Leading-twist Distribution Amplitude Research Articles

ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay* *Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12147102), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)

Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the ρ-meson leading-twist longitudinal DA in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of . However, the ξ-moments of are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero ξ-moments at the typical scale are given, e.g., at , , , , , and . By fitting these values with the least squares method, the DSE model for is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, i.e., , , and , and the ratio , . After extrapolating with a rapidly converging series based on -expansion, we present the -independent decay width for the semileptonic decays . Finally, the branching fractions are , , , and .

Properties of the ηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _q$$\\end{document} leading-twist distribution amplitude and its effects to the B/D+→η(′)ℓ+νℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B/D^+ \\rightarrow \\eta ^{(\\prime )}\\ell ^+ \ u _\\ell $$\\end{document} decays

The η(′)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta ^{(\\prime )}$$\\end{document}-mesons in the quark-flavor basis are mixtures of two mesonic states |ηq⟩=|u¯u+d¯d⟩/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\eta _{q}\\rangle =|{\\bar{u}} u+{\\bar{d}} d\\rangle /\\sqrt{2}$$\\end{document} and |ηs⟩=|s¯s⟩.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\eta _{s}\\rangle =|{\\bar{s}} s\\rangle .$$\\end{document} In previous work, we have made a detailed study on the ηs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _{s}$$\\end{document} leading-twist distribution amplitude by using the Ds+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^+_s$$\\end{document} meson semileptonic decays. As a sequential work, in the present paper, we fix the ηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _q$$\\end{document} leading-twist distribution amplitude by using the light-cone harmonic oscillator model for its wave function and by using the QCD sum rules within the QCD background field to calculate its moments. The input parameters of ηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _q$$\\end{document} leading-twist distribution amplitude ϕ2;ηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi _{2;\\eta _q}$$\\end{document} at the initial scale μ0∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _0\\sim 1$$\\end{document} GeV are fixed by using those moments. The QCD sum rules for the 0th\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0_{\ extrm{th}}$$\\end{document}-order moment can also be used to fix the magnitude of ηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _q$$\\end{document} decay constant, giving fηq=0.141±0.005\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\\eta _q}=0.141\\pm 0.005$$\\end{document} GeV. As an application of ϕ2;ηq,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi _{2;\\eta _q},$$\\end{document} we calculate the transition form factors B(D)+→η(′)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B(D)^+ \\rightarrow \\eta ^{(\\prime )}$$\\end{document} by using the QCD light-cone sum rules up to twist-4 accuracy and by including the next-to-leading order QCD corrections to the leading-twist part, and then fix the related CKM matrix element and the decay width for the semi-leptonic decays B(D)+→η(′)ℓ+νℓ.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B(D)^+ \\rightarrow \\eta ^{(\\prime )}\\ell ^+ \ u _\\ell .$$\\end{document}

K_0^*(1430) twist-2 distribution amplitude and B_s,D_s rightarrow K_0^*(1430) transition form factors

Based on the scenario that the K_0^*(1430) is viewed as the ground state of sbar{q} or qbar{s}, we study the K_0^*(1430) leading-twist distribution amplitude (DA) phi _{2;K_0^*}(x,mu ) with the QCD sum rules in the framework of background field theory. A more reasonable sum rule formula for xi -moments langle xi ^nrangle _{2;K_0^*} is suggested, which eliminates the influence brought by the fact that the sum rule of langle xi ^0_prangle _{3;K_0^*} cannot be normalized in whole Borel region. More accurate values of the first ten xi -moments, langle xi ^nrangle _{2;K_0^*} (n = 1,2,ldots ,10), are evaluated. A new light-cone harmonic oscillator (LCHO) model for K_0^*(1430) leading-twist DA is established for the first times. By fitting the resulted values of langle xi ^nrangle _{2;K_0^*} (n = 1,2,ldots ,10) via the least squares method, the behavior of K_0^*(1430) leading-twist DA described with LCHO model is determined. Further, by adopting the light-cone QCD sum rules, we calculate the B_s,D_s rightarrow K_0^*(1430) transition form factors and branching fractions of the semileptonic decays B_s,D_s rightarrow K_0^*(1430) ell nu _ell . The corresponding numerical results can be used to extract the Cabibbo-Kobayashi-Maskawa matrix elements by combining the relative experimental data in the future.

