We predict the cross-section for diffractive $ϕ$ electroproduction within the dipole model, using a holographic meson wavefunction for the $ϕ$. For the dipole cross-section, we use the Color Glass Condensate dipole model whose parameters are fitted to the latest 2015 combined HERA data on Deep Inelastic Scattering. Choosing a strange quark mass of $0.14$ GeV, we find good agreement with the available data.
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 present the first evaluation of the color dipole diffraction slope from the data on diffractive photo- and electroproduction of vector mesons. The energy and dipole size dependence of the found dipole diffraction slope are consistent with the color dipole gBFKL dynamics.
We study the diffractive electroproduction of quarkonia from quark-antiquark-gluon states in the photon wave function. We show that these states contribute to the leading-power and leading-logarithm level. We suggest the measurement of J/psi production via inelastic diffraction to study color-transparency and color-opacity effects in the diffractive gluon distribution.
We present the first evaluation of color dipole cross section from experimental data on diffractive photo- and electroproduction of vector mesons. The dipole-size and energy dependence of the found dipole cross section is consistent with expectations from the BFKL dynamics.
We use perturbative QCD and parton-hadron duality to estimate the cross sections for the diffractive electroproduction of rhoprime(1-) and rho(3-) resonances which occur in the 1.3-1.8 GeV mass interval. We present the cross sections and the ratios sigma_L/sigma_T as a function of Q^2. We compare the predictions with those for the diffractive electroproduction of rho mesons. We show how such diffractive electroproduction measurements at HERA can probe features of the perturbative QCD 'Pomeron'.
In these lectures, a simple introduction to the phenomenon of diffraction in deep inelastic scattering and its theoretical description is given. While the main focus is on the diffractive structure function F_2^D, some issues in diffractive vector meson production are also discussed.
Using a set of new odderon states, we calculate their contribution to the diffractive eta_c photo- and electroproduction process. Compared to previous simple 3-gluon exchange calculations we find an enhancement of about one order of magnitude in the cross section. The t-dependence of the cross section exhibits a dip structure in the small t region.
The electromagnetic radiative correction to the cross section of the vector meson electroproduction is calculated. Explicit covariant formulae for the observed cross section are obtained. The dependence of the radiative correction on the experimental resolution and on the inelasticity cut is discussed. FORTRAN code DIFFRAD based on both exact (ultrarelativistic) and approximate sets of the formulae for the radiative correction to the cross section is presented. The detailed numerical analysis for kinematical conditions of the recent experiments on the diffractive electroproduction of vector me…
A systematic multiple scattering formalism for vector meson electroproduction from nuclei is developed, with emphasis on the formation, propagation and hadronization scales for quark-gluon fluctuations of the virtual high-energy photon. The theory is compared to HERMES measurements of rho electroproduction on 14N. The nuclear transparency as a function of the vector meson propagation length is well reproduced.
Exclusive electroproduction of hard dijets can be described within the collinear factorization. This process has clear experimental signature and provides one with an interesting alternative venue to test QCD description of hard diffractive processes and extract information on generalized nucleon parton distributions. In this work we present detailed leading-order QCD calculations of the relevant cross sections, including longitudinal momentum fraction distribution of the dijets and their azimuthal angle dependence.
We give a general formula for the cross section for diffractive vector meson electroproduction, gamma^* p -> Vp. We first calculate diffractive qqbar production, and then use parton-hadron duality by projecting out the J^P = 1^- state in the appropriate mass interval. We compare the Q^2 dependence of the cross section for the diffractive production of rho and J/psi mesons with recent HERA data. We include the characteristic Q^2 dependence associated with the use of the skewed gluon distribution. We give predictions for sigma_L/sigma_T for both rho and J/psi production.
