Holographic QCD provides a unique framework in which to compute QCD observables. In this talk we summarize recent numerical work on computing the pion electromagnetic form factor using an AdS/QCD action that includes both spontaneous and explicit chiral symmetry breaking. We consider both hard- and soft-wall model results and develop an intermediate background that supports the best features of both. We also begin to see possible evidence in the fit for the presence of 1/N_c corrections.
We study the generalized parton distributions (GPDs) of pion for non-zero skewness by considering the leading $| q \bar{q} \rangle$ Fock state component. Inspired from AdS/QCD light-front wave functions, we calculate the pion GPDs. By taking the Fourier transforms we obtain the results for impact-parameter dependent parton distribution functions (ipdpdf) and for GPDs in longitudinal boost-invariant space. We also calculate the charge density and gravitational form factor of the pion. The pion unpolarized transverse momentum distribution (TMD) have also been calculated. The results provide rich…
We study the internal structure of the pion using a model inspired by the AdS/QCD correspondence. The holographic approach provides the light-front wave function (LFWF) for the leading Fock state component of the pion. We adopt two different forms for the LFWF derived from the AdS/QCD soft-wall model, with free parameters fitted to the available experimental information on the pion electromagnetic form factor and the leading-twist parton distribution function. The intrinsic scale of the model is taken as an additional fit parameter. Within this framework, we provide predictions for the unpolar…
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…
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.
This paper focuses on some issues about condensates and renormalization in AdS/QCD models. In particular we consider the consistency of the AdS/QCD approach for scale dependent quantities as the chiral condensate questioned in some recent papers and the 4D meaning of the 5D cosmological constant in a model in which the QCD is dual to a 5D gravity theory. We will be able to give some arguments that the cosmological constant is related to the QCD gluon condensate.
Pion Compton scattering is studied in perturbative QCD for real and space--like initial photons. Different methods for the convolution of the hard amplitude with the pion wave--functions, which have in the past led to conflicting results, are compared.
Using light-front holography, we predict simultaneously the pion decay constant and the pion charge radius by taking into account (higher twist) dynamical spin effects whose relative importance is constrained by QCD.
The coupling constant of g_phi-pion-gamma decay is calculated using light cone QCD sum rules. A comparison of our result with the ones existing in the literature is presented.
We calculate the stress tensor, or energy-momentum tensor, form factors of the pion and of axial vector mesons in the chiral limit of a hard wall AdS/CFT model of QCD. One (of the two) pion gravitational form factors is directly related to the second moment of the pion generalized parton distribution, thus providing a sum rule for the latter. As was also the case for vector mesons, both the pion and the axial vector mesons appear strikingly more compact measured by the gravitational form factor than by the electromagnetic form factor.
We calculate the leading twist valence quark distribution in the pion in the franework of QCD sum rules with nonlocal condensates. Particular attention has been paid to the correct account of the bilocal power corrections.
AdS/QCD is an extra-dimensional approach to modeling the light hadronic resonances in QCD. AdS/QCD models are generally successful at reproducing low-energy observables with around 10-20% accuracy, depending on the details of the model. We discuss the motivation for these models, their intrinsic limitations, and some recent results.
We report that the pion radius, decay constant, EM and transition form factors can simultaneously and accurately be predicted in light-front holographic QCD with a universal AdS/QCD mass scale, provided dynamical spin effects are taken into account.
We calculate the leading twist valence quark distribution in the pion in the framework of QCD sum rules with nonlocal condensates. Particular attention has been paid to the correct account for the bilocal power corrections.
We compare two approaches to the description of pion Compton scattering at moderate momentum transfer, one being based on local duality QCD sum rules for the invariant amplitudes of the process, which have been derived recently, and the other on the modified factorization formula with Sudakov effects included. We find that perturbative QCD predictions are dominant over those from QCD sum rules only for the scattering angle greater than 90$^o$.
Using the vacuum-to-pion matrix element of the correlation function of the interpolating fields of the two nucleons, the isospin splitting in the diagonal pion-nucleon coupling constant has been studied in the framework of the conventional QCD sum rule. Some of the implications of this splitting has also been discussed.
In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk.