Renormalon-Chain Contributions to Two-Point Correlators of Nonlocal Quark Currents

We calculate, within massless QCD, two-point correlator of nonlocal (composite) vector quark currents with arbitrary-length chains of the simplest fermion loops being inserted into gluon lines. Within the large $${{n}_{f}}$$ (or large $${{\beta }_{0}}$$ ) approximation, the correlator defines a perturbative contribution to the leading-twist distribution amplitudes for light mesons. Our results are consistent with a number of special cases in the literature. We consider functionals of the correlator, which are important for the phenomenology, and their properties as functional series.

Revisiting D-meson twist-2, 3 distribution amplitudes* *Supported in part by the National Natural Science Foundation of China (12265009, 12265010), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)

Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of of the semileptonic decay , researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) , , and are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study . Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs , , and . New sum rule formulae for the -moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ -moments via the least squares method.

Constraints of ξ-moments computed using QCD sum rules on piondistribution amplitude models* *Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12175025, 12147102); the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024); the Project of Guizhou Provincial Department of Education (KY[2021]030); and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)

To date, the behavior of the pionic leading-twist distribution amplitude (DA) which is a universal physical quantity and is introduced into high-energy processes involving pions based on the factorization theorem is not completely consistent. The form of is usually described by phenomenological models and constrained by the experimental data on exclusive processes containing pions or the moments computed using QCD sum rules and the lattice QCD theory. Evidently, an appropriate model is extremely important to determine the exact behavior of . In this paper, by adopting the least squares method to fit the ξ-moments calculated using QCD sum rules based on the background field theory, we perform an analysis on several commonly used models of the pionic leading-twist DA in the literature; these include the truncation form of the Gegenbauer polynomial series, the light-cone harmonic oscillator model, the form extracted from the Dyson-Schwinger equations, the model from the light-front holographic AdS/QCD, and a simple power-law parametrization form.

Ratio R(Ds) for Bs→Dsℓνℓ by using the QCD light-cone sum rules within the framework of heavy quark effective field theory

In the paper, we study the $B_s\to D_s$ transition form factors by using the light-cone sum rules within the framework of heavy quark effective field theory. We adopt a chiral current correlation function to do the calculation, the resultant transition form factors $f_+^{B_s\to D_s}(q^2)$ and $f_0^{B_s\to D_s}(q^2)$ are dominated by the contribution of $D_s$-meson leading-twist distribution amplitude, while the contributions from less certain $D_s$-meson twist-3 distribution amplitudes are greatly suppressed. At the largest recoil point, we obtain $f_{+,0}^{B_s \to D_s}(0)=0.533^{+0.112}_{-0.094}$. By further extrapolating the transition form factors into all the physically allowable $q^2$ region with the help of the $z$-series parametrization approach, we calculate the branching fractions $\mathcal{B}(B_s \to D_s \ell^\prime \nu_{\ell^\prime})$ with $(\ell^\prime= e,\mu)$ and $\mathcal{B}(B_s \to D_s \tau \nu_\tau)$, which gives $\mathcal{R}(D_s)=0.334\pm 0.017$.

Eta ^{(prime )}-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay D_s^+ rightarrow eta ^{(prime )}ell ^+ nu _ell

