the $b$ quark inside of the $Λ_b$ baryon. A bound is given on the forward matrix element of the axial current in a $Λ_b$ baryon which is relevant for the inclusive semileptonic decays of the polarized $Λ_b$ decays.
We study long-distance effects in rare exclusive semileptonic decays B -> K_{1}ell ^{+}ell ^{-}, K_{1} is the axial vector meson.The form factors, describing the meson transition amplitudes of the effective Hamiltonian, are calculated using Ward identites which are then used to calculate branching ratio and forward-backward asymmetry in these decay modes. The zero of forward-backward asymmetry is of special interest and provide us the precission test of Standard model.
Exclusive hadronic B-meson decays into two-body final states consisting of a light pseudoscalar or vector meson along with an eta or eta' meson are of great phenomenological interest. Their theoretical analysis involves decay mechanisms that are unique to flavor-singlet states, such as their coupling to gluons or their ``intrinsic charm'' content. These issues are studied systematically in the context of QCD factorization and the heavy-quark expansion. Theory can account for the experimental data on the B->K^{(*)} eta^{(')} branching fractions, albeit within large uncertainties.
