Twist-3 Distribution Amplitudes Research Articles

Distribution amplitude and decay constant of 1S and 2S state light mesons in the light-front quark model

Studying meson structures is essential for gaining insights into the nonperturbative nature of Quantum Chromodynamics (QCD). This study will focus on calculating the decay constant and distribution amplitudes (DAs) of unflavored light mesons (π and ρ) in the 1S and 2S states using the Light Front Quark Model. This study utilizes the QCD-motivated Hamiltonian, taking into account both contact and smeared spin-spin interactions. The two lowest harmonic oscillator bases are employed in this work to achieve improved results for the 2S states. The study found the optimal mixing parameter in basis expansion coefficients to be θ = 10°. Light meson properties, including the mass spectrum, decay constant, and twist-2 DAs, are then predicted using model parameters fixed through the variational principle. While the contact spin-spin interaction yields poor accuracy, the results from the smeared interaction generally agree well with experimental data and other theoretical models with $ f_{\pi}^{1S}=130 $ MeV and $ f_{\rho}^{1S}=210 $ MeV in the mixed state. Unlike the case for the 1S state, it should be noted that the properties of the 2S state are sensitive to the mixing parameter θ. In addition, we observe that the decay constant for ρ(2S) is $ f_{\rho}^{2S}=116 $ MeV. While for π(2S) the decay constant is extremely small with the value of $ f_{\pi}^{2S}=0.9 $ MeV, which is mainly due to the dynamical chiral symmetry breaking.

A0(980)-meson twist-2 distribution amplitude within the QCD sum rules and investigation of D → a0(980)(→ηπ)e+νe

In this paper, moments of a0(980)-meson twist-2 light-cone distribution amplitudes were deeply researched by using QCD sum rules approach within background field theory. Up to 9th-order accuracy, we present 〈ξ2;a0n〉|μ0 at the initial scale μ0=1GeV, i.e. 〈ξ2;a01〉|μ0=−0.307(43), 〈ξ2;a03〉|μ0=−0.181(34), 〈ξ2;a05〉|μ0=−0.078(28), 〈ξ2;a07〉|μ0=−0.049(26), 〈ξ2;a09〉|μ0=−0.036(24), respectively. An improved light-cone harmonic oscillator model for a0(980)-meson twist-2 light-cone distribution amplitudes is adopted, where its parameters are fixed by using the least squares method based on the 〈ξ2;a0n〉|μ0, and their goodness of fit reach to 95.4%. Then, we calculate the D→a0(980) transition form factors within the light-cone sum rules approach, and at largest recoil point, we obtain f+D→a0(0)=1.058−0.035+0.068 and f−D→a0(0)=0.764−0.036+0.044. As a further application, the branching fractions of the D→a0(980)ℓν¯ℓ semileptonic decays are given. Taking the decay a0(980)→ηπ into consideration, we obtain B(D0→a0(980)−(→ηπ−)e+νe)=(1.330−0.134+0.216)×10−4, B(D+→a0(980)0(→ηπ0)e+νe)=(1.675−0.169+0.272)×10−4, which are consistent with the BESIII collaboration and PDG data within errors. Finally, we present the angle observables of forward-backward asymmetries, q2-differential flat terms and lepton polarization asymmetry of the semileptonic decay D→a0(980)ℓν¯ℓ.

Perturbative calculations of gravitational form factors at large momentum transfer

We perform a perturbative QCD analysis of the gravitational form factors (GFFs) of nucleon at large momentum transfer. We derive the explicit factorization formula of the GFFs in terms of twist-3 and twist-4 light-cone distribution amplitudes of nucleon. Power behaviors for these GFFs are obtained from the leading order calculations. Numeric results of the quark and gluon contributions to various GFFs are presented with model assumptions for the distribution amplitudes in the literature. We also present the perturbative calculations of the scalar form factor 〈P′| F2| P〉 for pion and proton at large momentum transfer.

