B-meson Distribution Amplitude Research Articles

Precision calculations of Bd,s → π, K decay form factors in soft-collinear effective theory

We improve QCD calculations of the semileptonic Bd,s→ π, K decay form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework and by computing for the first time the non-vanishing spectator-quark mass correction dictating the SU(3)-flavour symmetry breaking effects between these fundamental quantities at the one-loop accuracy. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at mathcal{O}left({alpha}_s^0right) with the same methodology, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term in the SCETI representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory (HQET) matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes (LCDAs), and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive B-meson decay form factors under discussion, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist B-meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch (BCL) parametrization for the complete set of the semileptonic Bd,s→ π, K form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive B-meson decay form factors to both the achieved SCET sum rule predictions at small momentum transfer (q2) and the available lattice QCD results at large momentum transfer. Subsequently, we perform a comprehensive phenomenological analysis of the full angular observables, the lepton-flavour university ratios and the lepton polarization asymmetries for the flavour-changing charged- current Bto pi ell {overline{nu}}_{ell } and {B}_sto Kell {overline{nu}}_{ell } decays (with ℓ = μ, τ) together with the differential q2-distribution for the exclusive rare Bto K{nu}_{ell }{overline{nu}}_{ell } decays in the Standard Model.

B → D1(2420) and B → {mathrm{D}}_1^{prime } (2430) form factors from QCD light-cone sum rules

We perform the first calculation of form factors in the semileptonic decays B → D1(2420)ℓνℓ and B → {D}_1^{prime } (2430)ℓνℓ using QCD light-cone sum rules (LCSRs) with B-meson distribution amplitudes. In this calculation the c-quark mass is finite. Analytical expressions for two-particle contributions up to twist four are obtained. To disentangle the D1 and {D}_1^{prime } contributions in the LCSRs, we suggest a novel approach that introduces a combination of two interpolating currents for these charmed mesons. To fix all the parameters in the LCSRs, we use the two-point QCD sum rules for the decay constants of D1 and {D}_1^{prime } mesons augmented by a single experimental input, that is the B → D1(2420)ℓνℓ decay width. We provide numerical results for all B → D1 and B → {D}_1^{prime } form factors. As a byproduct, we also obtain the D1- and {D}_1^{prime } -meson decay constants and predict the lepton-flavour universality ratios R(D1) and R( {D}_1^{prime } ).

Charged and neutral {overline{B}}_{u,d,s} \u2192 \u03b3 form factors from light cone sum rules at NLO

We present the first analytic mathcal{O}left({alpha}_sright) -computation at twist-1,2 of the {overline{B}}_{u,d,s} → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay {overline{B}}_uto gamma {mathrm{ell}}^{-}overline{v} , contribute to the flavour changing neutral currents {overline{B}}_{d,s}to gamma {mathrm{ell}}^{+}{mathrm{ell}}^{-} and serve as inputs to more complicated processes. We provide a fit in terms of a z-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the gBB*γ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms in the supplementary material. We give binned predictions for the {overline{B}}_uto gamma {mathrm{ell}}^{-}overline{v} branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B-meson distribution amplitude parameter λB = 360(110) MeV. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, χq, compatible with the twist-expansion. The values χq = 3.21(15) GeV−2 and χs = 3.79(17) GeV−2 are obtained.

B \u2192P and B \u2192V form factors from B-meson light-cone sum rules beyond leading twist

We provide results for the full set of form factors describing semileptonic B-meson transitions to pseudoscalar mesons π, K, overline{D} and vector mesons ρ, K∗, {overline{D}}^{ast } . Our results are obtained within the framework of QCD Light-Cone Sum Rules with B-meson distribution amplitudes. We recalculate and confirm the results for the leading-twist two-particle contributions in the literature. Furthermore, we calculate and provide new expressions for the two-particle contributions up to twist four. Following new developments for the three-particle distribution amplitudes, we calculate and provide new results for the complete set of three-particle contributions up to twist four. The form factors are computed numerically at several phase space points using up-to-date input parameters, including correlations across phase space points and form factors. We use a model ansatz for all contributing B-meson distribution amplitudes that is self-consistent up to twist-four accuracy. We find that the higher-twist two-particle contributions have a substantial impact on the results, and dominate over the three-particle contributions. Our numerical results, including correlations, are provided as machine-readable files in the supplementary material. We discuss the qualitative phenomenological impact of our results on the present b anomalies.