In this paper, we make a detailed discussion on the eta and eta ^prime -meson leading-twist light-cone distribution amplitude phi _{2;eta ^{(prime )}}(u,mu ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments langle xi ^n_{2;eta ^{(prime )}}rangle |_{mu _0} with n = (2, 4, 6) can be determined, where the initial scale mu _0 is set as the usual choice of 1 GeV. Numerically, we obtain langle xi _{2;eta }^2rangle |_{mu _0} =0.231_{-0.013}^{+0.010}, langle xi _{2;eta }^4 rangle |_{mu _0} =0.109_{ - 0.007}^{ + 0.007}, and langle xi _{2;eta }^6 rangle |_{mu _0} =0.066_{-0.006}^{+0.006} for eta -meson, langle xi _{2;eta '}^2rangle |_{mu _0} =0.211_{-0.017}^{+0.015}, langle xi _{2;eta '}^4 rangle |_{mu _0} =0.093_{ - 0.009}^{ + 0.009}, and langle xi _{2;eta '}^6 rangle |_{mu _0} =0.054_{-0.008}^{+0.008} for eta '-meson. Next, we calculate the D_srightarrow eta ^{(prime )} transition form factors (TFFs) f^{eta ^{(prime )}}_{+}(q^2) within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are f^{eta }_+(0) = 0.476_{-0.036}^{+0.040} and f^{eta '}_+(0) = 0.544_{-0.042}^{+0.046}. After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. D_s^+rightarrow eta ^{(prime )}ell ^+ nu _ell , i.e. {{mathcal {B}}}(D_s^+ rightarrow eta ^{(prime )} e^+nu _e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})times 10^{-2} and {{mathcal {B}}}(D_s^+ rightarrow eta ^{(prime )} mu ^+nu _mu )=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})times 10^{-2} for ell = (e, mu ) channels respectively. And in addition to that, the mixing angle for eta -eta ' with varphi and ratio for the different decay channels {{mathcal {R}}}_{eta '/eta }^ell are given, which show good agreement with the recent BESIII measurements.

Light-cone distribution amplitudes of the nucleon and \u2206 baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

In this paper, we study the pion leading-twist distribution amplitude (DA) ${\ensuremath{\phi}}_{2;\ensuremath{\pi}}(x,\ensuremath{\mu})$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function ${\ensuremath{\varphi}}_{2;\ensuremath{\pi}}(x)$. In order to constrain the model parameters, we calculate its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ in the framework of the QCD background field theory sum rule up to tenth order. Considering the fact that the sum rule of the zeroth moment $⟨{\ensuremath{\xi}}^{0}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ cannot be normalized, we suggest a more reasonable sum rule formula for $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$. Then, we obtain the values of $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}$ with $n=(2,4,6,8,10)$ at the initial scale ${\ensuremath{\mu}}_{0}=1\text{ }\text{ }\mathrm{GeV}$. The first two moments are $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.271\ifmmode\pm\else\textpm\fi{}0.013$ and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.138\ifmmode\pm\else\textpm\fi{}0.010$, and the corresponding Gegenbauer moments are ${a}_{2}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.206\ifmmode\pm\else\textpm\fi{}0.038$ and ${a}_{4}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.047\ifmmode\pm\else\textpm\fi{}0.011$, respectively. After fitting the moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$, we obtain the appropriate model parameters by using the least squares method. The resultant behavior for the twist-2 pion DA is closer to the AdS/QCD and lattice results, but narrower than that obtained using the Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFFs) and $B\ensuremath{\rightarrow}\ensuremath{\pi}$ TFFs within the light-cone sum rule approach, which conform with experimental and theoretical results.

D Meson Leading-Twist Distribution Amplitude from $B\to Dl\bar {\nu }_{l}$ Semi-Leptonic Decay

The D-meson leading-twist distribution amplitude (DA) is an universal physical quantity for applying QCD light-cone sum rules or perturbative QCD method to exclusive processes involving D-meson. Although several models have been used in the literature, we do not have enough knowledge to determine it. Inversely, one expects that the D-meson DA can be constrained in principle by the processes containing D-meson. In this paper, we try to extract the information of D-meson DA’s behavior from the experimental data of B → D semi-leptonic decay. A revised light-cone harmonic oscillator model has been suggested. It can mimic most of the suggested D-meson DA behaviors, whose parameters can be fixed by the constraints from the processes involving D-meson. By combining the D-meson decay channel $D\to \mu \bar {\nu }$ , the semi-leptonic decay $B\to Dl\bar {\nu }_{l}$ and the constrain that the probability of finding the leading Fock-state $|\bar {c}q>$ in the D-meson Fock state expansion, we restrict the parameter BD in our DA model as BD ∈ [0.00, 0.23]. In order to improve the complexity of the evolution of the oscillator model, we give the fitting formulas for the evolution of the model parameters. Then we calculate the branching ratios ${\mathscr{B}}(\overline {B}^{0}\to D^{+}l\nu _{l})$ and ${\mathscr{B}}(B^{-}\to D^{0}l\bar {\nu }_{l})$ , which agree with the experimental data.