Mixing effects on 1S and 2S state heavy mesons in the light-front quark model

The mass spectra and wave functions of both $1S$ and $2S$ state heavy pseudoscalar ($P$) and vector ($V$) mesons are analyzed within the light-front quark model. Important empirical constraints employed in our analysis of the mass spectra and wave functions are the experimental mass-gap relation, $\mathrm{\ensuremath{\Delta}}{M}_{P}>\mathrm{\ensuremath{\Delta}}{M}_{V}$, where $\mathrm{\ensuremath{\Delta}}{M}_{P(V)}={M}_{P(V)}^{2S}\ensuremath{-}{M}_{P(V)}^{1S}$ and the hierarchy of the decay constants, ${f}_{1S}>{f}_{2S}$, between $1S$ and $2S$ meson states. We maintain the orthogonality of the trial wave functions of the $1S$ and $2S$ states in our variational calculation of the Hamiltonian with the Coulomb plus confining potentials and treat the hyperfine interaction perturbatively for the heavy-heavy and heavy-light $P$ and $V$ mesons due to the nature of the heavy quark symmetry. Realizing that the empirical constraints cannot be satisfied without mixing of the $1S$ and $2S$ states, we find the lower bound of the mixing angle $\ensuremath{\theta}$ between $1S$ and $2S$ states as ${\ensuremath{\theta}}_{c}={\mathrm{cot}}^{\ensuremath{-}1}(2\sqrt{6})/2\ensuremath{\simeq}6\ifmmode^\circ\else\textdegree\fi{}$ and obtain the optimum value of the mixing angle around 12\ifmmode^\circ\else\textdegree\fi{} to cover both the charm and bottom flavors of the heavy quark. The mixing effects are found to be more significant to the $2S$ state mesons than to the $1S$ state mesons. The properties of $1S$ and $2S$ state mesons including the mass spectra, decay constants, twist-2 distribution amplitudes, and electromagnetic form factors are computed. Our results are found to be in a good agreement with the available data and lattice simulations. In particular, the $2S$ state pseudoscalar ${D}_{s}$ meson is predicted to have a mass of 2600 MeV, which is very close to the mass of the newly discovered ${D}_{s0}(2590{)}^{+}$ meson by the LHCb Collaboration. This supports the interpretation of the observed state as a radial excitation of the ${D}_{s}^{+}$ meson.

A_1(1260)-meson longitudinal twist-2 distribution amplitude and the Drightarrow a_1(1260)ell ^+nu _ell decay processes

In the paper, we investigate the moments langle xi _{2;a_1}^{Vert ;n}rangle of the axial-vector a_1(1260)-meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale mu _0=1~{mathrm{GeV}} are langle xi _{2;a_1}^{Vert ;2}rangle |_{mu _0} = 0.223 pm 0.029, langle xi _{2;a_1}^{Vert ;4}rangle |_{mu _0} = 0.098 pm 0.008, langle xi _{2;a_1}^{Vert ;6}rangle |_{mu _0} = 0.056 pm 0.006, langle xi _{2;a_1}^{Vert ;8}rangle |_{mu _0} = 0.039 pm 0.004 and langle xi _{2;a_1}^{Vert ;10}rangle |_{mu _0} = 0.028 pm 0.003, respectively. We then construct a light-cone harmonic oscillator model for a_1(1260)-meson longitudinal twist-2 distribution amplitude phi _{2;a_1}^{Vert }(x,mu ), whose model parameters are fitted by using the least squares method. As an application of phi _{2;a_1}^{Vert }(x,mu ), we calculate the transition form factors (TFFs) of Drightarrow a_1(1260) in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point (q^2=0), we obtain A(0) = 0.130_{ - 0.013}^{ + 0.015}, V_1(0) = 1.898_{-0.121}^{+0.128}, V_2(0) = 0.228_{-0.021}^{ + 0.020}, and V_0(0) = 0.217_{ - 0.025}^{ + 0.023}. By applying the extrapolated TFFs to the semi-leptonic decay D^{0(+)} rightarrow a_1^{-(0)}(1260)ell ^+nu _ell , we obtain {mathcal {B}}(D^0rightarrow a_1^-(1260) e^+nu _e) = (5.261_{-0.639}^{+0.745}) times 10^{-5}, {mathcal {B}}(D^+rightarrow a_1^0(1260) e^+nu _e) = (6.673_{-0.811}^{+0.947}) times 10^{-5}, {mathcal {B}}(D^0rightarrow a_1^-(1260) mu ^+ nu _mu )=(4.732_{-0.590}^{+0.685}) times 10^{-5}, {mathcal {B}}(D^+ rightarrow a_1^0(1260) mu ^+ nu _mu )=(6.002_{-0.748}^{+0.796}) times 10^{-5}.