The AdS/QCD holographic wave function of basis light-front quantization (BLFQ) for vector meson $J/ψ$ is applied in this manuscript. The exclusive production of $J/ψ$ in diffractive process is computed in dipole model with AdS/QCD holographic wave function. We use IP-Sat and IIM model in the calculation of the differential cross section of the dipole scattering off the proton. The prediction of AdS/QCD holographic wave function in BLFQ gives a good agreement to the experimental data.
We describe the present status of the pion distribution amplitude as it originated from two sources: (i) a nonperturbative approach, based on QCD sum rules with nonlocal condensates and (ii) a NLO QCD analysis of the CLEO data on F^{γγ^*π}(Q^2), supplemented by the recent high-precision lattice calculations of the second moment of the pion distribution amplitude.
We present a study of electroexcitation of nucleon resonances with higher spins, in a soft-wall AdS/QCD model, comparing our results with existing data from the CLAS Collaboration at JLab, from MAMI, and other experiments.
The mass spectrum of Delta resonances is compared to predictions based on three quark-model variants, to predictions assuming that chiral symmetry is restored in high-mass baryon resonances, and to predictions derived from AdS/QCD. The latter approach yields a nearly perfect agreement when the confinement property of QCD is modeled by a soft wall in AdS.
We demonstrate another success of the AdS/QCD correspondence by showing that an AdS/QCD holographic light-front wavefunction for the $ρ$ meson generates predictions for the cross-sections of diffractive $ρ$ production that are in agreement with data collected at the HERA electron-proton collider.
We derive a set of consistency conditions for the pion-baryon coupling constants in the large-N limit of QCD. The consistency conditions have a unique solution which are precisely the values for the pion-baryon coupling constants in the Skyrme model. We also prove that non-relativistic $SU(2N_f)$ spin-flavor symmetry (where $N_f$ is the number of light flavors) is a symmetry of the baryon-pion couplings in the large-N limit of QCD. The symmetry breaking corrections to the pion-baryon couplings vanish to first order in $1/N$. Consistency conditions for other couplings, such as the magnetic mome…
A modified method for calculating the pion vacuum susceptibility from an effective quark-quark interaction model is derived. Within this approach it is shown that the pion vacuum susceptibility is free of ultraviolet divergence and is much smaller than the previous estimations.
The pion electromagnetic form factor is investigated by using the dispersion relation with the superconvergence condition, which was proposed to synthesize the vector meson dominance model and QCD. The absorptive part is given as an addition of the resonance and the QCD terms, the latter being parametrized so as to realize the prediction of perturbative QCD. The experimental data are analyzed and the parameters for the QCD part, the resonance part as well, are determined. Existing experiments for the form factor are reproduced very well both for the space-like and time-like momenta.
In this article, the three point QCD sum rules is used to compute the strong coupling constants of vertices containing the strange bottomed ( charmed ) mesons with pion. The coupling constants are calculated, when both the bottom ( charm ) and pion states are off-shell. A comparison of the obtained results of coupling constants with the existing predictions is also made. Key words: strong coupling constant, meson, QCD sum rules, bottom, charm.
Differential cross sections for inclusive dijet photoproduction on a virtual pion have been calculated in next-to-leading order QCD as a function of $E_T, η$, and $x_π$. The cross sections are compared with recent ZEUS data on photoproduction of dijets with a leading neutron in the final state.
We investigate the transverse charge densities of the deuteron in a soft-wall AdS/QCD model by considering both the unpolarized and the transversely polarized cases. The deuteron form factors are derived from the soft-wall AdS/QCD model and it is shown that the calculated results agree with the phenomenological parametrization and experimental data. The transverse charge densities of the deuteron are also derived from the soft-wall AdS/QCD model, and we notice slight deviations from those of the phenomenological parametrization.
Chiral symmetry is an essential concept in understanding QCD at low energy. We treat the chiral condensate, which measures the spontaneous breaking of chiral symmetry, as a free parameter to investigate the effect of partially restored chiral symmetry on the physical quantities in the frame work of an AdS/QCD model. We observe an interesting scaling behavior among the nucleon mass, pion decay constant and chiral condensate. We propose a phenomenological way to introduce the temperature dependence of a physical quantity in the AdS/QCD model with the thermal AdS metric.
