Light-cone Distribution Amplitudes Research Articles

Searching for a 0(980)-meson parton distribution function

In this paper, we calculate the scalar a 0(980)-meson leading-twist wave function by using the light-cone harmonic oscillator model (LCHO), where the model parameters are determined by fitting the ξ-moments of its light-cone distribution amplitudes. Then, the a 0(980)-meson leading-twist light-cone distribution amplitudes with three different scales ζ = (1.0, 2.0, 5.2)GeV are given. After constructing the relationship between the a 0(980)-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wave function, we exhibit the and with different scales. Furthermore, we also calculate the Mellin moments of the a 0(980)-meson’s valence quark distribution function with n = (1, 2, 3), i.e. , and . Finally, the scale evolution for the ratio of the Mellin moments are presented.

Light-cone distribution amplitudes of a light baryon in large-momentum effective theory

Momentum distributions of quarks/gluons inside a light baryon in a hard exclusive process are encoded in the light-cone distribution amplitudes (LCDAs). In this work, we point out that the leading twist LCDAs of a light baryon can be obtained through a simulation of a quasi-distribution amplitude calculable on lattice QCD within the framework of the large-momentum effective theory. We calculate the one-loop perturbative contributions to LCDA and quasi-distribution amplitudes and explicitly demonstrate the factorization of quasi-distribution amplitudes at the one-loop level. Based on the perturbative results, we derive the matching kernel in the overline{textrm{MS}} scheme and regularization-invariant momentum-subtraction scheme. Our result provides a first step to obtaining the LCDA from first principle lattice QCD calculations in the future.

Study pion distribution amplitudes from the electromagnetic form factor by data-driven dispersion relation

We study the pion electromagnetic form factor in the modulus squared dispersion relation, and do the model independent extraction of the chiral mass embedded in the sub-leading twist light-cone distribution amplitude. The motivation of this work is the recent measurement of timelike form factor in the resonant regions, which makes up the piece lacking solid QCD-based calculation. With the perturbative QCD calculation up to next-to-leading-order of strong coupling and twist four level of meson distribution amplitudes, we obtain the chiral mass of pion meson as m_0^pi (1 , textrm{GeV}) = 1.31^{+0.27}_{-0.30} , textrm{GeV}. Due to the chiral enhancement contribution from the sub-leading twist distribution amplitudes in the perturbative QCD calculation, we can not extract the lowest Gegenbauer moments of pion from the study of electromagnetic form factor. This problem could be settled down with the foresee Belle-II and BESIII measurement of the transition form factor especially in the large momentum transfers regions.

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

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

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.

Relativistic corrections toJ/ψ→pp¯decay

We study relativistic corrections to the exclusive decay of $J/\ensuremath{\psi}$ into proton-antiproton final state. We calculate the relativistic QCD corrections to the dominant decay amplitude, which depend on the nucleon twist-3 light-cone distribution amplitudes only. It is shown that in this case the collinear factorization is also valid beyond the leading-order approximation. Our numerical estimates show that relativistic correction of relative order ${v}^{2}$ provides a large numerical impact.

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.

Weak radiative decay Lambda _{c}^{+}rightarrow Sigma ^{+}gamma using light-cone sum rules

We calculate the decay width of the Lambda _{c}^{+}rightarrow Sigma ^{+}gamma using light-cone sum rules. For the initial quark radiation an effective Hamiltonian is constructed, where the internal quark line shrinks to a point. The final quark radiation is studied within the full theory. The leading twist light-cone distribution amplitudes of the Sigma ^+ serve as the non-perturbative input for the sum rules calculation, and the perturbative kernel is calculated at leading order. The branching fraction we obtain is mathcal{B}(Lambda _{c}^{+}rightarrow Sigma ^{+}gamma )=1.03pm 0.36 times 10^{-4}, which is below the recent upper limits <2.6 times 10^{-4} and <4.4 times 10^{-4} given by the Belle collaboration and the BESIII collaboration, respectively.