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 $\mathcal{R}(D_s)=0.334\pm 0.017$.

Wide-angle photo- and electroproduction of pions to twist-3 accuracy

We investigate wide-angle photo- and electroproduction of pions within the handbag mechanism in which the $\gamma^{(*)} N\to \pi N'$ amplitudes factorize into hard partonic subprocess amplitudes, $\gamma^{(*)} q\to \pi q'$, and form factors representing $1/x$-moments of generalized parton distributions (GPDs). The subprocess is calculated to twist-3 accuracy taking into account the 2- and 3-body Fock components of the pion. Both components are required for achieving gauge invariance in QED and QCD. The twist-2 and twist-3 distribution amplitudes (DAs) of the pion as well as the form factors are taken from our study of $\pi^0$ photoproduction. Extensive results on photoproduction of charged pions are presented and compared to experiment. Predictions on electroproduction of pions as well as on spin effects are also given. As a byproduct of our analysis we also obtain the complete twist-3 subprocess amplitudes contributing to deeply-virtual electroproduction of pions.

Pure annihilation decays of B s 0 → a 0 + a 0 − and B d 0 → in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays of and , where denotes the scalar a 0(980) and a 0(1450) [ and ], with the perturbative QCD factorization approach under the assumption of two-quark structure for the a 0 and states. The numerical results show that the branching ratios of the decays are in the order of 10−6, while the decay rates of the modes are in the order of 10−5. In light of the measured modes with the same quark components in the pseudoscalar sector, namely, and , the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-II experiments in the (near) future. Meanwhile, it is of great interest to find that the twist-3 distribution amplitudes ϕ S and ϕ T with inclusion of the Gegenbauer polynomials for the scalar a 0(1450) and states in scenario 2 contribute slightly to the branching ratios while significantly to the CP violations in the and decays, which indicates that, compared to the asymptotic ϕ S and ϕ T , these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels. These predictions await for the future confirmation experimentally, which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.

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.

Helicity form factors for D_{(s)} rightarrow A ell nu process in the light-cone QCD sum rules approach

The helicity form factors of the D_{(s)}rightarrow A ell ^+ nu with A=a_{1}^{-}, a_{1}^{0}, b_{1}^{-}, b_{1}^{0}, K_{1}(1270) and K_{1}(1400) are calculated in the light-cone sum rules approach, up to twist-3 distribution amplitudes of the axial vector meson A. In the helicity form factors parametrization the unitarity constraints are applied to the fitting parameters. In addition, the effects of the low-lying resonances are included in series expansions of aforementioned form factors. The properties of the D_{(s)}rightarrow A ell ^+ nu semileptonic decays are studied by extending the form factors to the whole physical region of q^2. For a better analysis, a comparison is also made between our results and the predictions obtained using transition form factors via LCSR, 3PSR and CLFQM methods.