We study light vector meson electroproduction at small $x$ within the generalized parton distributions (GPDs) model. The modified perturbative approach is used, where the quark transverse degrees of freedom in the vector meson wave function and hard subprocess are considered. Our results on the cross section and spin observables are in good agreement with experiment
The diffractive production of high-$p_{\perp}$ jets in deep-inelastic scattering is studied in the semiclassical approach. The $p_{\perp}$-spectra of $q {\bar q}$ and $q {\bar q} g$ diffractive final states are found to be qualitatively different. For $q {\bar q}$ final states, which are produced by `hard' colour-singlet exchange, the $p_{\perp}$-spectrum is much softer than for $q {\bar q} g$ final states, where the colour neutralization is `soft'. Furthermore, the two different final states can be clearly distinguished by their diffractive mass distributions.
We extract the S-matrix element for dipole-proton scattering using the data on diffractive electroproduction of vector mesons at HERA. By considering the full t dependence of this process we are able to reliably unfold the profile of the S-matrix for impact parameter values b>0.3 fm. We show that the results depend only weakly on the choice of the form for the vector meson wave function. We relate this result to the discussion about possible saturation effects at HERA.
The interference of Pomeron and Odderon amplitudes gives rise to a charge asymmetry in the diffractive electroproduction of a pi+pi- -pair. We calculate this charge asymmetry in perturbative QCD in the Born approximation and on the leading Q^2-level. The numerical evaluation shows a sizeable asymmetry in an experimentally accessible kinematical region. We find a characteristic m_{pi+pi} -dependence mainly dictated by the relevant Breit-Wigner-amplitudes and the corresponding phase-shifts.
Charge asymmetries in diffractive electroproduction of two mesons are proportional to the interference of Pomeron and Odderon exchange amplitudes. We calculate in the framework of QCD and in the Born approximation a forward-backward charge asymmetry which turns out to be sizable in a kinematical domain accessible to HERA experiments. We predict a distinctive dependence of this asymmetry on the invariant mass of the two pions. Testing this prediction is a crucial step in the discovery of the QCD-Odderon.
We show that diffractive production of a single neutral pion in photon-induced reactions at high energy is dynamically suppressed due to the approximate chiral symmetry of QCD. These reactions have been proposed as a test of the odderon exchange mechanism. We show that the odderon contribution to the amplitude for such reactions vanishes exactly in the chiral limit. This result is obtained in a nonperturbative framework and by using PCAC relations between the amplitudes for neutral pion and axial vector current production.
Order $α_s$-corrections to the diffractive structure functions $F_L^D$ and $F_2^D$ at large $Q^2$ and small $x$ are evaluated in the semiclassical approach, where the initial proton is treated as a classical colour field. The diffractive final state contains a fast gluon in addition to a quark-antiquark pair. Two of these partons may have large transverse momentum. Our calculations lead to an intuitive picture of deep-inelastic diffractive processes which is very similar to Bjorken's aligned-jet model. Both diffractive structure functions contain leading twist contributions from high-$p_{\perp…
We study the impact of the "intrinsic" hadron transverse momentum on the pre-asymptotic behavior of the diffractive electroproduction of longitudinally polarized $ ρ$-meson. Surprisingly, we find the onset of the asymptotic regime in this problem to be rather low, Q^2 ~ 10 GeV^2 where power corrections due to the transverse momentum do not exceed 20 % in the amplitude. This drastically contrasts with exclusive amplitudes where the asymptotics starts at much higher Q^2 = 50 - 100 GeV^2. The sources of such unexpected behavior are traced back to some general (the quark-hadron duality) as well as…
We consider the process gamma^* N -> M_1 M_2 N' with a large rapidity gap between the two mesons M_1 and M_2. Within the QCD collinear approximation, the scattering amplitude may be written as a convolution of an impact factor describing the gamma^* -> M_1 transition and an amplitude describing the N -> M_2 N' collinear process.
Through a determination of the $S$-matrix element for the scattering of a localized colour dipole on a proton, we show that saturation effects can already be sizable at HERA. The saturation scale is found to be around 1-1.5 $GeV^2$ for the highest available energies and for central collisions, and is a decreasing function of the impact parameter.
