B-meson Light-cone Distribution Amplitude Research Articles

Logarithmic moments of B-meson quasidistribution amplitude

It was demonstrated that the lattice simulation of B-meson light-cone distribution amplitude (LCDA) is feasible via the quasi-distribution amplitude (quasi-DA) in large momentum effective theory (LaMET). The structures of logarithmic moments (LMs) of B-meson quasi-DA are explored in this work. The one-loop results indicate mixing in the matching: the n-th LM would be not only factorized into the n-th LM of LCDA, but also other moments with different power, accompanied by short distance coefficients. These results supply the understanding of the matching in LaMET and may provide guidance to the lattice study of LMs or other parameters of B-meson LCDA.

Constraining inverse moment of B-meson distribution amplitude using Lattice QCD data

We constrain the inverse moment of the B-meson light-cone distribution amplitude (LCDA), λB in heavy quark effective theory, using form factor estimates from Lattice QCD collaboration. The estimation of the parameter λB has, until now, relied solely on QCD sum rule methods and deals with significant uncertainty. In this work, we express the form factors for the B→K channel, calculated within the light-cone sum rule (LCSR) approach, in terms of the B-meson LCDAs. By incorporating recent Lattice results from the HPQCD collaboration for the B→K form factors at zero momentum transfer (q2 = 0), we impose constraints on this parameter. Consequently, we achieve a twofold reduction in uncertainty compared to the QCD sum rule estimate, yielding λB=338±68 MeV, when the B-meson LCDAs are expressed in the Exponential model. Additionally, we compare the form factor predictions, using the constrained λB value, with the earlier analyses for other channels as well, such as B→π and B→D.

Non-factorisable effects in the decays {overline{B}}_s^0to {D}_s^{+}{pi}^{-} and {overline{B}}^0to {D}^{+}{K}^{-} from LCSR

In light of the current discrepancies between the recent predictions based on QCD factorisation (QCDF) and the experimental data for several non-leptonic colour-allowed two-body B-meson decays, we obtain new determinations of the non-factorisable soft-gluon contribution to the decays {overline{B}}_s^0to {D}_s^{+}{pi}^{-} and {overline{B}}^0to {D}^{+}{K}^{-} , using the framework of light-cone sum rule (LCSR), with a suitable three-point correlation function and B-meson light-cone distribution amplitudes. In particular, we discuss the problem associated with a double light-cone (LC) expansion of the correlator, and motivate future determinations of the three-particle B-meson matrix element with the gluon and the spectator quark aligned along different light-cone directions. Performing a LC-local operator product expansion of the correlation function, we find, for both modes considered, the non-factorisable part of the amplitude to be sizeable and positive, however, with very large systematic uncertainties. Furthermore, we also determine for the first time, using LCSR, the factorisable amplitudes at LO-QCD, and thus the corresponding branching fractions. Our predictions are in agreement with the experimental data and consistent with the results based on QCDF, although again within very large uncertainties. In this respect, we provide a rich outlook for future improvements and investigations.

Light-cone sum rules for S-wave B → Kπ form factors

We derive a set of light-cone sum rules relating the S-wave B → Kπ hadronic form factors to the B-meson light-cone distribution amplitudes (LCDAs), taking into account the complete set of LCDAs up to and including twist four. These results complement the sum rules for the P-wave B → Kπ form factors obtained earlier. We then use the new sum rules to estimate the S-wave contributions to B → Kπℓℓ decays as a function of the Kπ invariant mass. We pay particular attention to the fact that the S-wave Kπ spectrum cannot be modelled by a sum of Breit-Wigner resonances, and employ a more consistent dispersive coupled-channel approach. We compare our predictions for branching ratios and angular observables with LHCb measurements in two different kinematic regions, around K∗(892) and {K}_0^{ast }(1430) . We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the B → Kπ form factors over a large kinematic range.

Systematic parametrization of the leading B-meson light-cone distribution amplitude

We propose a parametrization of the leading B-meson light-cone distribution amplitude (LCDA) in heavy-quark effective theory (HQET). In position space, it uses a conformal transformation that yields a systematic Taylor expansion and an integral bound, which enables control of the truncation error. Our parametrization further produces compact analytical expressions for a variety of derived quantities. At a given reference scale, our momentum-space parametrization corresponds to an expansion in associated Laguerre polynomials, which turn into confluent hypergeometric functions 1F1 under renormalization-group evolution at one-loop accuracy. Our approach thus allows a straightforward and transparent implementation of a variety of phenomenological constraints, regardless of their origin. Moreover, we can include theoretical information on the Taylor coefficients by using the local operator product expansion. We showcase the versatility of the parametrization in a series of phenomenological pseudo-fits.

