We propose an effective lagrangian for the coupling of the neutral pion with gluons whose strength is determined by a low energy theorem. We calculate the contribution of the gluonic components arising from this interaction to the pion transition form factor $γ^*γ^*\toπ^0 $ using the instanton liquid model to describe the QCD vacuum. We find that this contribution is large and might explain the anomalous behavior of the form factor at large virtuality of one of the photons, a feature which was recently discovered by the BaBar Collaboration.
The estimates of parameters for the classical SU(3)-gluonic field responsible for linear confinement are given for pions and kaons. Also estimates for the characteristics of the mentioned field such as gluon concentrations, electric and magnetic colour field strengths are adduced along with those for quark velocities in mesons under discussion. Possible connection of the obtained results with potential approach and string-like picture of confinement is outlined as well.
The confinement mechanism proposed earlier by the author is employed for to compute the decay constants $f_P$ corresponding to leptonic decays $P\to l^\pm+ν_l$, $l=μ, e$, where $P$ stands for any meson from $π^\pm$, $K^\pm$. For this aim the weak axial form factor of $P$-meson is nonperturbatively calculated. The study entails estimates for parameters of the confining SU(3)-gluonic field in charged pions and kaons. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the mesons under cons…
We study the distribution of gluons in transverse space in the nucleon at moderately small x (~10^{-2}). At large transverse distances (impact parameters) the gluon density is generated by the 'pion cloud' of the nucleon, and can be calculated in terms of the gluon density in the pion. We investigate the large-distance behavior in two different approaches to chiral dynamics: i) phenomenological soft-pion exchange, ii) the large-N_c picture of the nucleon as a classical soliton of the pion field, which corresponds to degenerate N and Delta states. The large-distance contributions from the 'pion…
We calculate the flavor-singlet contribution to the $B\toη^{(\prime)}$ transition form factors from the gluonic content of the $η^{(\prime)}$ meson in the large-recoil region using the perturbative QCD approach. The formulation for the $η$-$η'$ mixing in the quark-flavor and singlet-octet schemes is compared, and employed to determine the chiral enhancement scales associated with the two-parton twist-3 $η^{(\prime)}$ meson distribution amplitudes. It is found that the gluonic contribution is negligible in the $B\toη$ form factors, and reaches few percents in the $B\toη'$ ones. Its impact on th…
Instanton effects can give large contribution to strong interacting processes, especially at the energy scale where perturbative QCD is no longer valid. However instanton contribution to the gluon contribution in constituent quark and nucleon has never been calculated before. Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon for the first time. We find that the pion field plays an important role in producing both the unpolarized and the polarized gluon di…
The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effecti…
Gluonic contributions to the self-energy of a nucleon have been investigated in an effective theory. The couplings of the topological charge density to nucleons give rise to OZI violating nucleon interactions. The one-loop self-energy of a nucleon arising due to these interactions have been calculated using a heavy baryon chiral perturbation theory. The divergences have been regularized using form factors. The nontrivial structure of the QCD vacuum has also been taken into account.
Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon. Our approach consists of the two main steps. At the first step, we calculate the gluon distributions inside the constituent quark generated by the perturbative quark-gluon interaction, the non-perturbative quark-gluon interaction, and the non-perturbative quark-gluon-pion anomalous chromomagnetic interaction. The non-perturbative interactions are related to the existence of the instantons, strong topologi…
A new mechanism for the pion production in the high energy reactions is suggested. It is related to the possibility for direct production of the pions induced by instantons, topologically nontrivial gluonic excitations of QCD vacuum. This mechanism does not require any fragmentation functions for production of pseudoscalar mesons in high energy reactions with hadrons. We calculate the contribution of a new mechanism to the inclusive $π^0$-meson production in high energy proton-proton collision. It is shown that it gives the dominated contribution to the inclusive cross-sections in the few GeV …
The confinement mechanism proposed earlier by the author is applied to estimate the possible parameters of the confining SU(3)-gluonic field in an $η^\prime$-meson. For this aim the electric form factor of an $η^\prime$-meson is nonperturbatively computed in an explicit analytic form. The estimates obtained are also consistent with the width of the electromagnetic decay $η^\prime\to2γ$. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the meson under consideration.
We evaluate differential distributions for exclusive scalar $f_0(1500)$ meson (glueball candidate) production. Both QCD diffractive, pion-pion meson exchange current (MEC) components as well as double-diffractive mechanism with intermediate pionic loop are calculated. The pion-pion component, which can be reliably calculated, dominates close to the threshold while the diffractive component may take over only for larger energies. At the moment only upper limit for the QCD-diffractive component can be obtained. The diffractive component is calculated based on the Khoze-Martin-Ryskin approach pro…
We calculate the matrix elements of the gluonic contributions to the energy-momentum tensor for a pion of mass 600 < Mpi < 1100 MeV in quenched lattice QCD. We find that gluons contribute (37 +/- 8 +/- 12)% of the pion's light cone momentum. The bare matrix elements corresponding to the trace anomaly contribution to the pion mass are also obtained. The discretizations of the energy-momentum tensor we use have other promising applications, ranging from calculating the origin of hadron spin to QCD thermodynamics.