Subleading-power corrections to the radiative leptonic B \u2192 \u03b3\u2113\u03bd decay in QCD

Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic B → γℓν decay from the twist-two hadronic photon contribution at next-to-leading order in QCD; and further evaluate the higher-twist “resolved photon” corrections at leading order in αs, up to twist-four accuracy. QCD factorization for the vacuum-to-photon correlation function with an interpolating current for the B-meson is established explicitly at leading power in Λ/mb employing the evanescent operator approach. Resummation of the parametrically large logarithms of mb2/Λ2 entering the hard function of the leading-twist factorization formula is achieved by solving the QCD evolution equation for the light-ray tensor operator at two loops. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two B → γ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30% correction to the leading-power “direct photon” effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of mathcal{O}left(3sim 5%right) with the light-cone sum rule approach. We further predict the partial branching fractions of B → γℓν with a photon-energy cut Eγ ≥ Ecut, which are of interest for determining the inverse moment of the leading-twist B-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.

Perturbative corrections to B \u2192 D form factors in QCD

We compute perturbative QCD corrections to B → D form factors at leading power in Λ/mb, at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to-B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme {m}_csim mathcal{O}left(sqrt{Lambda {m}_b}right) . The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale mc, compared to the counterparts entering the factorization formula of the vacuum-to-B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors fBD+,0(q2) are explored by investigating the (differential) branching fractions and the R(D) ratio of B → Dℓν and by determining the CKM matrix element |Vcb| from the total decay rate of B → Dμνμ.

B \u2192\u03c0\u03c0 form factors from light-cone sum rules with B-meson distribution amplitudes

We study B → ππ form factors using QCD light-cone sum rules with B-meson distribution amplitudes. These form factors describe the semileptonic decay Bto pi pi ell {overline{nu}}_{ell } , and constitute an essential input in B → ππℓ+ℓ− and B → πππ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the P -wave {overline{B}}^0to {pi}^{+}{pi}^0 form factors with the timelike pion vector form factor are related to universal B-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for B → ρ form factors in the limit of ρ-dominance and zero width, thus providing a systematics for so far unaccounted corrections to B → ρ transitions. Using data for the pion vector form factor, we estimate finite-width effects and the contribution of excited ρ-resonances to the B → ππ form factors. We find that these contributions amount up to ∼ 20% in the small dipion mass region where they can be effectively regarded as a nonresonant (P -wave) background to the B → ρ transition.

Subleading power corrections in radiative leptonic B decay

I discuss the two-particle subleading power corrections in radiative leptonic B→γℓν decay at next-to-leading order in αs with the dispersion approach. Employing the method of regions, factorization of the B→γ⁎ form factors is demonstrated explicitly, at one loop, for a space-like hard-collinear photon. The two-particle soft (end-point) contribution is shown to be suppressed by one power of Λ/mb, in the heavy quark limit, compared with the leading power contribution computed from QCD factorization. I further report the recent calculation on the three-particle subleading power contribution to the on-shell B→γ form factors at tree level and demonstrate that the “soft” and the “hard” three-particle corrections are of the same power, in contrast to the two-particle counterparts, as already speculated from the rapidity divergence in the corresponding factorization formulae. Phenomenological implications of the subleading power contributions to the B→γℓν amplitude are also addressed in detail, focusing on the determination of the inverse moment of the leading-twist B-meson distribution amplitude.

QCD corrections to [formula omitted] form factors from light-cone sum rules

We compute perturbative corrections to B→π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+(q2) and fBπ0(q2) at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B→π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub|=(3.05−0.38+0.54|th.±0.09|exp.)×10−3 with the inverse moment of the B-meson distribution amplitude ϕB+(ω) determined by reproducing fBπ+(q2=0) obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B→πℓνℓ (ℓ=μ,τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→π form factors fBπ+(q2) and fBπ0(q2) in brief.

