B-meson Wave Function Research Articles

Renormalization-group evolution of the none-local matrix element of B-meson in QCD and B → π transition form factor

We consider the renormalization-group evolution of the matrix element of 〈0|q¯(z)β[z,0]b(0)α|B¯〉, which can be used to define the distribution amplitudes for B meson and widely applied in studies of B meson decays. The contribution to the renormalization constant of the non-local operator q¯(z)β[z,0]b(0)α is considered up to one-loop order in QCD. Since the quark fields in this operator are not directly coupled fields, momentum can not flow freely through this non-local operator. Momentum involved in this operator can be treated stringently in coordinate space. We find that the ultraviolet divergences regulated by dimensional parameter ϵ cancel with each other, and the evolution effect vanishes. The matrix element 〈0|q¯(z)β[z,0]b(0)α|B¯〉 escapes from the renormalization-group evolution. We then apply the matrix element in calculating B→π transition form factor, where the matrix element is obtained by using the B meson wave function calculated in QCD-inspired potential model. By comparing with experimental data for the semileptonic decay of B→πℓν and light-cone sum rule calculation, we analyze the perturbative and non-perturbative contributions to B→π transition form factor in the frame work of perturbative QCD approach. We find that the effectiveness of the suppression of Sudakov factor to soft contribution depends on the end-point behavior of B meson wave function, and with the B-meson wave function used in this work, soft contribution can not be well suppressed. The hard contribution to the B→π transition form factor is about 59%, and soft contribution can be as large as 41% in the naive calculation. To make the perturbative calculation reliable, a soft momentum cutoff in the calculation and soft form factor have to be introduced.

QCD sum rules for quark–gluon three-body components in the B meson

We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, λE and λH, which correspond to matrix elements representing quark–gluon three-body components in the B-meson wavefunction. We derive the sum rules for λE,H calculating the new higher-order QCD corrections, i.e., the order αs radiative corrections to the Wilson coefficients associated with the dimension-5 quark–gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of λE,H. We also discuss the renormalization-group improvement for the sum rules and present update on the values of λE,H.

Bs → f0(980) Transition Form Factors Within the kT Factorization Approach

In the paper, we apply the kT factorization approach to deal with the Bs → f0 (980) transition form factors in the large recoil regions, i.e. the small q2 regions. For the purpose, we adopt the B-meson wave-functions ΦB, and δ that include the three-Fock states contributions to do our discussion. Although the scalar meson f0(980) is widely perceived as the 4-quark bound state (scenario 2), but the distribution amplitudes of 4-quark states are still unknown to us, so we adopt 2-quark model (scenario 1) for scalar meson f0(980) in our discussion. By varying the B-meson wave-function parameters within their reasonable regions, we obtain F0(0) = F+(0) = 0.20 ± 0.02, FT(0) = 0.24 ± 0.02. Our present results for these form factors are consistent with the light-cone sum rule results obtained in the literature.

B-Meson Wavefunction by a Comparative Analysis of the B → π, K Transition Form Factors

Properties of the B-meson light-cone wavefunction up to next-to-leading order Fock state expansion are studied by a comparative study of the B → π, K form factors within the kT factorization approach and the light-cone sum rule analysis. The form factors F+, 0,TB → π and F+,0,TB → K are carefully re-calculated up to O(1/mb2) within the kT factorization approach in the large recoil region. The QCD light-cone sum rule is applicable in the large and intermediate energy regions, and the QCD light-cone sum rule results of Ball and Zwicky [Phys. Rev. D 71 (2005) 014015] are adopted for such a comparative study. It is found that when the two phenomenological parameters λ̄ [0.50, 0.55] and δ ∊ [0.25, 0.30], the results of F+,0,TB → π(Q2) and F+,0,TB → K(Q2) from these two approaches are consistent with each other in the large recoil energy region.

B → K Transition Form Factor with Tensor Current within the kTFactorization Approach

We apply the kT factorization approach to deal with the B → K transition form factor with tensor current in the large recoil regions. Main uncertainties for the estimation are discussed and we obtain FTB→K(0) = 0.25 ± 0.01 ± 0.02, where the first error is caused by the uncertainties from the pionic wavefunctions and the second is from that of the B-meson wavefunctions. This result is consistent with the light-cone sum rule results obtained in the literature.