We consider diagrams with up to four t-channel gluons in order to specify gluonic twist-four contributions to deep inelastic structure functions. This enables us to extend the method developed by R.K.Ellis, W.Furmanski, and R.Petronzio (EFP) to the gluonic case. The method is based on low-order Feynman diagrams in combination with a dimensional analysis. It results in explicitly gauge invariant expressions for the factorization of twist-four gluon-operator matrix elements and the corresponding coefficient functions.
The $B\to ππ$ hadronic matrix element of the chromomagnetic dipole operator $O_{8g}$ (gluonic penguin) is calculated using the QCD light-cone sum rule approach. The resulting sum rule for $<ππ|O_{8g}|B>$ contains, in addition to the $O(α_s)$ part induced by hard gluon exchanges, a contribution due to soft gluons. We find that in the limit $m_b\to \infty$ the soft-gluon contribution is suppressed as a second power of $1/m_b$ with respect to the leading-order factorizable $B\to ππ$ amplitude, whereas the hard-gluon contribution has only an $α_s$ suppression. Nevertheless, at finite $m_b$, soft a…
The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarised gluon distribution is studied in nuclei up to atomic number $A=3$ at quark masses corresponding to pion masses of $m_π\sim 450$ and $806$ MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than $\sim 10$% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combina…
The spin-independent and transversity generalised form factors (GFFs) of the $ϕ$ meson are studied using lattice QCD calculations with light quark masses corresponding to a pion mass $m_π\sim450(5)$ MeV. One transversity and three spin-independent GFFs related to the lowest moments of leading-twist spin-independent and transversity gluon distributions are obtained at six non-zero values of the momentum transfer up to 1.2 GeV$^2$. These quantities are compared with the analogous spin-independent quark GFFs and the electromagnetic form factors determined on the same lattice ensemble. The results…
We perform a perturbative QCD analysis of the gluonic gravitational form factors (GFFs) of the proton and pion at large momentum transfer. We derive the explicit factorization formula of the GFFs in terms of the distribution amplitudes of hadrons. At the leading power, we find that $A_g^π(t)=C_g^π(t)\sim 1/(-t)$ for pion, $A_g^p(t)\sim 1/(-t)^2$ and $C_g^p(t)\sim \ln^2(-t/Λ^2)/(-t)^3$ for proton, respectively, where $t$ is the momentum transfer and $Λ$ a non-perturbative scale to regulate the endpoint singularity in $C_g^p$ calculation. Our results provide a unique perspective of the momentum …
New precise data on the low energy electron-positron annihilation into hadrons from Novosibirsk are used to obtain bounds on the elasticity parameter and the difference between the phase of the pion form factor and that of pion pion scattering
The pion form factor at very large $Q^2$ is obtained by using a new pion wave function. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${α_s(Q^2)\over Q^2}$
The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pionic strong interactions is used to compute the rho-meson propagator at the two-loop level.
We study the $η'-g^*-g$ transition form factor by using the $η'$ wave function constrained by the experimental data on the $η'-γ^*-γ$ transition form factor provided by CLEO and L3 . We also take into account the contribution of the possible gluonic content of the $η'$ meson.
We investigate restrictions on the hadronic contribution to the muon $(g-2)$ factor and to the pion electromagnetic formfactor from the analytical properties of the pion formfactor and the experimental data of the pion formfactor in the space-like [1] region. The values of the pion formfactor of [1] have been improved (see Table 1) and the values of the pion formfactor have been calculated at 20 additional points (see Table 2).
The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form factor of the nucleon cannot be accessed through threshold pion electroproduction is unfounded.
A new limit of pion form factor at very large $Q^2$ is obtained by using a pion wave function determined from an effective chiral field theory of mesons. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${α_s(Q^2)\over Q^2}$.
We review the determination of the NLO Brodsky-Lepage-Mackenzie (BLM) renormalization scale for the pion transition form factor. We argue that the prediction for the pion transition form factor is independent of the factorization scale at every order in the strong coupling constant.
By reanalysing transverse momentum dependence in the perturbative calculation of pion form factor an improved expression of pion form factor which takes into account the transverse momentum dependenc in hard scattering amplitude and intrinsic transverse momentum dependence associated with pion wave functions is given to leading order, which is available for momentum transfers of the order of a few GeV as well as for $Q \to \infty$. Our scheme can be extended to evaluate the contributions to the pion form factor beyond leading order.