The semileptonic decay within the LCSR approach under heavy quark effective field theory * * Supported in part by the Natural Science Foundation of China (11625520, 11765007, 11375008, 11647307, 11847301), the Project of Guizhou Provincial Department of Science and Technology ([2017]1089), and the Key Project for Innovation Research Groups of Guizhou Provincial Department of Education (KY[2016]028)

The heavy quark effective field theory (HQEFT) provides an effective way to deal with heavy meson decays. In this paper, we adopt two different correlators to derive the light-cone sum rules (LCSR) for the transition form factors (TFFs) in the framework of HQEFT. We label the two LCSR results as LCSR- and LCSR- , which stand for the conventional correlator and the right-handed correlator. We observe that the correlation parameter for the branching ratio is , implying a consistency of LCSRs with the other correlators. Furthermore, we obtain and . We also obtain and , both of which agree with the lattice QCD predictions. Thus, HQEFT provides a useful framework for studying B meson decays. Moreover, by using the right-handed correlator, the twist-2 terms are dominant in TFF , as their contribution is over ~97% in the whole region, while the large twist-3 uncertainty of the conventional correlator is greatly suppressed. Hence, the LCSR- predictions can be used to test the properties of the various models for the pion twist-2 distribution amplitudes.

Semileptonic D(s) → Aℓ+ν and nonleptonic D → K1(1270, 1400)π decays in LCSR

In this work, the transition form factors are calculated for the semileptonic D(s) → Aℓ+ν where A = a1, b1, K1(1270, 1400), i.e. , , and in the frame work of the light-cone QCD sum rules (LCSR) approach up to the twist-3 distribution amplitudes (DAs). Since the masses of these axial vector mesons are comparable to the charm quark mass, we keep out in our calculations all terms including mA/mc (all orders) in expansion of two-parton DAs. Branching ratio values are estimated for the semileptonic D(s) → Aℓν and nonleptonic D→K1 (1270, 1400) π decays. A comparison is also made between our results and predictions of other methods and the existing experimental values.

Semileptonic and nonleptonic decays of D into tensor mesons with light-cone sum rule

Form factors of $D$ decays into $J^{PC}=2^{++}$ tensor mesons are calculated in the light-cone sum rules approach up to twist-4 distribution amplitudes of the tensor meson. The masses of the tensor mesons are comparable to that of the charm quark mass $m_c$; therefore all terms including powers of $m_T/m_c$ are kept out in the expansion of the two-particle distribution amplitude $\langle T|\bar q_{1\alpha}(x) \, q_{2\delta}(0)|0\rangle$. Branching ratios of the semileptonic $D \to T\,\mu \,\bar{\nu}_{\mu}$ decays and nonleptonic $D\to T~ P ~(P=K, \pi)$ decays are taken into consideration. A comparison is also made between our results and predictions of other methods and the existing experimental values for the nonleptonic case. The semileptonic branching ratios are typically of the order of $10^{-5}$, and the nonleptonic ones show better agreement with the experimental data in comparison to the Isgur-Scora-Grinstein-Wise predictions.

Two-photon exchange effects in e+e−→π+π− and timelike pion electromagnetic form factor

The two-photon-exchange (TPE) effects in the process $e^+e^- \rightarrow \pi^+\pi^-$ at large momentum transfer are discussed within the perturbative QCD (pQCD). The contributions from the twist-2 and twist-3 distribution amplitudes (DAs) of pion are considered in the estimation. Different with the results under the one-photon-exchange (OPE) approximation, the TPE effects result in an asymmetry of the differential cross section on the scattering angle. The precise measurement of this asymmetry by the further experiment is an precise test of pQCD at large momentum transfer. The time-like electromagnetic form factor of pion at the leading order of pQCD is re-discussed and the comparison of our results with those in the references are presented.

Systematic twist expansion of (ηc,ηb)→γ*γ transition form factors in the light-front quark model

The light-front quark model analysis of the meson-photon transition form factor $F_{P\gamma} (Q^2)$ amenable both for the spacelike region ($Q^2 >0$) and the timelike region ($Q^2 <0$) provides a systematic twist expansion of $Q^2 F_{P\gamma} (Q^2)$ for the high $|Q^2|$ region. Investigating $F_{P\gamma} (Q^2) (P = \eta_c,\eta_b)$ for the entire kinematic regions of $Q^2$, we examine the twist-2 and twist-3 distribution amplitudes of $(\eta_c,\eta_b)$ mesons in the light-front quark model and quantify their contributions to $Q^2 F_{(\eta_c,\eta_b)\gamma}(Q^2)$. Our numerical results for the normalized transition form factor $F_{(\eta_c,\eta_b)\gamma}(Q^2)/F_{(\eta_c,\eta_b)\gamma}(0)$ and the decay width $\Gamma_{(\eta_c,\eta_b)\to\gamma\gamma}$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.