We present a simple physical description of the off-diagonal gluon distribution g (x,x^\prime,Q^2) and splitting function P_{gg}(x,x^\prime) which enter the amplitude for diffractive vector meson production. We study the off-diagonal effects both on the evolution in Q^2 and on the input distribution. We predict the ratio $R$ of the off-diagonal to the diagonal gluon density, x^\prime g(x,x^\prime,Q^2)/xg(x, Q^2), as a function of the kinematic variables.
We have calculated the leading order amplitude of hard diffractive electroproduction of two pions in lepton nucleon scattering. At the leading twist level a pion pair can be produced only in an isospin one or zero state. We have shown that isoscalar states are produced dominantly for x_{Bj}>0.3 and with an invariant mass of the two pions close to the threshold (S-wave) and in the f_2 resonance region (D-wave). These isoscalar pion pairs are dominantly produced by two collinear gluons. Comparing the production of charged and neutral pion pairs as a function of x_{Bj} and m_pipi one can get info…
Hard diffractive electroproduction of longitudinally polarized vector mesons is calculated within the leading $α_s\ln{Q^2\overΛ_{QCD}^2}$ approximation of QCD using the leading order parton densities within the nucleon. Novel QCD features of the production of excited states and of the restoration of flavor symmetry are analyzed. At the onset of the asymptotic regime, our analysis finds an important role of quark Fermi motion within the diffractively produced vector mesons, and we suggest to use this effect to measure the high momentum tail of the wave function of the vector mesons. We deduce a…
We present the color dipole phenomenology of diffractive photo- and electroproduction $γ^{*} N\to V(V') N$ of vector mesons ($V(1S) = ϕ^0, ω^0, ρ^0, J/Ψ, Υ$) and their radial excitations ($V'(2S) = ϕ', ω', ρ', Ψ', Υ'$). The main emphasis is related to light vector mesons. We discuss how the energy dependence of the color dipole cross section in conjuction with the node of the radial wave function of the $2S$ states can lead to an anomalous $Q^2$ and energy dependence of diffractive production of $V'(2S)$ vector mesons. The color dipole model predictions for $V(1S)$ light vector meson productio…
Diffractive production of $J/Ψ$ particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importa…
We study in perturbative QCD the helicity ampltiudes of the process $γ^{*} p \to ρp $ at large virtualities $Q$ of the photon $γ^{*}$. We estimate all spin flip amplitudes taking into account an important effect of the scale behaviour of the gluon density. The transition of a transverse virtual photon to a longitudinal vector meson is not small at typical HERA conditions. This helicity non-conserving amplitude leads by interference to a measurable effect in the distribution of the angle between the electron scattering and the meson production planes.
