Light-cone Distribution Amplitudes Research Articles

Improved analysis of the rare decay processes of Λ b

It is noted that in the new Particle Data Group (PDG) version the rare decays of the baryon have been revised with more accuracy. The new results show that most of the existing theoretical results on the process are larger than those of experiments. With the improved higher-order light-cone distribution amplitudes of the Λ baryon, we reanalyze the process in the framework of light-cone quantum chromodynamics sum rules and the branching ratio is estimated to be , which is consistent with the new experimental result. Furthermore, another process is also analyzed in the same frame. The final branching ratio is calculated to be , which is in good accordance with the data from the PDG and other theoretical predictions.

Global analysis of hadronic two-body B decays in the perturbative QCD approach

Based on the flavor structure of four-quark effective operators, we develop an automatic computation program to calculate hadronic two-body $B$ meson decay amplitudes, and apply it to their global analysis in the perturbative QCD (PQCD) approach. Fitting the PQCD factorization formulas for $B\to PP,VP$ decays at leading order in the strong coupling $\alpha_s$ to measured branching ratios and direct CP asymmetries, we determine the Gegenbauer moments in light meson light-cone distribution amplitudes (LCDAs). It is found that most of the fitted Gegenbauer moments of the twist-2 and twist-3 LCDAs for the pseudoscalar meson $P$ ($P=\pi$, $K$) and vector meson $V$ ($V=\rho$, $K^*$) agree with those derived in QCD sum rules. The shape parameter for the $B_s$ meson distribution amplitude and the weak phase $\phi_3(\gamma)=(75.1\pm2.9)^\circ$ consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers in the PQCD approach, and to the global determination of LCDAs for other hadrons.

QCD sum rules for parameters of the B -meson distribution amplitudes

We obtain new estimates for the parameters $\lambda_{E}^2$, $\lambda_H^2$ and their ratio $\mathcal{R} = \lambda_{E}^2/\lambda_H^2$, which appear in the second moments of the $B$-meson light-cone distribution amplitudes defined in the heavy-quark effective field theory. The computation is based on two-point QCD sum rules for the diagonal correlation function and includes all contributions up to mass dimension seven in the operator-product expansion. For the ratio we get $\mathcal{R} = (0.1 \pm 0.1)$ with $\lambda_H^2 = (0.15 \pm 0.05) \, \text{GeV}^2$ and $\lambda_E^2 = (0.01 \pm 0.01) \, \text{GeV}^2$.

QCD factorization of the four-lepton decay B^-rightarrow ell bar{nu }_ell ell ^{(prime )} bar{ell }^{(prime )}

Motivated by the first search for the rare charged-current B decay to four leptons, ell bar{nu }_ell ell ^{(prime )} bar{ell }^{(prime )}, we calculate the decay amplitude with factorization methods. We obtain the Brightarrow gamma ^* form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in Lambda _mathrm{QCD}/m_b to next-to-leading order in alpha _s, and at mathcal {O}(alpha _s^0) at next-to-leading power. Our calculations predict branching fractions of a few times 10^{-8} in the ell ^{(prime )} bar{ell }^{(prime )} mass-squared bin up to q^2=1~GeV^2 with n_+q>3~GeV. The branching fraction rapidly drops with increasing q^2. An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment lambda _B of the leading-twist B meson light-cone distribution amplitude. We find that in the small-q^2 bin, the sensitivity to lambda _B is almost comparable to B^- rightarrow mathrm {ell }^- bar{nu }_{mathrm {ell }}gamma when lambda _B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger q^2.

Ds -meson leading-twist distribution amplitude within the QCD sum rules and its application to the Bs→Ds transition form factor

We make a detailed study of the ${D}_{s}$-meson leading-twist light-cone distribution amplitude ${\ensuremath{\phi}}_{2;{D}_{s}}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;{D}_{s}}$ are calculated up to dimension-six condensates. At the scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$, we obtain $⟨{\ensuremath{\xi}}^{1}{⟩}_{2;{D}_{s}}=\ensuremath{-}{0.261}_{\ensuremath{-}0.020}^{+0.020}$, $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;{D}_{s}}={0.184}_{\ensuremath{-}0.012}^{+0.012}$, $⟨{\ensuremath{\xi}}^{3}{⟩}_{2;{D}_{s}}={\ensuremath{-}0.111}_{\ensuremath{-}0.012}^{+0.007}$, and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;{D}_{s}}={0.075}_{\ensuremath{-}0.005}^{+0.005}$. Using those moments, the ${\ensuremath{\phi}}_{2;{D}_{s}}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving ${\ensuremath{\phi}}_{2;{D}_{s}}$ dominate the LCSR. It is noted that the extrapolated ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ agrees with the lattice QCD prediction. After extrapolating the transition form factor to the physically allowable ${q}^{2}$ region, we calculate the branching ratio and the CKM matrix element, which give $\mathcal{B}({\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}})=({2.03}_{\ensuremath{-}0.49}^{+0.35})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and $|{V}_{cb}|=({40.00}_{\ensuremath{-}4.08}^{+4.93})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Chiral dynamics and S-wave contributions in {bar{B}}^0/D^0 rightarrow pi ^{pm }eta l^{mp } nu decays