Factorization and Sudakov resummation in leptonic radiative B decay — a reappraisal

The B-meson light-cone distribution amplitude is an important non- perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of B mesons, such as B− → γℓ− overline{nu} . We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the B decay processes at leading order in ΛQCD/mb is most directly contained in the distribution amplitude in Laplace space evaluated near the origin, we propose a convenient parameterization of this object in terms of a small set of uncorrelated hadronic parameters. Using recent results on the three-loop anomalous dimension for heavy-light current operators, we derive an expression for the convolution integral appearing in the B− → γℓ− overline{nu} factorization formula that is explicitly scale independent, and we evaluate this formula at (approximate) NNLO.

B → Dℓνℓ form factors beyond leading power and extraction of |Vcb| and R(D)

We investigate the subleading-power corrections to the exclusive B → Dℓνℓ form factors at mathcal{O} ( {alpha}_s^0 ) in the light-cone sum rules (LCSR) framework by including the two- and three-particle higher-twist contributions from the B-meson light-cone distribution amplitudes up to the twist-six accuracy, by taking into account the subleading terms in expanding the hard-collinear charm-quark propagator, and by evaluating the hadronic matrix element of the subleading effective current . Employing further the available leading-power results for the semileptonic B → D form factors at the next-to- leading-logarithmic level and combining our improved LCSR predictions with the recent lattice determinations, we then carry out a comprehensive phenomenological analysis on the semi-leptonic B → Dℓνℓ decay. We extract left|{V}_{cb}right|=left({40.2}_{-0.5}^{+0.6}{left|{{}_{mathrm{th}}}_{-1.4}^{+1.4}right|}_{mathrm{exp}}right)times {10}^{-3}left(left|{V}_{cb}right|=left({40.9}_{-0.5}^{+0.6}{left|{{}_{mathrm{th}}}_{-1.0}^{+1.0}right|}_{mathrm{exp}}right)times {10}^{-3}right) using the BaBar (Belle) experimental data, and particularly obtain for the gold-plated ratio R(D) = 0.302 ± 0.003.

QCD factorization for the four-body leptonic B-meson decays

Employing the QCD factorization formalism we compute {B}_u^{-}to {gamma}^{ast}mathrm{ell}{overline{v}}_{mathrm{ell}} form factors with an off-shell photon state possessing the virtuality of order mb ΛQCD and {m}_b^2 , respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of mb/ΛQCD in the resulting factorization formulae is subsequently accomplished at next-to-leading logarithmic accuracy with the renormalization-group technique in momentum space. In particular, we derive the soft-collinear factorization formulae for a variety of the subleading power corrections to the exclusive radiative {B}_u^{-}to {gamma}^{ast }{W}^{ast } form factors with a hard-collinear photon at mathcal{O}left({alpha}_s^0right) . We further construct a complete set of the angular observables governing the full differential distribution of the four-body leptonic decays {B}_u^{-}to {mathrm{ell}}^{prime }{overline{mathrm{ell}}}^{prime}mathrm{ell}{overline{v}}_{mathrm{ell}} with ℓ, ℓ′ ∈ {e, μ} and then perform an exploratory phenomenological analysis for a number of decay observables accessible at the LHCb and Belle II experiments, with an emphasis on the systematic uncertainties arising from the shape parameters of the leading-twist B-meson light-cone distribution amplitude in heavy quark effective theory.

Bd,s \u2192 gamma mathrm{ell}overline{mathrm{ell}} decay with an energetic photon

We calculate the differential branching fraction, lepton forward-backward asymmetry and direct CP asymmetry for Bd,s → gamma mathrm{ell}overline{mathrm{ell}} decays with an energetic photon. We employ factorization methods, which result in rigorous next-to-leading order predic- tions in the strong coupling at leading power in the large-energy/heavy-quark expansion, together with estimates of power corrections and a resonance parameterization of sub- leading power form factors in the region of small lepton invariant mass q2. The Bd,s → gamma mathrm{ell}overline{mathrm{ell}} decay shares features of the charged-current decay Bu → gamma mathrm{ell}{overline{nu}}_{mathrm{ell}} ., and the FCNC decays B → {K}^{left(ast right)}mathrm{ell}overline{mathrm{ell}} . As in the former, the leading-power decay rates can be expressed in terms of the B-meson light-cone distribution amplitude and short-distance factors. However, similar to B → {K}^{left(ast right)}mathrm{ell}overline{mathrm{ell}} , four-quark and dipole operators contribute to the Bd,s → gamma mathrm{ell}overline{mathrm{ell}} decay in an essential way, limiting the calculation to q2 ≲ 6 GeV2 below the charmonium resonances in the lepton invariant mass spectrum. A detailed analysis of the main observables and theoretical uncertainties is presented.