B→K transition form factor up to $\mathcal{O}(1/m^2_b)$ within the kT factorization approach

We apply the k(T) factorization approach to deal with the B-->K transition form factor F-+,0(B-->K) (q(2)) in the large recoil regions. The B-meson wave functions Psi(B) and Psi(B) that include the 3-particle Fock states' contributions are adopted to give a consistent PQCD analysis of the form factor up to O(1/m(b)(2)). It has been found that the two wave functions Psi(B) and Psi(B) can give sizable contributions to the form factor and should be kept for a better understanding of the B-meson decays. Next the contributions from different twist structures of the kaon wave function are discussed, including SUf(3)-breaking effects. A sizable contribution from the twist-3 wave function Psi(p) is found, whose model dependence is discussed by taking two groups of parameters that are determined by different distribution amplitude moments obtained in the literature. It is also shown that F-+,0(B-->K) (0) = 0.30 +/- 0.04 and [F-+,0(B-->K) (0)/F-+,0(B-->pi) (0)] = 1.13 +/- 0.02, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.

B-meson wavefunction in the Wandzura–Wilczek approximation

The B-meson wavefunction has been studied with the help of the vacuum-to-meson matrix element of the non-local operators in the heavy quark effective theory. In order to obtain the Wandzura–Wilczek-type B-meson wavefunction, we solve the equations which are derived from the equation of motion of the light spectator quark in the B meson by using two different assumptions. Under the condition that ω0=2Λ¯, the solutions for the B-meson wavefunction in this paper agree well with the one obtained by directly taking the heavy quark limit mb→∞. Our results show that the equation of motion of the light spectator quark in the B meson can impose a strong constraint on the B-meson wavefunctions Ψ±(ω,z2). Based on the obtained results, we claim that both its distribution amplitudes ϕB(ω) and ϕ¯B(ω) are important for calculating the B meson decays.

Dispersion approach to quark-binding effects in weak decays of heavy mesons

Dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed: Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at $q^2>0$ are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full $q^2$ range of the weak decay in terms of the wave functions of the participating mesons. The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by long-distance QCD for these limits is demonstrated. Predictions for form factors for B, B(s), D, and D(s) decays to light mesons are given. The B\to\gamma l\nu decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B^0-\bar B^0 mixing are calculated. Inclusive weak B-decays are analysed and the differential distributions are obtained in terms of the B-meson wave function.

Non-factorizable effects in the B– [formula omitted] mixing

We analyse the corrections to factorization for the B– B ̄ mixing amplitude assuming that non-factorizable soft gluon exchanges can be described by the local gluon condensate. Within this approximation the 〈 α s GG〉-correction to the mixing amplitude can be expressed through the B-meson transition form factors at zero momentum transfer. The correction is negative independent of the particular values of the form factors. As a next step, we study these form factors making use of the relativistic dispersion approach based on the constituent quark picture. We obtain spectral representations for the form factors in terms of the B-meson soft wave function and the propagator of the color-octet b q ̄ system. The B-meson wave function has been determined previously from weak exclusive B decays, so the main uncertainty in our estimates comes from the unknown details of the propagator in the non-perturbative region. We obtain ΔB B d ( m b )=−0.06±0.035 and ΔB B s ( m b )=−0.05±0.03.