Conformal symmetry of the Lange–Neubert evolution equation

The Lange–Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD. It has numerous applications to the studies of B-meson decays. We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy–light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form.

Soft contribution to [formula omitted] and the B-meson distribution amplitude

The B→γℓνℓ decay at large energies of the photon receives a numerically important soft-overlap contribution which is formally of the next-to-leading order in the expansion in the inverse photon energy. We point out that this contribution can be calculated within the framework of heavy-quark expansion and soft-collinear effective theory, making use of dispersion relations and quark–hadron duality. The soft-overlap contribution is obtained in a full analogy with the similar contribution to the γ⁎γ→π transition form factor. This result strengthens the case for using the B→γℓνℓ decay to constrain the B-meson distribution amplitude and determine its most important parameter, the inverse moment λB.

B→D (*) form factors from QCD light-cone sum rules

We derive new QCD sum rules for B→D and B→D * form factors. The underlying correlation functions are expanded near the light-cone in terms of B-meson distribution amplitudes defined in HQET, whereas the c-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B→D (*) form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur–Wise function. We compare our predictions with the form factors extracted from experimental B→(*) l ν l decay rates fitted to dispersive parameterizations.

Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators

When the bilocal heavy-quark effective theory (HQET) operator for the B-meson distribution amplitude has a light-like distance t between the quark and antiquark fields, the scale ∼1/t separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat these notorious UV and IR behaviors simultaneously using the operator product expansion, with the local operators of dimension d⩽5 and radiative corrections at order αs for the corresponding Wilson coefficients. The result is derived in the coordinate space, which manifests the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This result yields the B-meson distribution amplitude for t less than ∼1 GeV−1, in terms of Λ¯=mB−mb and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive B decays, λB, is also discussed.

SCET sum rules forB→PandB→Vtransition form factors

We investigate sum rules for heavy-to-light transition form factors at large recoil derived from correlation functions with interpolating currents for light pseudoscalar or vector fields in soft-collinear effective theory (SCET). We consider both, factorizable and nonfactorizable contributions at leading power in the {Lambda}/m{sub b} expansion and to first order in the strong coupling constant {alpha}{sub s}, neglecting contributions from 3-particle distribution amplitudes in the B-meson. We pay particular attention to various sources of parametric and systematic uncertainties. We also discuss certain form factor ratios where part of the hadronic uncertainties related to the B-meson distribution amplitude and to logarithmically enhanced {alpha}{sub s} corrections cancel.

Form factors from light-cone sum rules withB-meson distribution amplitudes

New sum rules for B{yields}{pi},K and B{yields}{rho},K* form factors are derived from the correlation functions expanded near the light cone in terms of B-meson distribution amplitudes. The contributions of quark-antiquark and quark-antiquark-gluon components in the B meson are taken into account. Models for the B-meson three-particle distribution amplitudes are suggested, based on QCD sum rules in heavy-quark effective theory. Employing the new light-cone sum rules, we calculate the form factors at small momentum transfers, including SU(3)-violation effects. The results agree with the predictions of the conventional light-cone sum rules.

B-meson distribution amplitude from the [formula omitted] form factor

Employing the light-cone sum rule approach in QCD, we relate the B-meson distribution amplitude to the B→π form factor at zero momentum transfer. In leading order, the sum rule is converted into a simple expression for the inverse moment λB of the distribution amplitude ϕ+B. Using as an input the B→π form factor calculated from the light-cone sum rule in terms of pion distribution amplitudes, we obtain an estimate: λB=460±160 MeV. We investigate how this result is modified by the B-meson three-particle distribution amplitudes.

B-meson distribution amplitude in QCD

The B-meson distribution amplitude is calculated using QCD sum rules. In particular we obtain an estimate for the integral relevant to exclusive B decays ${\ensuremath{\lambda}}_{B}=460\ifmmode\pm\else\textpm\fi{}110\mathrm{MeV}$ at the scale of 1 GeV. A simple QCD-motivated parametrization of the distribution amplitude is suggested.