We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA $ϕ_-(ω)$ so that the evolution equation for the latter is the same as for the leading-twist DA $ϕ_+(ω)$ up to a constant shift in the anomalous dimension. Thus, ``genuine'' three-particle states that belong to the continuous spectrum effectively decouple from $ϕ_-(ω)$ to the leading-order accuracy. In turn, the scale dependence of the full three-particle DA turns out to be nontrivial so that the contribution with the lowest anomalous dimension does not become leading at any scale. The results are illustrated on a simple model that can be used in studies of $1/m_b$ corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules.
We present a systematic study of twist-4 light-cone distribution amplitudes of vector mesons in QCD, which is based on conformal expansion. The structure of meson mass corrections is studied in detail. A complete set of distribution amplitudes is constructed, which satisfies all (exact) equations of motion and constraints from conformal expansion. Nonperturbative input parameters are estimated from QCD sum rules. Our study suggests that meson mass corrections may present a dominant source of higher twist effects in exclusive processes.
We present a systematic study of twist three light-cone distribution amplitudes of vector mesons in QCD, which is based on conformal expansion and takes into account meson and quark mass corrections. A complete set of distribution amplitudes is constructed for rho, omega, K* and phi mesons, which satisfies all (exact) equations of motion and constraints from conformal expansion. Nonperturbative input parameters are calculated from QCD sum rules, including an update of SU(3) breaking corrections in the leading twist distributions.
We show that in the large N_c limit four-quark twist-4 distributions in the pion can be expressed in terms of twist-2 pion distribution amplitude. This allows us to compute the isospin-2 structure function of the pion F_2^{I=2}(x_B) in the large N_c limit. The method can be easily applied to other mesons as well.
Two- and three-particle distribution amplitudes of heavy pseudoscalar mesons of well-defined geometric twist are introduced. They are obtained from appropriately parametrized vacuum-to-meson matrix elements by applying those twist projectors which determine the enclosed light-cone operators of definite geometric twist and, in addition, observing the heavy quark constraint. Comparing these distribution amplitudes with the conventional ones of dynamical twist we derive relations between them, partially being of Wandzura-Wilczek type; also sum rules of Burkhardt-Cottingham type are derived.The de…
We present a systematic study of twist-3 light-cone distribution amplitudes of $K^*$ and $ϕ$ mesons in QCD. The structure of SU(3)-breaking corrections is studied in detail. Non-perturbative input parameters are estimated from QCD sum rules. As a by-product, we update the parameters describing the twist-3 distribution amplitudes of the $ρ$ meson. We also review and update predictions for the twist-2 distribution amplitudes of $ρ$, $K^*$ and $ϕ$.
We discuss the two and three particle light-cone distribution amplitudes (DAs) of pseudoscalar nonsinglet mesons of twist 3 and 4. Using nonlocal operator identities and conformal expansion, we derive closed expressions for several DAs. We also include meson-mass corrections which prove to be dominant in the twist 4 DAs of K and eta mesons. Explicit parametrizations for the DAs of pi, K and eta mesons are given, with the numerical input parameters determined from QCD sum rules.
We present a systematic study of twist-3 and twist-4 light-cone distribution amplitudes of the K meson in QCD. The structure of SU(3)-breaking corrections is studied in detail. Non-perturbative input parameters are estimated from QCD sum rules and renormalons. As a by-product, we give a complete reanalysis of the twist-3 and -4 parameters of the pi-meson distribution amplitudes; some of the results differ from those usually quoted in the literature.
We present a systematic study of twist-4 light-cone distribution amplitudes of the $K^*$ and $ϕ$ meson in QCD. The structure of SU(3)-breaking corrections is studied in detail. Non-perturbative input parameters are estimated from QCD sum rules and a renormalon based model. As a by-product, we give a complete reanalysis of the parameters of the twist-4 $ρ$-meson distribution amplitudes.
We analyze light meson electroproduction within the handbag model. We study cross sections and spin asymmetries for various mesons. The essential role of the transversity $\tilde H_T$ and $\tilde E_T$ GPDs in electroproduction of pseudoscalar mesons is found. Our results are in good agrement with experiment.