We critically review the QCD predictions for the cross sections sigma_L and sigma_T for diffractive rho meson electroproduction in longitudinally and transversely polarised states in the HERA energy region. We show that both perturbative and non-perturbative approaches which involve convolution with the rho meson wave function predict values of sigma_T which fall-off too quickly with increasing Q^2, in comparison with the data. We present a perturbative QCD model based on the open production of light qqbar pairs and parton-hadron duality, which describes all features of the data for rho electr…
Diffractive production of J/Psi particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importa…
We determine the leading Fock-state light front wave functions (LF-LFWFs) of the $ρ$ and J/$ψ$ mesons, for the first time from the Dyson-Schwinger and Bethe-Salpeter equations (DS-BSEs) approach. A unique advantage of this method is that it renders a direct extraction of LF-LFWFs in presence of a number of higher Fock-states. Modulated by the current quark mass and driven by the dynamical chiral symmetry breaking (DCSB), we find the $ρ$ and $J/ψ$ LF-LFWFs different in profile, i.e., the former are broadly distributed in $x$ (the longitudinal light-cone momentum fraction of meson carried by qua…
Hard diffractive photo- and electroproduction of heavy vector mesons ($J/ψ$ and $Υ$) is evaluated within the leading $α_s\ln{Q^2 \overΛ_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a sig…
We develop the color dipole phenomenology of diffractive photo- and electroproduction $γ^{*}\,N\rightarrow V(V')\,N$ of light vector mesons ($V(1S) = ϕ^0, ω^0, ρ^0$) and their radial excitations ($V'(2S) = ϕ', ω', ρ'$). The node of the radial wave function of the $2S$ states in conjunction with the energy dependence of the color dipole cross section is shown to lead to a strikingly different $Q^2$ and $ν$ dependence of diffractive production of the $V(1S)$ and $V'(2S)$ vector mesons. We discuss the restoration of flavor symmetry and universality properties of production of different vector mes…
A Dyson-Schwinger-based model of pomeron exchange is employed to calculate diffractive rho-, phi- and J/psi-meson electroproduction cross sections. It is shown that the magnitude of the current-quark mass m_f of the quark and antiquark inside the produced vector meson determines the onset of the asymptotic-q^2 power-law behavior of the cross section, and how correlated quark-exchanges are included to provide a complete picture of the diffractive electroproduction of light vector mesons applicable over all energies and photon momenta q^2.
We consider the electroproduction of two vector mesons with a large rapidity gap between them on a nucleon target in the process $ γ^* N \to ρ_1 ρ_2 N'$. We calculate the Born term for this process within the collinear factorization framework. The resulting scattering amplitude may be represented as a convolution of an impact factor describing the $γ^* \to ρ_1$ transition and an amplitude describing the $N\to ρ_2 N'$ transition. The latter amplitude is analogous to deeply virtual electroproduction of a meson, the virtual photon being replaced by two gluon (Pomeron) exchange . The long distance…
The ``asymmetric'' matrix element <p-r|G...G|p> that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f_g(x). I outline a pQCD formalism based on a concept of the double distribution F_g(x,y), which specifies the fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. For $t \equiv r^2 =0$, r is proportional to p: $r = ζp$, and it is convenient to parameterize the matrix element <p-r|G...G|p> by an asymmetric distribution function ${\cal F}_ζ^g …
We studied the $ep\rightarrow ep+2jets$ diffractive cross section with ZEUS phase space. Neglecting the $t$-channel momentum in the Born and gluon dipole impact factors, we calculated the corresponding contributions to the cross section differential in $β=\frac{Q^{2}}{Q^{2}+M_{2jets}^{2}}$ and the angle $ϕ$ between the leptonic and hadronic planes. The gluon dipole contribution was obtained in the exclusive $k_{t}$-algorithm with the exclusive cut $y_{cut}=0.15$ in the small $y_{cut}$ approximation. In the collinear approximation we canceled singularities between real and virtual contributions…
Within the color dipole gBFKL dynamics applied to the diffraction slope we predict an anomalous t dependence of the differential cross section as a function of energy and Q^2 for production of radially excited V'(2S) light vector mesons in contradiction with a well known standard monotonous t- behaviour for V(1S) mesons. The origin of this phenomenon is based on the interplay of the nodal structure of V'(2S) radial wave function with the energy and dipole size dependence of the color dipole cross section and of the diffraction slope. We present how a different position of the node in V'(2S) wa…
In this work we present for the first time the comprehensive study of the Melosh spin rotation effects in diffractive electroproduction of S-wave heavy quarkonia off a nucleon target. Such a study has been performed within the color dipole approach using, as an example and a reference point, two popular parametrizations of the dipole cross section and two potentials describing the interaction between Q and bar{Q} and entering in the Schroedinger equation based formalism for determination of the quarkonia wave functions. We find a strong onset of spin rotation effects in 1S charmonium photoprod…
We argue that study of the cross section of coherent photo(electro) production of $ρ,ρ^{\prime}, ...$-mesons provides an effective method to probe onset of black body limit(BBL) in the soft and hard QCD interactions. We illustrate the expected features of the onset of BBL using generalized vector dominance model(GVDM). We show that this model describes very well $ρ$-meson coherent photoproduction at $6 \leq E_γ \leq 10$ GeV. The advantages of the process of coherent dijet production and hard diffractive processes in general for probing the onset of BBL and measuring the light-cone wave functio…
The processes of exclusive diffractive scattering $p+p\to p+p$, $\bar p+p\to\bar p+p$, and $γ^*+p\to V+p$ at high energies are considered in the framework of a unified Regge-eikonal model with a very simple reggeon structure of the eikonal. It is demonstrated that the pomeron trajectory is universal in all reactions and having intercept about 1.31 which could be exctracted explicitly from the data on the proton structure function $F_2(x,Q^2)$. The predictions for the proton-proton cross-sections at LHC energies are given.