In this work, we analyze the semi-leptonic decays bar{B}^0/D^0 rightarrow (a_0(980)^{pm }rightarrow pi ^{pm }eta ) l^{mp } nu within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the a_0(980), we use a scalar form factor to describe the final-state interaction between the pi eta mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the D^0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the {bar{B}}^0 decay can be tested in future experiments.

B -meson Ioffe-time distribution amplitude at short distances

We propose the approach for a lattice investigation of light cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$ meson, using the formalism of parton pseudodistributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$ meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice.

Revisiting the production of J/ψ+ηc via the e+e− annihilation within the QCD light-cone sum rules

We make a detailed study on the typical production channel of double charmoniums, $e^+e^-\to J/\psi+\eta_c$, at the center-of-mass collision energy $\sqrt{s}=10.58$ GeV. The key component of the process is the form factor $F_{\rm VP}(q^2)$, which has been calculated within the QCD light-cone sum rules (LCSR). To improve the accuracy of the derived LCSR, we keep the $J/\psi$ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for $e^+e^-\to J/\psi+\eta_c$ at three typical factorization scales are $\sigma|_{\mu_s} = 22.53^{+3.46}_{-3.49}~{\rm fb}$, $\sigma|_{\mu_k} = 21.98^{+3.35}_{-3.38}~{\rm fb}$ and $\sigma|_{\mu_0} = 21.74^{+3.29}_{-3.33}~{\rm fb}$, respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors.

The D\u2217D\u03c0 and B\u2217B\u03c0 couplings from light-cone sum rules

We revisit the calculation of the strong couplings D∗Dπ and B∗Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at mathcal{O}left({alpha}_sright) and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict {g}_{D^{ast } Dpi}={14.1}_{-1.2}^{+1.3} and {g}_{B^{ast } Bpi}={30.0}_{-2.4}^{+2.6} when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

B_{(s)} to light tensor meson form factors via LCSR in HQEFT with applications to semileptonic decays

In the present work, the form factors of B_{(s)} to light P-wave tensor mesons (a_2(1320), K^*_2(1430), f_2(1270), f^prime _2(1525)) are calculated via the light cone sum rules (LCSR) in the framework of heavy quark effective field theory (HQEFT). Firstly, the expressions of form factors in terms of the light cone distribution amplitudes (DAs) of tensor mesons are derived via the LCSR at the leading order of heavy quark expansion. It is found that the penguin type form factors can be obtained directly from the corresponding semileptonic ones, which is similar to the case of S-wave mesons. Considering the light tensor meson DAs to twist-3, we give the numerical results of form factors systematically. As applications, we investigate the branching ratios, longitudinal polarization fractions and forward-backward asymmetries of relevant semileptonic decays induced by charged current and flavor changing neutral current (FCNC) separately. Our results may be tested by more precise experiments in the future.

Precision calculations of the double radiative bottom-meson decays in soft-collinear effective theory

Employing the systematic framework of soft-collinear effective theory (SCET) we perform an improved calculation of the leading-power contributions to the double radiative Bd,s-meson decay amplitudes in the heavy quark expansion by including the perturbative resummation of enhanced logarithms of mb/ΛQCD at the next-to-leading-logarithmic accuracy. We then construct the QCD factorization formulae for the subleading power contributions arising from the energetic photon radiation off the constituent light-flavour quark of the bottom meson at tree level. Furthermore, we explore the factorization properties of the subleading power correction from the effective SCET current at mathcal{O}left({alpha}_s^0right) by virtue of the operator identities due to the classical equations of motion. The higher-twist contributions to the Bd,s→ γγ helicity form factors from the two-particle and three-particle bottom-meson distribution amplitudes are evaluated with the perturbative factorization technique, up to the twist-six accuracy. In addition, the subleading power weak-annihilation contributions from both the current-current and QCD penguin operators are taken into account at the one-loop accuracy. We proceed to apply the operator-production-expansion-controlled dispersion relation for estimating the power-suppressed soft contributions to the double radiative Bd,s-meson decay form factors, which cannot be factorized into the light-cone distribution amplitudes of the heavy-meson and the resolved photon as well as the hard-scattering kernel calculable in perturbation theory canonically. Phenomenological explorations of the radiative Bd,s→ γγ decay observables in the presence of the neutral-meson mixing, including the CP-averaged branching fractions, the polarization fractions and the time-dependent CP asymmetries, are carried out subsequently with an emphasis on the numerical impacts of the newly computed ingredients together with the theory uncertainties from the shape parameters of the HQET bottom-meson distribution amplitudes.