This paper is devoted to the study of leading twist light cone wave functions of J/Psi meson. The moments of these wave functions have been calculated within three approaches: potential models, nonrelativistic QCD and QCD sum rules. Using the results obtained within these approaches the models for the light cone wave functions of leading twist have been proposed. Similarly to the wave function of eta_c meson the leading twist light cone wave functions of J/Psi meson have very interesting properties at scales greater than m_c: improvement of the accuracy of the model, appearance of relativistic…
We give a summary of existing results on higher twist distribution amplitudes of vector mesons in QCD. Special attention is payed to meson mass corrections which turn out to be large. A ``shopping list'' is presented of most important nonperturbative parameters which enter distribution amplitudes.
In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, it is derived relations which allow one to calculate the masses of nonrelativistic pseudoscalar and vector meson if the leading twist distribution amplitudes are known. These relations can be also rewritten as relations between the masses of nonrelativistic mesons and infinite series of QCD operators, what can be considered as an exact version of Gremm-Kapustin relation in NRQCD.
We introduce chiral-even and chiral-odd meson wave functions as vacuum-to-meson matrix elements of bilocal quark operators with well-defined (geometric) twist. Thereby, we achieve a Lorentz invariant classification of these distributions which differ from the conventional ones by explicitly taking into account the trace terms. The relations between conventional and new wave functions are given.
We discuss the light-front zero-mode issue in the light-front quark model prediction of the twist-3 distribution amplitude of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD.
A complete set of asymptotic three particle light cone distribution amplitudes of twist 3 and 4 for a transversely polarized massive vector meson built out of massless current quarks is constructed. The method used is based on a modified conformal projectors technique which allows to handle kinematical corrections due to a finite hadron mass. Consequences of our finding for the ρ-meson hard diffractive electroproduction and γρπform factor are discussed. Our results may imply a breakdown of OPE for some exclusive processes beyond the leading twist level.
The decays of $χ_{cJ} \to π^+π^-, K^+K^-$ $(J=0,2)$ are discussed within the standard and modified hard scattering approach when including the contributions from twist-3 distribution amplitudes and wave functions of the light pseudoscalar meson. A model for twist-2 and twist-3 distribution amplitudes and wave functions of the pion and kaon with BHL prescription are proposed as the solution to the end-point singularities. The results show that the contributions from twist-3 parts are actually not power suppressed comparing with the leading-twist contribution. After including the effects from th…
We describe hard exclusive processes involving a transversally polarized rho meson in the twist 3 approximation, in a framework based on the Taylor expansion of the amplitude around the dominant light-cone direction.
We give the geometric Wandzura-Wilczek-type relations between the meson wave functions of dynamical twist by means of the meson wave functions of geometric twist. We discuss the difference between geometric and dynamical Wandzura-Wilczek-type relations. Additionally, the interrelations between the different twist notations of meson wave functions are discussed.
We give a complete re-analysis of the leading twist quark-antiquark light-cone distribution amplitudes of longitudinal and transverse $ρ$ mesons. We derive Wandzura-Wilczek type relations between different distributions and update the coefficients in their conformal expansion using QCD sum rules including next-to-leading order radiative corrections. We find that the distribution amplitudes of quarks inside longitudinally and transversely polarized $ρ$ mesons have a similar shape, which is in contradiction to previous analyses.
We present the one-loop anomalous dimension matrices for the chiral-even twist-3 (nonsinglet) conformal operators, which govern the scale-dependence of the vector meson light-cone wave functions through the conformal expansion. It is clarified that the constraints from the charge-conjugation invariance and the chirality conservation allow only one independent anomalous dimension matrix for each conformal spin.