Two-loop radiative jet function for exclusive B-meson and Higgs decays

The rare radiative B-meson decay {B}^{-}to gamma {mathrm{ell}}^{-}overline{v} and the radiative Higgs-boson decay h → γγ mediated by light-quark loops both receive large logarithmic corrections in QCD, which can be resummed using factorization theorems derived in soft-collinear effective theory. In these factorization theorems the same radiative jet function appears, which is a central object in the study of factorization beyond the leading order in scale ratios. We calculate this function at two-loop order both in momentum space and in a dual space, where its renormalization-group evolution takes on a simpler form. We also derive the two-loop anomalous dimension of the jet function and present the exact solution to its evolution equation at two-loop order. Another important outcome of our analysis is the explicit form of the two-loop anomalous dimension of the B-meson light-cone distribution amplitude in momentum space.

Light-cone sum rules for B \u2192 K \u03c0 form factors and applications to rare decays

We derive a set of light-cone sum rules relating the hadronic form factors relevant for B → Kπℓ+ℓ− decays to the B-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all B → K π form factors of (axial)vector and (pseudo)tensor b → s currents with a P -wave K π system. Our results reduce to the known light-cone sum rules for B → K∗ form factors in the limit of a single narrow-width resonance. We update the operator-product expansion for the underlying correlation function by including a more complete set of B-meson LCDAs with higher twists, and produce numerical results for all B → K∗ form factors in the narrow-width limit. We then use the new sum rules to estimate the effect of a non-vanishing K∗ width in B → K∗ transitions, and find that this effect is universal and increases the factorizable part of the rate of B → K∗X decays by a factor of 20%. This effect, by itself, goes in the direction of increasing the current tension in the differential B → K∗μμ branching fractions. We also discuss B → K π transitions outside the K∗ window, and explain how measurements of B → K πℓℓ observables above the K∗ region can be used to further constrain the B → K∗ form factors.

Two-loop evolution equation for the B -meson distribution amplitude

We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We argue that the evolution kernel to all orders in perturbation theory can be written as a logarithm of the generator of special conformal transformations times the cusp anomalous dimension, up to a scheme-dependent overall constant. Up to this constant term, the evolution kernel to a given order in perturbation theory can be obtained from the calculation of special conformal anomaly at one order less.

QCD calculations of B \u2192 \u03c0, K form factors with higher-twist corrections

We update QCD calculations of B → π, K form factors at large hadronic recoil by including the subleading-power corrections from the higher-twist B-meson light-cone distribution amplitudes (LCDAs) up to the twist-six accuracy and the strange-quark mass effects at leading-power in Λ/mb from the twist-two B-meson LCDA ϕB+(ω, μ). The higher-twist corrections from both the two-particle and three-particle B-meson LCDAs are computed from the light-cone QCD sum rules (LCSR) at tree level. In particular, we construct the local duality model for the twist-five and -six B-meson LCDAs, in agreement with the corresponding asymptotic behaviours at small quark and gluon momenta, employing the method of QCD sum rules in heavy quark effective theory at leading order in αs. The strange quark mass effects in semileptonic B → K form factors yield the leading-power contribution in the heavy quark expansion, consistent with the power-counting analysis in soft-collinear effective theory, and they are also computed from the LCSR approach due to the appearance of the rapidity singularities. We demonstrate explicitly that the SU(3)-flavour symmetry breaking effects between B → π and B → K form factors, free of the power suppression in Λ/mb, are suppressed by a factor of {alpha}_sleft(sqrt{m_bLambda}right) in perturbative expansion, and they also respect the large-recoil symmetry relations of the heavy-to-light form factors at least at one-loop accuracy. An exploratory analysis of the obtained sum rules for B → π, K form factors with two distinct models for the B-meson LCDAs indicates that the dominant higher-twist corrections are from the Wandzura-Wilczek part of the two-particle LCDA of twist five gB−(ω, μ) instead of the three-particle B-meson LCDAs. The resulting SU(3)-flavour symmetry violation effects of B → π, K form factors turn out to be insensitive to the non-perturbative models of B-meson LCDAs. We further explore the phenomenological aspects of the semileptonic B → πℓν decays and the rare exclusive processes B → Kνν, including the determination of the CKM matrix element |Vub|, the normalized differential q2 distributions and precision observables defined by the ratios of branching fractions for the above-mentioned two channels in the same intervals of q2.