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.

Light-Cone Distribution Amplitudes of Doubly-Heavy Baryons

Doubly-heavy baryons, whose dynamics is determined by a light quark situated in a color field of a static pair of heavy quarks, are investigated. Non-local interpolation currents are introduced and corresponding matrix elements between the baryon and vacuum state are expressed in terms of light-cone distribution amplitudes. Model functions for baryon distribution amplitudes are suggested and their scale dependence is studied in the perturbative QCD framework. The similarity between the heavy meson and doubly-heavy baryon distribution amplitudes is discussed.

Addendum to: Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

We update our lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes [1]

QED factorization of non-leptonic B decays

We show that the QCD factorization approach for B-meson decays to charmless hadronic two-body final states can be extended to include electromagnetic corrections. The presence of electrically charged final-state particles complicates the framework. Nevertheless, the factorization formula takes the same form as in QCD alone, with appropriate generalizations of the definitions of light-cone distribution amplitudes and form factors to include QED effects. More precisely, we factorize QED effects above the strong interaction scale ΛQCD for the non-radiative matrix elements leftlangle {M}_1{M}_2left|{Q}_iright|overline{B}rightrangle of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables overline{B}to {M}_1{M}_2left(gamma right) with photons of maximal energy ∆E ≪ ΛQCD is then obtained by multiplying with the soft-photon exponentiation factors. We provide first estimates for the various electromagnetic corrections, and in particular quantify their impact on the πK ratios and sum rules that are often used as diagnostics of New Physics.

Evolution of the B meson light-cone distribution amplitude in Laplace space

The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$ in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in terms of a small set of uncorrelated hadronic parameters.

Pion light-cone distribution amplitude from the pion electromagnetic form factor

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_\pi(Q^2)$ and the integrated modulus of the timelike form factor. For $F_\pi(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BaBar collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single $a_2\neq 0$ is disfavoured by the fit. Considering the models with $a_{n>2}\neq 0$, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals $a_2 (1 \mbox{GeV}) = (0.22 - 0.33) $, $a_4 (1 \mbox{GeV}) = (0.12 - 0.25) $. The higher moments starting from $a_{8}$ are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab $F_\pi$ collaboration.

Inverse moment of the Bs-meson distribution amplitude from QCD sum rule

We derive a QCD sum rule for the inverse moment of the Bs-meson light-cone distribution amplitude in HQET. Within this method, the SU(3)f l symmetry violation is traced to the strange quark mass and to the difference between strange and nonstrange quark condensate densities. We predict the ratio of inverse moments λBs/λB = 1.19 ± 0.14 which can be used in various applications of these distribution amplitudes to the analyses of Bs-meson decays, provided an accurate value of λB is available from other sources, such as the B → ℓνℓγ decay.

Factorization Theorem Connecting the Light-Cone Distribution Amplitudes of Heavy-Flavor Mesons in QCD and Heavy-Quark Effective Theory.

The light-cone distribution amplitude (LCDA) of a heavy-light meson defined in heavy quark effective theory (HQET) is a fundamental nonperturbative input to account for innumerable B meson exclusive decay and production processes. On the other hand, the conventional heavy-flavored meson LCDA defined in QCD also ubiquitously enters the factorization formula for hard exclusive B production processes. Inspired by the observation that these two LCDAs exhibit the identical infrared behaviors, yet differ in the ultraviolet scale of order m_{b} or greater, we propose a novel factorization theorem for the heavy-light mesons, that the LCDA defined in QCD can be further expressed as a convolution between the LCDA in HQET and a perturbatively calculable coefficient function thanks to asymptotic freedom. This refactorization program can be invoked to fully disentangle the effects from three disparate scales Q, m_{b}, and Λ_{QCD} for a hard exclusive B production process, particularly to facilitate the resummation of logarithms of type lnQ/m_{b} and lnm_{b}/Λ_{QCD} in a systematic fashion.

B -meson light-cone distribution amplitude from Euclidean quantities

A new method for the model-independent determination of the light-cone distribution amplitude (LCDA) of the $B$-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory (LaMET) and the numerical simulation technique on the Euclidean lattice. We demonstrate the autonomous scale dependence of the non-local quasi-HQET operator with the aid of the auxiliary field approach, and further determine the perturbative matching coefficient entering the hard-collinear factorization formula for the $B$-meson quasi-distribution amplitude at the one-loop accuracy. These results will be crucial to explore the partonic structure of heavy-quark hadrons in the static limit and to improve the theory description of exclusive $B$-meson decay amplitudes based upon perturbative QCD factorization theorems.