In this work, we consider an extension to the matching procedure proposed by Brodsky and de Teramond to obtain the two-body wave functions in the light-front formalism for holographic models. We compute the light-front wave function (LFWF) considering different static dilaton fields and AdS-like geometric deformations. We also prove that this procedure holds for general AdS/QCD models in asymptotically AdS geometries.
Pion parton distribution functions and pion-nucleus induced $J/ψ$ production in extended light-front holographic QCD
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；State Key Laboratory of Heavy Ion Science and Technology（重离子物理国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
The two flavour AdS/QCD, with chiral and gluon condensates, sets in the description of the pion family and its mass spectra. Using gravity-dilaton-gluon backgrounds, entropic Regge-like trajectories for the pion family are then derived. They relate the $π$ mesons underlying configurational entropy to both the pions excitation wave mode number and the pions experimental mass spectra, yielding a reliable prediction for the mass spectra of higher excitation pion modes, to be experimentally detected.
We discuss the pion and kaon distribution amplitudes up to twist-3 in the context of the random instanton vacuum (RIV). We construct explicitly the pertinent quasi-pion and quasi-kaon distributions in the RIV, and analyze them in leading order in the diluteness factor, at a resolution fixed by the inverse instanton size. The distribution amplitudes (DA) follow from the large momentum limit. The results at higher resolution are discussed using QCD evolution, and compared to their asymptotic limits and some lattice results.
We present a comparative study of nucleon structure such as electromagnetic form factors, transverse charge and magnetization densities in three different models within AdS/QCD framework.
We describe the present status of the pion distribution amplitude (DA) as it originated from several sources: (i) a nonperturbative approach, based on QCD sum rules with nonlocal condensates, (ii) an O(α_s) QCD analysis of the CLEO data on F^{γγ^*π}(Q^2) with asymptotic and renormalon models for higher twists, and (iii) recent high-precision lattice QCD calculations of the second moment of the pion DA. Then we show the comparison of the results for the pion electromagnetic form factor, obtained in analytic perturbation theory, with JLab data on F_π(Q^2). After that we introduce the improved mo…
We illustrate the general scheme of the Sum Rule (SR) method using 2D Quantum Harmonic Oscillator (2DQHO) as a toy model. We introduce correlator, related to Green function of 2DQHO, and describe the property of Asymptotic Freedom for 2DQHO. We explain how the duality conception allows one to describe excited states. Finally we present numerical results and extract some lessons to learn from our exposition. Then we switch to the QCD and show that QCD SRs supply us the method to study hadrons in non-perturbative QCD. Here the main emphasis is put on the pion and its distribution amplitude and f…
We present a study of proton GPDs in both momentum and position spaces using proton wavefunction obtained from AdS/ QCD. Here we consider the soft wall model. The results are compared with a phenomenological model of proton GPDs.
We present results of a calculation of the electromagnetic pion form factor within the framework of QCD Sum Rules with nonlocal condensates, using a perturbative spectral density which includes $O(α_s)$ contributions.
We calculate the photon emission rate and the electrical conductivity of the QGP at finite temperature and finite chemical potential using AdS/QCD approximations in an AdS Reissner Nordstrom background. To do so, we supposed the medium properties to be encoded in a geometric background. The results obtained in the hard wall and soft wall model are consistent with the observed phenomenology and they also in agree with other holographic results, as the D3/D7 or the Sakai Sugimoto models, suggesting the universality of AdS/CFT conjecture as tool to explore QCD.
We propose a model for baryons at finite temperature using AdS/QCD correspondence. In this model, we modify the AdS spacetime into the AdS-Schwarzchild spacetime and consider a couple of bulk spinors in this background. Solving this model, we get an eigenvalue equation for the baryon masses. We then investigate the effects of temperature on the baryon masses numerically, and find an interesting temperature dependence. Our result is consistent with the results from lattice QCD and other phenomenological models.
We show that AdS/QCD generates predictions for the rate of diffractive rho meson electroproduction that are in agreement with data collected at the HERA electron-proton collider.
We calculate the "pi Sigma Lambda" and "pi Sigma Sigma" coupling constants in light cone QCD sum rules for the structure "sigma_{alpha beta} gamma_5 p^alpha q^beta". A comparison of our results on these coupling constants with prediction of the SU(3) symmetry is presented.