Matching the B -meson quasidistribution amplitude in the RI/MOM scheme

Within the framework of large-momentum effective theory, the light-cone distribution amplitude (LCDA) of the $B$ meson in heavy-quark effective theory can be extracted from lattice calculations of the quasidistribution amplitude through the hard-collinear factorization formula. This quasiquantity can be renormalized in a regularization-independent momentum subtraction (RI/MOM) scheme. In this work, we derive the matching coefficient which connects the renormalized quasidistribution amplitude in the RI/MOM scheme and the standard LCDA in the $\overline{\mathrm{MS}}$ scheme at one-loop accuracy. Our numerical analysis verifies the feasibility of the RI/MOM scheme for renormalizing the $B$-meson quasidistribution amplitude. These results will be crucial for exploring the partonic structure of heavy-quark hadrons.

Semileptonic decay of Ξc→Ξℓ+νℓ from light-cone QCD sum rules

Semileptonic decay processes of $\Xi_c \to \Xi\ell\nu_\ell$ are studied by light-cone QCD sum rules in this paper. The six form factors of $\Xi_c \to \Xi$ semileptonic transition matrix elements are calculated by this method with the light-cone distribution amplitudes of $\Xi$ baryon up to twist six. With the six form factors, the absolute branching ratios of $\Xi_c^0 \to \Xi^- \ell^+ \nu_\ell$ and $\Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell$ are calculated by the helicity amplitudes formalism of semileptonic differential decay widths. The ratios of absolute branching ratios of electron and muon final states processes give the proof of lepton flavor universality. Our results are in accordance with the recent experimental and theoretical reports.

Light-cone sum rule analysis of semileptonic decays varLambda _b^0 rightarrow varLambda _c^+ ell ^- {overline{nu }}_ell

In this work, we analyze the semileptonic decay processes of varLambda _b rightarrow varLambda _c in the light-cone sum rule approach. In order to calculate the form factors of the varLambda _b baryon transition matrix element, we use the light-cone distribution amplitudes of varLambda _b obtained from the QCD sum rule in the heavy quark effective field theory framework. With the calculation of the six form factors of the varLambda _b rightarrow varLambda _c transition matrix element, the differential decay widths of varLambda _b^0 rightarrow varLambda _c^+ ell ^- {overline{nu }}_ell (ell = e, ~mu , ~tau ) and their absolute branching fractions are obtained. Additionally, the ratio of R(varLambda _c^+) equiv {mathcal {B}}r(varLambda _b^0 rightarrow varLambda _c^+ tau ^- {overline{nu }}_tau )/{mathcal {B}}r(varLambda _b^0 rightarrow varLambda _c^+ mu ^- {overline{nu }}_mu ) is also obtained in this work. Our results are in accord with the newest experimental result and other theoretical calculations and predictions.

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

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

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.

Pion and Kaon Distribution Amplitudes from Lattice QCD.

We present a state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings a≈{0.06,0.09,0.12} fm and physical pion and kaon masses, with the meson momenta P_{z}={1.29,1.72,2.15} GeV. The result is nonperturbatively renormalized in a recently proposed hybrid scheme with self-renormalization, and extrapolated reliably to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and a large SU(3) flavor breaking effect in the kaon DA.

B-meson decay into a proton and dark antibaryon from QCD light-cone sum rules

The recently developed B-Mesogenesis scenario predicts decays of B mesons into a baryon and hypothetical dark antibaryon Ψ. We suggest a method to calculate the amplitude of the simplest exclusive decay mode B+→pΨ. Considering two models of B-Mesogenesis, we obtain the B→p hadronic matrix elements by applying QCD light-cone sum rules with the proton light-cone distribution amplitudes. We estimate the B+→pΨ decay width as a function of the mass and effective coupling of the dark antibaryon.