This paper is devoted to the study of leading twist light cone wave function of $η_c$ meson. The moments of this wave function have been calculated within three approaches: potential models, nonrelativistic QCD and QCD sum rules. Using the results obtained within these approaches the model for the light cone wave function of leading twist has been proposed. Being scale dependent light cone wave function has very interesting properties at scales $μ> m_c$: improvement of the accuracy of the model, appearance of relativistic tail and violation of nonrelativistic QCD velocity scaling rules. The la…
We present a systematic study of twist-3 light-cone distribution amplitudes of vector mesons in QCD, which is based on conformal expansion. A complete set of distribution amplitudes is constructed for ρ, ω, K^* and ϕmesons, which satisfies all (exact) equations of motion and constraints from conformal expansion.
We present a systematic study of higher-twist distribution amplitudes (DAs) of the B-meson which give rise to power-suppressed $1/m_B$ contributions to B-decays in final states with energetic light particles in the framework of QCD factorization. As the main result, we find that the renormalization group equations for the three-particle distributions are completely integrable in the large $N_c$ limit and can be solved exactly. General properties of the solutions are studied. We propose simple models for higher-twist DAs which satify all existing constraints and can be used in phenomenological …
Single pseudoscalar and vector mesons hard semi-inclusive photoproduction $γh \to MX" via higher twist (HT) mechanism is calculated using the QCD running coupling constant method. The structure of infrared renormalon singularities of the HT subprocess cross section and the Borel sum for it are found. The problem of normalization of HT process cross section in terms of the meson elm form factor is discussed.
I briefly review the formalism for treating the leading-twist two-gluon states appearing in processes which involve eta and eta' mesons. The constraints on the size of the lowest order Gegenbauer coefficients of the two-gluon distribution amplitude are obtained from the fit to the eta and eta' transition form factor data. The results are applied to chi -> eta eta (eta' eta') decays and deeply virtual electroproduction of eta and eta' mesons.
We present the detailed analysis of genuine twist-3 contributions to the exclusive electroproduction amplitude of transversely polarized vector mesons. Using the formalism based on the QCD factorization in the momentum representation we calculated all the genuine twist-3 terms and found the total expression of this amplitude at 1/Q level. Generally speaking, these terms violate standard factorization owing to the existence of the infrared divergencies in the amplitude of hard sub-processes, although the strongest divergencies cancel due to the QCD equations of motion. We discuss the possible t…
Using collinear factorization, we have calculated twist-six corrections to $ηγ$ and $η^{\prime}γ$ transition form factors in QCD. Only a sub-set of light-cone operators of twist-six which can be factorized as a product of two gauge invariant operators has been considered. Resulting power corrections start as $1/Q^{4}$ but coefficients are smaller compared to their counterparts for twist-four operators. Matrix element of pseudoscalar quark densities for $u$- and $d$-quarks between vacuum and meson state, $h_{q}$, has considerable influence on the result. Results obtained by superimposing our re…
We present a theoretical estimate for the cross-section of exclusive $ρ^+ρ^-$ and $ρ^0ρ^0$-meson production in two photon collisions when one of the initial photons is highly virtual. We focus on the discussion of the twist 4 contributions which are related to the production of an exotic isospin 2 resonance of two $ρ$ mesons. Our analysis shows that the recent experimental data obtained by the L3 Collaboration at LEP can be understood as a signal for the existence of an exotic isotensor resonance with a mass around $1.5 {\rm GeV}$.
Exclusive electroproduction of vector mesons is a crucial way to probe QCD factorization properties. Such a factorization is up to now only proven, at the twist 2 level, for a longitudinaly polarized meson. It is crucial to extend our understanding to the case of transversely polarized vector mesons. As a first step in this direction, we evaluate the impact factor of the transition gamma* -> rhoT, which is the relevant part of the amplitude within the kt-factorization approach valid at large energies, taking into account the twist 3 contributions, coming both from quark antiquark and from quar…
We present an analysis of genuine twist-3 quark contributions to the amplitude of exclusive electro-production of transversely polarized vector mesons. Using the formalism based on the momentum representation we calculated all the genuine twist-3 terms of quark contributions to gamma_T^* --> rho_T amplitude. We found that these terms can not be factorized owing to the existence of the infrared divergencies in the amplitude of hard sub-processes.