In this manuscript, a unified approach to hadron physics from holographic point of view is described. After introduction of a general setup for meson-nucleon system based on the bottom-up approach of QCD (AdS/QCD), as an illustration, we specifically examine meson-nucleon couplings. This is an example of the notion we call "holographic unification" in hadron physics.
It is known that the short distance QCD contribution to the mass difference of pions is quadratic on the quark masses, and irrelevant with respect to the long distance part. It is also considered in the literature that its calculation contain infinities, which should be absorbed by the quark mass renormalization. Following a prescription by Craigie, Narison and Riazuddin, of a renormalization group improved perturbation theory to deal with the electromagnetic mass shift problem in QCD, we show that the short distance QCD contribution to the electroweak pion mass difference (with $m_u=m_d\neq0$…
This note focuses on the large-N behaviour of the Hard Wall model of QCD and clarifies the AdS/QCD dictionary formulated on the basis of the AdS/CFT correspondence. It is shown how short-distance studies performed in the framework of the AdS/QCD Soft Wall model allow one to determine unambiguously the chiral symmetry breaking function in the Hard Wall model. Especially, the different forms of the field/operator prescription are emphasized. The large-N behaviour of the Hard Wall model is then checked considering the vector and gravitational form factors of the pion in the chiral limit.
Using the light front wave functions for the nucleons in a quark model in AdS/QCD, we calculate the nucleon electromagnetic form factors. The flavor decompositions of the nucleon form factors are calculated from the GPDs in this model. We show that the nucleon form factors and their flavor decompositions calculated in AdS/QCD are in agreement with experimental data.
We use the functional form of the QCD running coupling to modify the conformal metric in AdS/CFT mapping the fifth-dimensional z-coordinate to the energy scale in the four-dimensional QCD. The resulting type-0 string theory in five dimensions is solved with the Nambu-Goto action giving good agreement with the Coulombic and confinement $Q \bar Q$ potential.
We use an AdS/QCD holographic wavefunction to generate predictions for the rate of diffractive ρ-meson electroproduction that are in reasonable agreement with data collected at the HERA electron-proton collider.
A fully back-reaction geometry model of AdS/QCD including the strange quark is described. We find that with the inclusion of the strange quark the impact on the metric is very small and the final predictions are changed only negligibly.
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained…
We argue that in QCD near the chiral limit, at all temperatures below the chiral phase transition, the dispersion relation of soft pions can be expressed entirely in terms of three temperature-dependent quantities: the pion screening mass, a pion decay constant, and the axial isospin susceptibility. The definitions of these quantities are given in terms of equal-time (static) correlation functions. Thus, all three quantities can be determined directly by lattice methods. The precise meaning of the Gell-Mann--Oakes--Renner relation at finite temperature is given.
The couplings of pions with lowest three doublets (0^-,1^-), (0^+,1^+) and (1^+,2^+) of heavy mesons are studied with ligh cone QCD sum rules in the leading order of heavy quark effective theory. The ambiguity due to the presence of two distinct 1^+ states are solved.
QCD sum rules are used to calculate the couplings of heavy-light quark pseudoscalar and vector mesons ($D, D^*$ and $B, B^*$) with soft pions, both for finite and infinitely heavy quark mass. The couplings are also computed in the framework of a QCD relativistic potential model; in this approach the relativistic corrections due to the light quark are relevant.
We present a study of the $N^*(1535)$ resonance electroexcitation in a soft-wall AdS/QCD model. Both the transverse $A_{1/2}^p$ and longitudinal $S_{1/2}^p$ helicity amplitudes are calculated resulting in good agreement with data and with the MAID parametrization.
We present results of a calculation of the electromagnetic pion form factor within a framework of QCD Sum Rules with nonlocal condensates and using a perturbative spectral density which includes \mathcal{O}(α_s) contributions.
We evaluate the pion-nucleon and the pion-Delta sigma terms by employing the method of quantum chromodynamics (QCD) sum rules. The obtained value of the pion-nucleon sigma term is compatible with the larger values already anticipated by the recent calculations. It is also found that the pion-Delta sigma term is as large as the pion-nucleon sigma term.