Exclusive and inclusive weak decays of the B-meson

A relativistic quark model is applied to the description of semileptonic and non-leptonic charmed decays of the B-meson. The exclusive semileptonic modes B → D lve and → D ∗ lve are described through the universal Isgur-Wise form factor, which is calculated in terms of a constituent quark model wave function for the B-meson. Different approximations for the latter, either based on a phenomenological ansatz or derived from analyses of the meson spectra, are adopted. In particular, two wave functions, constructed via the Hamiltonian light-front formalism using a relativized and a non-relativistic constituent quark model, are considered, obtaining a link between standard spectroscopic quark models and the B-meson decay physics. The inclusive semileptonic and non-leptonic branching ratios are calculated within a convolution approach, inspired by the partonic model and involving the same B-meson wave function used for the evaluation of the exclusive semileptonic modes. Our results for the major branching ratios are consistent with available experimental data and the sum of all the calculated branching ratios turns out to be close to unity. In particular, we found that (i) a remarkable fraction (∼ 35%) of semileptonic decay modes occur in non- D, non- D ∗ final states; (ii) non-perturbative effects enhance the inclusive b → c ud decay channels, with a sizable contribution provided by internal decays into heavy mesons and baryon-antibaryon pairs; the resulting reduction of the semileptonic branching ratio brings the theoretical prediction in agreement with the experimental value without increasing at the same time the charm counting.

Perturbative QCD estimation of the [formula omitted] branching ratio

Working in a perturbative QCD model approach, we obtain the essential form factor of the radiative transition B → V ∗γ and estimate the branching ratio BR(B → K ∗γ) . The results are determined by a parameter expressing the momentum distribution in the B-meson wave function. Our estimations are compared to other theoretical predictions as well as to experimental data.

Photon energy spectrum in B → XS + γ and comparison with data

A comparison of the inclusive photon energy spectrum in the radiative decay B → X S + γ, measured recently by the CLEO Collaboration, with the standard model is presented, using a B-meson wave function model and improving earlier perturbative QCD-based computations of the same. The dependence of the photon energy spectrum on the non-perturbative model parameters, p F , the b-quark Fermi momentum in the B hadron, and m q , the spectator quark mass, is explicitly shown, allowing a comparison of these parameters with the ones obtained from the analysis of the lepton energy spectrum in semileptonic B decays. Taking into account present uncertainties, we estimate BR( B → X s + γ) = (2.55 ± 1.28) × 10 −4 in the standard model, assuming |V ts| |V cb| = 1.0 . Comparing this with the CLEO measurement BR( B → X s + γ) = (2.32±0.67) × 10 −4 implies |V ts| |V cb| = 1.1 ± 0.43 , in agreement with the CKM unitarity.

Rare decays B → X d + γ in the standard model

We present an estimate of the inclusive decay rate and photon energy- and hadron mass-spectrum for the CKM-suppressed radiative rare decays B → X d + γ, based on perturbative QCD and a phenomenological model for the B-meson wave function (here X d denotes nonstrange hadrons). Present constraints on | V td| are used to predict BR(B → X d + γ) = (0.8−4) × 10 −5 for the top quark mass in the range 100 ⩽ m t ⩽ 200 GeV. From the inclusive invariant hadron-mass spectrum and using vector meson dominance in the region m(X d) ⩽ 1 GeV, we estimate the branching ratio for the exclusive rare decay mode B → ϱ + γ and the ratio Γ( B → ϱ + γ)/Γ( B → K ∗ + γ) . The importance of measuring these decays in determining the CKM matrix element | V td| is emphasized.

Lattice calculation of the B-meson decay constant

Using the static approximation for the b-quark, we discuss a lattice calculation of the pseudoscalar B-meson decay constant f B . We test the factorization of the residue of the ground state B-meson pole by considering the matrix of correlators between local and nonlocal Q q operators. Calculation of the B-meson wavefunction is discussed.

A profile of the final states in B→X s+ γ and an estimate of the branching ratio [formula omitted

We present an estimate of the inclusive photon energy- and hadron mass-spectrum in rare B decays B→X s+gg, based on perturbative QCD and a phenomenological model for the B-meson wave function (here X s denotes hadrons with total strangeness quantum number S=−1. The shapes of the spectra are sensitive to the details of the wave function and the top quark mass, m t, but the normalization is essentially determined by m t. We find BR(B→X s+γ)=(3−4)×10 −4 for 100⩽ m t⩽200 GeV. With the additional assumption that the K ∗ resonance saturates the recoil hadron mass spectrum in the interval ( M K+ M π )⩽ m X s ⩽1 GeV, we calculate the branching ratio BR(B→K ∗+γ and predict BR(B→K ∗+γ ) = (5 +3 −2) × 10 −5 , where the err reflect the uncertainties on the hadronic wave function and the top quark mass in the stated range.