Transversity generalized parton distributions (GPDs) can be probed in diffractive electro- and photoproduction of two vector mesons on a hadron in kinematics where the two vector mesons are separated by a large rapidity gap. We report on calculations for this process in the case of coherent $ρ^0-ω$ meson production on a deuteron target. Our cross section results show that an electron-ion collider with deuteron beams and forward detectors could probe deuteron transversity GPDs.
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 calculate $p_T$-dependences of diffractive vector meson photo- and electroproduction in electron-proton collisions with and without proton dissociation at small momenta transfers. The calculated slopes are in good agreement with the data.
The backgrounds due to the direct diffractive dissociation of the photon into the $π^+π^-$ as well as $K^+K^-$ pairs to the "elastic" diffractive $ρ'$ and $ϕ$ mesons production in electron-proton collisions are calculated. It is shown that the role of background and background-resonant interference contributions is very important in experimental distribution of $M_{π^+ π^-}$ in the $ρ'$ mass region. The amplitude for the background process is proportional to the $π$-meson - proton or K-meson - proton cross sections. Therefore, describing the HERA data, one can estimate $σ(πp)$ and $σ(Kp)$ at e…
We reexamine the Fermi motion effects on the diffractive photo- and electroproductions of heavy vector-mesons, J/psi and psi', off a nucleon in the leading ln(Q^2/Lambda_QCD^2) approximation (LLA) of QCD. We take into account all the Fermi motion corrections arising from the relative motion of quarks inside the charmonium, which is treated as a nonrelativistic bound state of c and \bar{c}. Our key ingredients are the correct spin structure for the ^3S_1 c\bar{c} bound state, the off-shellness in the c\bar{c} \to J/psi (psi') hadronization vertex, and the modification of the gluon's longitudina…
We compute the rate for diffractive $ϕ$ electro-production using the Color Glass Condensate dipole model. The model parameters are obtained from fits to the most recent combined HERA data on inclusive deep inelastic scattering. As for the $ϕ$ meson, we use an AdS/QCD holographic light front wavefunction. Our predictions are compared to the available data collected at the HERA collider.
The end-point contributions in the quark longitudinal momentum fraction of the virtual photon ($γ^*$) to vector meson ($V$) impact factor to the diffractive electroproduction amplitude can be factorized in terms of a generalized parton evolution of the target parton distribution. The result is used to model the helicity amplitudes $γ^* p \to V p$ in terms of small $x$ generalized parton distributions.
Exclusive diffractive processes on the nucleon are investigated within a model in which the quark-nucleon interaction is mediated by Pomeron exchange and the quark substructure of mesons is described within a framework based on the Dyson-Schwinger equations of QCD. The model quark-nucleon interaction has four parameters which are completely determined by high-energy $πN$ and $K N$ elastic scattering data. The model is then used to predict vector-meson electroproduction observables. The obtained $ρ$- and $ϕ$-meson electroproduction cross sections are in excellent agreement with experimental dat…
A two-component model is developed for diffractive electroproduction of $ρ^0$, $ϕ$ and $\jpsi$, based on non-perturbative and perturbative two-gluon exchange. This provides a common kinematical structure for non-perturbative and perturbative effects, and allows the role of the vector-meson vertex functions to be explored independently of the production dynamics. A good global description of the vector-meson data is obtained.