Radiative leptonic decay B \u2192 \u03b3\u2113\u03bd\u2113 with subleading power corrections

We reconsider the QCD predictions for the radiative decay B → γℓνℓ with an energetic photon in the final state by taking into account the 1/Eγ, 1/mb power-suppressed hard-collinear and soft corrections from higher-twist B-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA ϕ+(ω) shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of ϕ+(ω), including the first inverse moment, 1/λB, from the expected high-statistics data of the BELLE II experiment.

Evolution equation for the higher twistB-meson distribution amplitude

We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA $\phi_-(\omega)$ so that the evolution equation for the latter is the same as for the leading-twist DA $\phi_+(\omega)$ up to a constant shift in the anomalous dimension. Thus, ``genuine'' three-particle states that belong to the continuous spectrum effectively decouple from $\phi_-(\omega)$ to the leading-order accuracy. In turn, the scale dependence of the full three-particle DA turns out to be nontrivial so that the contribution with the lowest anomalous dimension does not become leading at any scale. The results are illustrated on a simple model that can be used in studies of $1/m_b$ corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules.

The B-meson Light-Cone Distribution Amplitude in Dual Space

We describe a representation of the leading B-meson light-cone distribution amplitude in heavy-quark effective theory based on the eigenfunctions of its anomalous dimension kernel. In this representation (called the dual LCDA) different dual momenta no longer mix under renormalization. We discuss the perturbative and non-perturbative nature of different regions in this space.

B-meson light-cone distribution amplitude: Perturbative constraints and asymptotic behavior in dual space

Based on the dual representation in terms of the recently established eigenfunctions of the evolution kernel in heavy-quark effective theory, we investigate the description of the B-meson light-cone distribution amplitude (LCDA) beyond tree-level. In particular, in dual space, small and large momenta do not mix under renormalization, and therefore perturbative constraints from a short-distance expansion in the parton picture can be implemented independently from non-perturbative modelling of long-distance effects. It also allows to (locally) resum perturbative logarithms from large dual momenta at fixed values of the renormalization scale. We construct a generic procedure to combine perturbative and non-perturbative information on the B-meson LCDA and compare different model functions and the resulting logarithmic moments which are the relevant hadronic parameters in QCD factorization theorems for exclusive B-meson decays.

ANALYSIS OF THE $B \to K^*_2(1430), a_2(1320), f_2(1270)$ FORM-FACTORS WITH LIGHT-CONE QCD SUM RULES

In this paper, we study the [Formula: see text] form-factors with the light-cone QCD sum rules, where the B-meson light-cone distribution amplitudes are used. In calculations, we observe that the line-shapes of the B-meson light-cone distribution amplitude ϕ+(ω) have significant impacts on the values of the form-factors, and expect to obtain severe constraints on the parameters of the B-meson light-cone distribution amplitudes from the experimental data in the future.

B-MESON DISTRIBUTION AMPLITUDES

B-meson light-cone distribution amplitudes are discussed in these lectures in the framework of HQET. The evolution equation for the leading-twist distribution amplitude is derived in one-loop approximation. QCD sum rules for distribution amplitudes are discussed.

Model-independent properties of theB-meson distribution amplitude

The operator product expansion is used to obtain model-independent predictions for the first two moments of the renormalized B-meson light-cone distribution amplitude phi_+(omega,mu), defined with a cutoff omega<Lambda_UV. The leading hadronic power corrections are given in terms of the parameter Lambda(bar)=m_B-m_b. From the cutoff dependence of the zeroth moment an analytical expression for the asymptotic behavior of the distribution amplitude is derived, which exhibits a negative radiation tail for omega>>mu. By solving the evolution equation for the distribution amplitude, an integral representation for phi_+(omega,mu) is obtained in terms an initial function phi_+(omega,mu_0) defined at a lower renormalization scale. A realistic model of the B-meson light-cone distribution amplitude is proposed, which satisfies the moment relations and has the correct asymptotic behavior. This model provides an estimate for the first inverse moment and the associated parameter lambda_B.