This paper is devoted to the study of the leading twist distribution amplitudes of P-wave nonrelativistic mesons. It is shown that at the leading order approximation in relative velocity of quark-antiquark pair inside the mesons these distribution amplitudes can be expressed through one universal function. As an example, the distribution amplitudes of the P-wave charmonia mesons are considered. Within QCD sum rules the model for the universal function of P-wave charmonia mesons is built. In addition, it is found the relations between the moments of the universal function and the nonrelativisti…
We study the twist-3 distribution amplitudes for scalar mesons made up of two valence quarks based on QCD sum rules. By choosing the proper correlation functions, we derive the moments of the scalar mesons up to the first two order. Making use of these moments, we then calculate the first two Gegenbauer coefficients for twist-3 distribution amplitudes of scalar mesons. It is found that the second Gegenbauer coefficients of scalar density twist-3 distribution amplitudes for $K^{*}_0$ and $f_0$ mesons are quite close to that for $a_0$, which indicates that the SU(3) symmetry breaking effect is t…
Single pseudoscalar and vector mesons inclusive photoproduction $γh\rightarrow MX$ via higher twist mechanism is calculated using the QCD running coupling constant method. It is proved that in the context of this method a higher twist contribution to the photoproduction cross section cannot be normalized in terms of the meson electromagnetic form factor. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. Comparisons are made with earlier results, as well as with leading twist cross sectio…
Under the constraints of HQET the equations of motion of heavy meson distribution amplitudes of definite geometric twist, using the knowledge of their off-cone structure, are reformulated as a set of algebraic equations. Together with equations due to various Dirac structures various relations between the (sets of) independent two- and three particle distribution amplitudes of definite geometric twist are derived and presented using both the notion of (double) Mellin moments and re-summed non-local distribution amplitudes. Resolving these relations for the independent two-particle moments in t…
We link the recent computation beyond leading twist of the impact factor of the transition gamma*T -> rhoT performed in the light-cone collinear approach, to the dipole picture by expressing the hard part of the process through its Fourier transform in coordinate space. We show that in the Wandzura-Wilczek approximation the impact factor up to twist 3 factorises in the wave function of the photon combined with the distribution amplitudes of the rho-meson and the colour dipole scattering amplitude with the t-channel gluons. We show also that beyond the Wandzura-Wilczek approximation, the hard c…
We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.
We provide results for the full set of form factors describing semileptonic $B$-meson transitions to pseudoscalar mesons $π$, $K$, $\bar{D}$ and vector mesons $ρ$, $K^*$, $\bar{D}^*$. Our results are obtained within the framework of QCD Light-Cone Sum Rules with $B$-meson distribution amplitudes. We recalculate and confirm the results for the leading-twist two-particle contributions in the literature. Furthermore, we calculate and provide new expressions for the two-particle contributions up to twist four. Following new developments for the three-particle distribution amplitudes, we calculate …
Although the meson decay amplitude described by a two-point function may be regarded as one of the simplest possible physical observable, it is interesting that this apparently simple amplitude bears abundant fundamental informations on QCD vacuum dynamics and chiral symmetry. The light-front zero-mode issue of the vector meson decay constant $f_V$ is in this respect highly non-trivial and deserves careful analyses. We discuss the zero-mode issue in the light-front quark model (LFQM) prediction of $f_V$ from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. …
In this article, we investigate the next-to-leading order contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive pion production cross section in proton-proton collisions and present the general formulae for the higher-twist differential cross sections in the case of the running coupling and frozen coupling approaches. We compared the resummed next-to-leading order higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. The structure of infrared renormalon singularities of the higher twist subp…
The light-cone distribution amplitudes (LCDAs) serve as important non-perturbative inputs for the study of hard exclusive processes. In this paper, we calculate ten LCDAs at twist-2 for the S-wave and P-wave $B_c$ mesons up to the next-to-leading order (NLO) of the strong coupling $α_s$ and leading order of the velocity expansion. Each one of these ten LCDAs is expressed as a product of a perturbatively calculable distribution and a universal NRQCD matrix-element. By use of the spin symmetry, only two NRQCD matrix-elements will be involved. The reduction of the number of non-perturbative input…
Within the kt-factorization approach, we evaluate the impact factor of the transition gamma* -> rhoT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. More generally, relying on these equations and on the invariance under rotation on the light-cone of the factorized amplitude, the non-perturbative Distribution Amplitudes can be reduced to a minimal set. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson. We prove the equival…
We compute the static-light meson spectrum with N_f = 2 flavours of sea quarks using Wilson twisted mass lattice QCD. We consider five different values for the light quark mass corresponding to 300 MeV < m_PS < 600 MeV and we present results for angular momentum j = 1/2, j = 3/2 and j = 5/2 and for parity P = + and P = -. We extrapolate our results to physical quark masses and make predictions regarding the spectrum of B and B_s mesons.