The pion wave function is discussed in the light of the recent CLEO data on the pion gamma transition form factor. It turns out that the wave function is close to the asymptotic form whereas wave functions strongly concentrated in the end-point regions are disfavoured. Consequences for other exclusive quantities, as for instance the pion's electromagnetic form factor, are also discussed.
We propose a perturbative evaluation for the next-to-leading-order (NLO) $O(1/Q^4)$ power correction to the photon-pion transition form factor. The effects of the NLO power correction are analyzed.
We develop a formalism to calculate form factor and charge density distribution of pion in the chiral limit using the holographic dual model of QCD with hard-wall cutoff. We introduce two conjugate pion wave functions and present analytic expressions for these functions and for the pion form factor. They allow to relate such observables as the pion decay constant and the pion charge electric radius to the values of chiral condensate and hard-wall cutoff scale. The evolution of the pion form factor to large values of the momentum transfer is discussed, and results are compared to existing exper…
We calculate electromagnetic pion form factors with an analytic model for $α_{\rm s}(Q^2)$ which is infrared (IR) finite without invoking a ``freezing'' hypothesis. We show that for the asymptotic pion distribution amplitude, $F_{π^{0}γ^{*}γ}$ agrees well with the data, whereas the IR-enhanced hard contribution to $F_π$ and the soft (nonfactorizing) part can jointly account for the data.
The light-front approach is applied to calculate the electromagnetic current for quark-antiquark bound states for the pion. The pion electromagnetic form factor is obtnaide from the "+" and "-" components of the electromagnetic current in the Drell-Yan frame, with different models of the pi-q\bar{q} vertex and the results for the pion electromagnetic form factor are compared with the experimental data up to 10 [GeV/c]^2 and anothers hadronic models. The rotational symmetry propreties of the pion electromagnetic current related with the zero-modes in the light-front are investigate.
We study the pion Distribution Amplitude (πDA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained πDA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This πDA is applied to leading order and next-to-leading order calculations of the pion-photon transition form factor. Implications of the results are…
In holographic QCD the effects of gluonic condensate can be encoded in a suitable deformation of the 5D metric. We develop two different methods for the evaluation of first order perturbative corrections to masses and decay constants of vector resonances in 5D Hard-Wall models of QCD due to small deformations of the metric. They are extracted either from a novel compact form for the first order correction to the vector two-point function, or from perturbation theory for vector bound-state eigenfunctions: the equivalence of the two methods is shown. Our procedures are then applied to flat and t…
We review a nonlocal-condensate approach and its application in QCD sum rules for the spacelike electromagnetic pion form factor. It is shown that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor.
Using the results recently obtained for the non-forward quark and gluon impact factors, it is shown that their form in the gluon colour channel is consistent with the ``third bootstrap condition'', namely, that they should be proportional to the gluon wave function. The gluon wave function found from this assumption is used to write the full bootstrap condition for the gluonic potential in the next-to-leading order.
An overview on chiral perturbation theory calculations of form factors is presented. The main focus is given on the form factors related to the lightest meson, pion, namely: pion decay constant, pion vector and scalar form factor, radiative pion decay and transition form factor. A pure calculation within the effective theory can be extended using further methods, as resonance chiral theory and leading logarithm calculations.
The behavior of the transition pion form factor for processes γ^*γ-> π^0 and γ^* γ^* -> π^0 at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pio…
The first three coefficients of the Taylor's series expansion of the vector pion form factor as a function of the momentum transfer are evaluated using experimental data on the pion form factor and the P-wave pi pi phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons these results with Chiral Perturbation Theory and unitarized models are given.
We study the pion form factor in a broad range of spacelike momentum transfers within the local-duality version of QCD sum rules. We make use of the recently calculated two-loop double spectral density of the $<AVA>$ correlator including O(1) and $O(α_s)$ terms, which allows us to give predictions for the pion form factor and to study the interplay between the nonperturbative and perturbative contributions to the pion form factor without any reference to the pion distribution amplitude. Our results demonstrate the dominance of the nonperturbative contribution to the form factor up to relativel…
The holographic QCD prediction for the pion distribution amplitude (DA) $ϕ_{hol}(u)$ is used to compute the pion spacelike electromagnetic form factor $F_π(Q^2)$ within the QCD light-cone sum rule method. In calculations the pion's renormalon-based model twist-4 DA, as well as the asymptotic twist-4 DA are employed. Obtained theoretical predictions are compared with experimental data and with results of the holographic QCD.
We study the form factors of the low energy anomalous pion-2-photon and photon-3-pion processes in the nonlocal chiral quark model which incorporates the momentum dependence of the dynamical quark mass and realizes correctly the chiral symmetries. The obtained slope parameter for pion-2-photon is in reasonable agreement with the direct experimental results but smaller than the ones invoking vector meson dominance. Our result for the photon-3-pion form factor interpolates between the two extremes of theoretical approaches, with the largest one provided by the vector meson dominance and the smal…