Charmless decays in the QCD factorization approach

In this paper, we present a study of the charmless (V denotes the light ground vector meson) decays within the framework of QCD factorization. In the evaluation, two different schemes for regulating the end-point divergence are adopted. One (scheme I) is to use a parameterization model, which is usually employed in the QCD factorization approach; the other (scheme II) is based on the infrared finite gluon propagator of the Cornwall prescription. It is found that, in the annihilation amplitudes, the end-point divergence appears only in the power-suppressed corrections related to the twist-3 distribution amplitudes of the V-meson. The strengths of the annihilation amplitudes evaluated in scheme II are generally larger than those in scheme I. Numerically, in the decay modes considered in this paper, the CKM-favored decays have relatively large branching fractions, , and hence are likely to be the first observed by future experiments. In addition, all of the decay modes are dominated by the longitudinal polarization state; numerically, .

Spin effects in the pion holographic light-front wavefunction

We account for dynamical spin effects in the holographic light-front wavefunction of the pion in order to predict its mean charge radius, decay constant, spacelike electromagnetic form factor, twist-2 Distribution Amplitude and the photon-to-pion transition form factor. Using a universal fundamental AdS/QCD scale of 523 MeV and a constituent quark mass of 330 MeV, we find a remarkable improvement in describing all observables.

Gamma gamma rightarrow M^{+}M^{-}(M=pi , K) processes with twist-3 corrections in QCD

We study the gamma gamma rightarrow M^{+}M^{-}(M=pi , K) processes with the contributions from the two-particle twist-2 and twist-3 distribution amplitudes of pion and kaon mesons on BHL prescription in the standard hard-scattering approach. The results show that the contributions from twist-3 parts are actually not power suppressed compared with the leading-twist contributions in the low energy region. The cross sections with twist-3 corrections agree well with the experimental data in the two-photon center-of-mass energy W>2.8 GeV and we also predict the cross section ratio sigma _{0}(K^{+}K^{-})/sigma _{0}(pi ^{+}pi ^{-}), which is compatible with the experimental data from TPC and Belle.

Two-particle twist-3 distribution amplitudes of the pion and kaon in the light-front quark model

We investigate the two-particle twist-3 distribution amplitudes (DAs) of the pseudoscalar mesons, in particular pseudoscalar ($\phi^P_{3;M}(x)$) and pseudotensor ($\phi^\sigma_{3;M}(x)$) DAs of the pion and kaon, in the light-front quark model based on the variational principle. We find that the behavior of the conformal symmetry in each meson distribution amplitude depends on the chiral limit characteristics of the light-front trial wave function taken in the variational principle. We specifically take the two different light-front trial wave functions, Gaussian vs. power-law type, and discuss their characteristics of the conformal symmetry in the chiral symmetry limit as well as their resulting degree of the conformal symmetry breaking in $\phi^P_{3;M}(x)$ and $\phi^\sigma_{3;M}(x)$ depending on the trial wave function taken in the computation. We present numerical results of transverse moments, Gegenbauer-moments and $\xi$-moments and compare them with other available model estimates. The SU(3) flavor-symmetry breaking effect is also quantified with the numerical computation.

Twist-3 Distribution Amplitudes of Pion in the Light-Front Quark Model

We analyzed two twist-3 distribution amplitudes of pion, i.e. pseudoscalar $\phi^P_{3;\pi}(x)$ and pseudotensor $\phi^\sigma_{3;\pi}(x)$, within the LFQM. Our LFQM descriptions both for twist-3 $\phi^P_{3;\pi}$ and $\phi^\sigma_{3;\pi}$ not only satisfy the fundamental constraint required from the isospin symmetry, but also reproduce exactly the asymptotic forms anticipated from QCD's conformal limit.