Study of the radiative decay J/ψ → ηc + γ in light cone sum rules

At present, there are many experimental and theoretical results for J/ψ→ηc+γ process, while the results are inconsistent based on different methods and considerations. In this paper, the light cone sum rules method is used in studying the radiative decay J/ψ→ηc+γ. We give the transition form factor of this process based on the leading twist distribution amplitude of ηc meson, with this form factor further obtain the decay width. Our result is consistent with those of other sum rules. A comparison of our result with others' about the decay width is also presented.

Longitudinal leading-twist distribution amplitude of the J/ψ meson within the background field theory

We make a detailed study on the $J/\psi$ meson longitudinal leading-twist distribution amplitude $\phi_{2;J/\psi}^\|$ by using the QCD sum rules within the background field theory. By keeping all the non-perturbative condensates up to dimension-six, we obtain accurate QCD sum rules for the moments $\langle\xi_{n;J/\psi}^\|\rangle$. The first three ones are $\langle\xi_{2;J/\psi}^\|\rangle=0.083(12)$, $\langle\xi_{4;J/\psi}^\|\rangle=0.015(5)$ and $\langle\xi_{6;J/\psi}^\|\rangle=0.003(2)$, leading to a single peaked behavior for $\phi_{2;J/\psi}^\|$ which is sharper than the previous ones around the region of $x\sim0.5$. As an application, we adopt the QCD light-cone sum rules to calculate the $B_c$ meson semileptonic decay $B_c^+ \to J/\psi \ell^+ \nu_\ell$. We obtain $\Gamma(B_c^+ \to J/\psi \ell^+ \nu_\ell) = (89.67^{+24.76}_{-19.06}) \times 10^{-15}~{\rm GeV}$ and $\Re(J/\psi \ell^+ \nu_\ell) = 0.217^{+0.069}_{-0.057}$, which agree with the next-to-leading order pQCD prediction and the new CDF measurement within errors.

Uncertainties of the Brightarrow D transition form factor from the D-meson leading-twist distribution amplitude

The Brightarrow D transition form factor (TFF) f^{Brightarrow D}_+(q^2) is determined mainly by the D-meson leading-twist distribution amplitude (DA) , phi _{2;D}, if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA phi _{2;D} and its impact on f^{Brightarrow D}_+(q^2). In this paper, we calculate the moments of phi _{2;D} with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments leftlangle xi ^nrightrangle _D up to fourth order and up to dimension-six condensates are presented. At the scale mu = 2 ,mathrm{GeV}, the values of the first four moments are: leftlangle xi ^1rightrangle _D = -0.418^{+0.021}_{-0.022}, leftlangle xi ^2rightrangle _D = 0.289^{+0.023}_{-0.022}, leftlangle xi ^3rightrangle _D = -0.178 pm 0.010 and leftlangle xi ^4rightrangle _D = 0.142^{+0.013}_{-0.012}. Basing on the values of leftlangle xi ^nrightrangle _D(n=1,2,3,4), a better model of phi _{2;D} is constructed. Applying this model for the TFF f^{Brightarrow D}_+(q^2) under the light cone sum rules, we obtain f^{Brightarrow D}_+(0) = 0.673^{+0.038}_{-0.041} and f^{Brightarrow D}_+(q^2_{mathrm{max}}) = 1.117^{+0.051}_{-0.054}. The uncertainty of f^{Brightarrow D}_+(q^2) from phi _{2;D} is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio mathcal {B}(Brightarrow Dlbar{nu }_l) is calculated, which is consistent with experimental data.

Comparison of two Minkowski-space approaches to heavy quarkonia

In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Basis Light-Front Quantization approach, where light-front wave functions are naturally formulated; and, the Covariant Spectator Theory (CST), based on a reorganization of the Bethe–Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the two approaches as well as with experiment where available. We also apply the Brodsky–Huang–Lepage prescription to convert the CST amplitudes into functions of light-front variables. This provides an ideal opportunity to investigate the similarities and differences at the level of the wave functions. Several qualitative features are observed in remarkable agreement between the two approaches even for the rarely addressed excited states. Leading-twist distribution amplitudes as well as parton distribution functions of heavy quarkonia are also analyzed.