Dispersive derivation of the pion distribution amplitude

We derive the dependence of the leading-twist pion light-cone distribution amplitude (LCDA) on a parton momentum fraction $x$ by directly solving the dispersion relations for the moments with inputs from the operator product expansion (OPE) of the corresponding correlation function. It is noticed that these dispersion relations must be organized into those for the Gegenbauer coefficients first in order to avoid the ill-posed problem appearing in the conversion from the moments to the Gegenbauer coefficients. Given the values of various condensates in the OPE, we find solutions for the pion LCDA, which are convergent and stable in the Gegenbauer expansion. Moreover, the solution from summing contributions up to 18 Gegenbauer polynomials is smooth, and can be well approximated by a function proportional to ${x}^{p}(1\ensuremath{-}x{)}^{p}$ with $p\ensuremath{\approx}0.45$ at the scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$. Turning off the condensates, we get the asymptotic form for the pion LCDA as expected. We then solve for the pion LCDA at a different scale $\ensuremath{\mu}=1.5\text{ }\text{ }\mathrm{GeV}$ with the condensate inputs at this $\ensuremath{\mu}$, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$ to 1.5 GeV. That is, our formalism is compatible with the QCD evolution. The strength of the above framework that goes beyond analyses limited to only the first few moments of a LCDA in conventional QCD sum rules is highlighted. The precision of our results can be improved systematically by including higher-order and higher-power terms in the OPE.

Analysis of FCNC ΞQQ→ΛQl+l− decay in light-cone sum rules

The weak decays of doubly heavy ${\mathrm{\ensuremath{\Xi}}}_{QQ}$ baryon induced by flavor changing $b\ensuremath{\rightarrow}d$ and $c\ensuremath{\rightarrow}u$ flavor changing neutral current within the light-cone sum rules are studied. The sum rules are constructed and analyzed for the corresponding transition form factors using the parallel components of the light-cone distribution amplitudes for ${\mathrm{\ensuremath{\Lambda}}}_{Q}$ baryon. Having the results for the form factors, the corresponding branching ratios for ${\mathrm{\ensuremath{\Xi}}}_{QQ}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{Q}{l}^{+}{l}^{\ensuremath{-}}$ decays are estimated. While the branching ratio due to $b\ensuremath{\rightarrow}d$ transition is around ${10}^{\ensuremath{-}9}$, in $c\ensuremath{\rightarrow}u$ transition case, it is found as around ${10}^{\ensuremath{-}13}$. Hence, ${\mathrm{\ensuremath{\Xi}}}_{bb}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}{l}^{+}{l}^{\ensuremath{-}}$ decay has the potential of being discovered at LHCb. However, ${\mathrm{\ensuremath{\Xi}}}_{bb}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}{l}^{+}{l}^{\ensuremath{-}}$ is difficult to be measured due to the extremely small values of obtained branching ratio. Our results on the branching ratio are also compared with the results of the light-front approach.

Lambda _brightarrow p transition form factors in perturbative QCD

We reanalyze the Lambda _brightarrow p transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a Lambda _b baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist Lambda _b baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 Lambda _b baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays Lambda _brightarrow pell {bar{nu }}_ell and the hadronic decay Lambda _brightarrow ppi are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.

W -exchange contribution to the decays Ξcc++→Ξc+(′)π+ using light-cone sum rules

We calculate the W-exchange contribution to the $\Xi_{cc}^{++}\to\Xi_{c}^{+(\prime)}\pi^{+}$ decay using light-cone sum rules. The two-particle light-cone distribution amplitudes of the pion are used as non-perturbative input for the sum rules calculation, and the perturbative kernel is calculated at the leading order. We obtain the corresponding decay branching fractions by combining our W-exchange amplitudes with the factorizable amplitudes given by various theoretical methods from the literature. It is shown that with the factorizable amplitudes from heavy quark effective theory, we obtain the branching fraction ratio ${\cal B}(\Xi_{cc}^{++}\to\Xi_{c}^{+\prime}\pi^{+})/{\cal B}(\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+})= 1.42\pm 0.78$, which is consistent with the experimental value of $1.41\pm 0.17\pm 0.1$.

Light-cone distribution amplitudes of heavy mesons with QED effects

We discuss the QED-generalized leading-twist light-cone distribution amplitudes of heavy mesons, that appear in QCD QED factorization theorems for exclusive two-body B decays. In the presence of electrically charged particles, these functions should be more appropriately regarded as soft functions for heavy-meson decays into two back-to-back particles. In this paper, we derive the one-loop anomalous dimension of these soft functions and study their behaviour under renormalization-scale evolution, obtaining an exact solution in Laplace space. In addition, we provide numerical solutions for the soft functions and analytical solutions to all orders in the strong and to first order in the electromagnetic coupling. For the inverse (and inverse-logarithmic) moments, we obtain an all-order solution in both couplings. We further provide numerical estimates for QED corrections to the inverse moments.