We extract the leading twist-2 and subleading twist-3 Distribution Amplitudes (DAs) of the rho meson using the HERA data on diffractive rho photoproduction. We do so using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. We find that our extracted twist-2 DA is not much model dependent and is consistent with QCD Sum Rules and lattice predictions. The extracted twist-3 DA is more model dependent but is still consistent with the Sum Rules prediction.
In this article, we investigate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive single meson production cross section in photon-photon collisions and present the general formulas for the higher-twist differential cross sections in case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher-twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling…
We critically reexamine the formalism for treating the leading-twist contributions from the two-gluon Fock components occurring in hard processes that involve eta and eta' mesons and establish a consistent set of conventions for the definition of the gluon distribution amplitudes, the anomalous dimensions as well as the projector of a two-gluon state onto an eta or eta' state. We calculate the eta, eta'--photon transition form factor to order alpha_s and show the cancellation of the collinear and UV singularities explicitly. An estimate of the lowest Gegenbauer coefficients of the gluon and qu…
We study properties of pseudoscalar flavour-singlet mesons from Wilson twisted mass lattice QCD with Nf=2+1+1 dynamical quark flavors. Results for masses are presented at three values of the lattice spacing and light quark masses corresponding to values of the pion mass from 230 MeV to 500 MeV. We briefly discuss scaling effects and the light and strange quark mass dependence of the eta mass. In addition we present an exploratory study using Osterwalder-Seiler type strange and charm valence quarks. This approach avoids some of the complications of the twisted mass heavy doublet. We present fir…
I calculate the form factors describing semileptonic and penguin induced decays of B mesons into light pseudoscalar and vector mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3) breaking effects. The theoretical uncertainty is estimated to be $\sim$ (15-20)%.
We compute the amplitudes for non-leptonic annihilation decays of $B$ mesons into two particles within the pQCD collinear approach. The end point divergences are regulated with the help of an infrared finite gluon propagator characterized by a non-perturbative dynamical gluon mass consistent with recent lattice simulations. The divergences at twist-3 are regulated by a dynamical quark mass. Our results fit quite well the existent data of $B^0\to D_s^-K^+$ and $B^0\to D_s^{-*}\bar{K}^+$ for the expected range of dynamical gluon masses. We also make predictions for the rare decays $\bar{B}^0\to …
We investigate wide-angle photoproduction of the $η'$ meson within the handbag approach to twist-3 accuracy. It turns out that, due to the gluon content of the $η'$, this process is dominated by twist-2 in contrast with pion and $η$ photoproduction. Using the presently available information on the twist-2 and twist-3 distribution amplitudes and on the $η- η'$ mixing, we provide prediction for the $η'$ cross section and helicity correlations. It is argued that $η'$ photoproduction is well suited to improve our knowledge of the two-gluon distribution amplitude.
In this article, we investigate the contribution of the high twist Feynman diagrams to the large $p_{T}$ single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients $a_2$ and $a_4$ have been extracted from the CLEO data, Braun-Filyanov pion wave function, the asymptotic and the Chernyak-Zhitnitsky wave functions are used in the calculations. For $ρ$-meson we used Ball-Braun wave function. The r…