Leading-twist distribution amplitudes of scalar and vector mesons

A symmetry-preserving truncation of the two-body light-quark bound-state problem in relativistic quantum field theory is used to calculate the leading-twist parton distribution amplitudes (PDAs) of scalar systems, both ground-state and radial excitations, and the radial excitations of vector mesons. Owing to the fact that the scale-independent leptonic decay constant of a scalar meson constituted from equal-mass valence-constituents vanishes, it is found that the PDA of a given scalar system possesses one more zero than that of an analogous vector meson. Consequently, whereas the mean light-front relative momentum of the valence-constituents within a vector meson is zero, that within a scalar meson is large, an outcome which hints at a greater role for light-front angular momentum in systems classified as $P$-wave in quantum mechanical models. Values for the scale-dependent decay constants of ground-state scalar and vector systems are a by-product of this analysis, and they turn out to be roughly equal, viz. $\simeq 0.2\,$GeV at an hadronic scale. In addition, it is confirmed that the dilation characterising ground-state PDAs is manifest in the PDAs of radial excitations too. The impact of $SU(3)$-flavour symmetry breaking is also considered. When compared with pseudoscalar states, it is a little stronger in scalar systems, but the size is nevertheless determined by the flavour-dependence of dynamical chiral symmetry breaking and the PDAs are still skewed toward the heavier valence-quark in asymmetric systems.

ρ-meson longitudinal leading-twist distribution amplitude within QCD background field theory

We revisit the $\rho$-meson longitudinal leading-twist distribution amplitude (DA) $\phi_{2;\rho}^\|$ by using the QCD sum rules approach within the background field theory. To improve the accuracy of the sum rules for its moments $\langle\xi_{n;\rho}^\|\rangle$, we include the next-to-leading order QCD correction to the perturbative part and keep all non-perturbative condensates up to dimension-six consistently within the background field theory. The first two moments read $\langle \xi_{2;\rho}^\| \rangle|_{1{\rm GeV}} = 0.241(28)$ and $\langle \xi_{4;\rho}^\| \rangle|_{1{\rm GeV}} = 0.109(10)$, indicating a double humped behavior for $\phi_{2;\rho}^\|$ at small energy scale. As an application, we apply them to the $B\to \rho $ transition form factors within the QCD light-cone sum rules, which are key components for the decay width $\Gamma(B\to \rho \ell \nu_\ell)$. To compare with the world-average of $\Gamma(B\to \rho \ell \nu_\ell)$ issued by Particle Data Group, we predict $|V_{\rm ub}| = 3.19^{+0.65}_{-0.62}$, which agrees with the BABAR and Omn\`{e}s parameterization prediction within errors.

Hadron Wave Functions from Lattice QCD

I give a brief account of the status and perspectives of lattice calculations of the light-front wave functions at small transverse separations, usually referred to as hadron distribution amplitudes (DAs). The existing calculations indicate that the corrections to the asymptotic form of such distributions at large scales are rather small as compared to earlier model estimates. Lattice calculations also suggest an alternating pattern of such corrections for the nucleon resonances with increasing mass. Several recent results are discussed, including precise determination of the second moment of the pion DA, leading-twist DAs of the nucleon and \(N^*(1535)\), and the first calculation of the flavor-symmetry breaking corrections in the DAs of the baryon octet.

Light-cone distribution amplitudes of the baryon octet

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using $N_f=2+1$ flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.

The B → K* transition form factors within the QCD light-cone sum rules and their application to the semi-leptonic decay B → K* μ+μ−

We present a detailed calculation on the transition form factors (TFFs), V and within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude provides over 90% contribution, thus those TFFs provide good platforms for testing the property of We suggest a model for in which two parameters and dominantly control its longitudinal distribution. With a proper choice of and our predictions on TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay The predicted differential branching fraction is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q2-region, we get the branching fraction, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of