The differential cross section $dσ/dq^2$ of diffractive electroproduction of heavy quarkonia on protons is a sensitive study tool for the interaction dynamics within the dipole representation. Knowledge of the transverse momentum transfer $\vec q$ provides a unique opportunity to identify the reaction plane, due to a strong correlation between the directions of $\vec q$ and impact parameter $\vec b$. On top of that, the elastic dipole-proton amplitude is subject to a strong correlation between $\vec b$ and dipole orientation $\vec r$. Most of models for $b$-dependent dipole cross section eithe…
We report on the results of our recent research published in [1] that shows that AdS/QCD generates predictions for the rate of diffractive ρ-meson electroproduction that are in agreement with data collected at the HERA electron-proton collider [2,3]. Preliminary results of this research were presented in [4].
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $ρ$ and $ϕ$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $ρ$ and $ϕ$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $ρ$ and $ϕ$ production data provided we use a set of light quark masses …
We investigate the momentum transfer dependence of differential cross sections $dσ/dt$ in diffractive electroproduction of heavy quarkonia on proton targets. Model predictions for $dσ/dt$ within the light-front QCD dipole formalism are based on a realistic model for a proper correlation between the impact parameter $\vec b$ of a collision and color dipole orientation $\vec r$. We demonstrate a significance of $\vec b-\vec r$ correlation by comparing with a standard simplification $\vec{b}\parallel\vec{r}$, frequently used in the literature.
We present the calculation of the impact factor for the $γ^{(*)}\to q\bar{q}$ transition with one loop accuracy in arbitrary kinematics. The calculation was done within Balitsky's high energy operator expansion. Together with our previous result for the $γ^{(*)}\to q\bar{q} g$ Born impact factor it allows one to derive cross-sections for 2- (one loop) and 3-jet (Born) difractive electroproduction. We write such cross sections for the 2 and 3 jet exclusive diffractive electroproduction off a proton in terms of hadronic matrix elements of Wilson lines. For the 2-jet cross section we demonstrate …
We study Pomeron-Odderon interference effects giving rise to charge and single-spin asymmetries in diffractive electroproduction of a $π^+ π^-$ pair. The final state interactions and the role of $f_0$ meson are discussed. The absence of $f_0$ signal in the charge asymmetry observed by HERMES may be due to the smalness of its quark component.
We compute the exclusive electroproduction, $γ^* p \rightarrow V p$, of heavy quarkonia $V$ to NLO in the collinear factorisation scheme, which has been formally proven for this process. The inclusion of an off-shell virtuality $Q^2$ carried by the photon extends the photoproduction phase space of the exclusive heavy quarkonia observable to electroproduction kinematics. This process is relevant for diffractive scattering at HERA and the upcoming EIC, as well as at the proposed LHeC and FCC.
One of the challenging aspects of electroproduction at high-energy is the understanding of the transition from real photons to virtual photons in the GeV^2 region. We study inclusive electroproduction on the proton at small x_B using a nonperturbative dipole-proton cross section calculated from the gauge invariant gluon field correlators as input. By quark-hadron duality, we construct a photon light cone wave function which links the ``hadronic'' behavior at small Q^2 to the ``perturbative'' behavior at large Q^2. It contains quark masses which implement the transition from constituent quarks …
We present a detailed comparison of a variety of predictions for diffractive light vector meson production with the data collected at the HERA collider. All our calculations are performed within a dipole model framework and make use of different models for the meson light-cone wavefunction. There are no free parameters in any of the scenarios we consider. Generally we find good agreement with the data using rather simple Gaussian motivated wavefunctions in conjunction with dipole cross-sections which have been fitted to other data.
