The quantum field theoretic treatment of inclusive deep--inelastic diffractive scattering given in a previous paper \cite{BGR2006} is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. We consider the off-cone twist--2 light-cone operators to derive the target mass and finite $t$ corrections to diffractive deep--inelastic scattering and deep--inelastic scattering. The corrections turn out to be at most proportional to $x |t|/Q^2, x M^2/Q^2, x = x_{\rm BJ} {\rm or} x_\PP$, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson--exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit $t, M^2 \to 0$ one obtains the results of \cite{Blumlein:2001xf} and \cite{Blumlein:2002fw}.
Diffractive deeply inelastic scattering from a hadron is described in terms of diffractive quark and gluon distributions. If the transverse size of the hadronic state is sufficiently small, these distributions are calculable using perturbation theory. We present such a calculation and discuss the underlying dynamics. We comment on the relation between this dynamics and the pattern of scaling violation observed in the hard diffraction of large-size states at HERA.
The measurement of the total $pp$ cross section and its various sub-components (elastic, inelastic and diffractive) is a very powerful tool to understand the proton macro structure and fundamental QCD dynamics. In this contribution I first provide a theoretical introduction to the topic, then a summary of the experimental techniques and finally I review the new results from AUGER and LHC experiments.
The recent data from H1 Collaboration on hadron multiplicity in diffractive DIS has been studied in the framework of perturbative QCD as a function of invariant diffractive mass. The formulas obtained explain the observed excess of particle production in diffractive DIS relative to that in DIS and $e^+e^-$ annihilation. It is shown that the results are sensitive to the quark--gluon structure of the Pomeron. Namely, the data say in favour of a super-hard gluon distribution at the initial scale.
Hard processes in diffractive deep-inelastic scattering can be described by a factorisation into parton-level subprocesses and diffractive parton distributions. In this framework, cross sections for inclusive dijet production in diffractive deep-inelastic electron-proton scattering (DIS) are computed to next-to-next-to-leading order (NNLO) QCD accuracy and compared to a comprehensive selection of data. Predictions for the total cross sections, 39 single-differential and four double-differential distributions for six measurements at HERA by the H1 and ZEUS collaborations are calculated. In the …
Diffractive deeply virtual Compton scattering (DiDVCS) is the process $γ^*(- Q^2) + N \rightarrow ρ^0 + γ^* (Q'^2)+ N'$, where N is a nucleon or light nucleus, in the kinematical regime of large rapidity gap between the $ρ^0$ and the final photon-nucleus system, and in the generalized Bjorken regime where both photon virtualities $Q^2$ and $ Q'^2$ are large. We show that this process has the unique virtue of combining the large diffractive cross sections at high energy with the tomographic ability of deeply virtual Compton scattering to scrutinize the quark and gluon content of nucleons and li…
We further analyze the holographic dipole-dipole scattering amplitude developed in arXiv:1202.0831, 1205.3223. Gribov diffusion at strong coupling yields the scattering amplitude in a confining background. We compare the holographic result for the differential cross section to proton-proton and deeply virtual Compton scattering data.
We discuss the high-energy dependencies of diffractive and non-diffractive inelastic cross-sections in view of the recent LHC data which revealed a presence of the reflective scattering mode.
The distribution of a suitably defined azimuthal angle in diffractive deep inelastic scattering contains information on the polarisation of the exchanged photon. In particular it allows one to constrain the longitudinal diffractive structure function. We investigate the potential of such bounds in general and for particular diffractive final states.
We analyse the newest diffractive deep inelastic scattering data from the DESY collider HERA with the help of dipole models. We find good agreement with the data on the diffractive structure functions provided the diffractive open charm contribution is taken into account. However, the region of large diffractive mass (small values of a parameter beta) needs some refinement with the help of an additional gluon radiation.
We suggest a simple physical picture for the diffractive parton distributions that appear in diffractive deeply inelastic scattering. In this picture, partons impinging on the proton can have any transverse separation, but only when the separation is small can they penetrate the proton without breaking it up. By comparing the predictions from this picture with the diffractive data from HERA, we determine rough values for the small separations that dominate the diffraction process.
The impact of nonlinear effects in the diffractive observables that will be measured in future electron-ion collisions is investigated. We present, for the first time, the predictions for the diffractive structure function and reduced cross sections derived using the solution to the Balitsky--Kovchegov equation with the collinearly-improved kernel and including the impact-parameter dependence. We demonstrate that the contribution of the diffractive events is enhanced in nuclear collisions and that the study of the ratio between the nuclear and proton predictions will be useful to discriminate …
The contribution of subleading reggeons to the diffractive structure function ${dF_{2}^D / dx_{\funp} dt}$ is estimated from the soft physics data. This contribution leads in a natural way to the violation of the factorization property of the diffractive structure function.
Polarized inclusive deep-inelastic diffractive scattering is dealt with in a quantum field theoretic approach. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region applying the generalized optical theorem. The diffractive structure functions $g_1^{D(3)}$ and $g_2^{D(3)}$ are calculated in the twist-2 approximation and are expressed by diffractive parton distributions, which are derived from pseudo-scalar two-variable operator expectation values. In this approximation the structure functions $g…
A Pomeron model applicable to both "`soft" and "hard" processes is suggested and tested against the high-energy data from virtual photon-induced reactions. The Pomeron is universal, containing two terms, a "soft" and a "hard" one, whose relative weight varies with $\widetilde {Q^2}=Q^2+M_V^2$, where $Q^2$ is the virtuality of the incoming photon and $M_V$ is the mass of the produced vector particle. With a small number of adjustable parameters, the model fits all available data on vector meson production and deeply virtual Compton scattering from HERA. Furthermore, we attempt to apply the mode…
We report on our recent observation that the occurrence of diffractive patterns in the scattering of electrons off nuclei obeys the same law as the fluctuations of the height of genealogical trees in branching diffusion processes.
We study the contribution of diffractive $Q \bar Q$ production to the $F_2^D$ proton structure function and the longitudinal double-spin asymmetry in polarized deep--inelastic $lp$ scattering. We show the strong dependence of the $F_2^D$ structure function and the $A_{ll}$ asymmetry on the quark--pomeron coupling structure.
We derive helicity amplitudes for diffractive leptoproduction of the S and D wave states of vector mesons. We predict a dramatically different spin dependence for production of the S and D wave vector mesons. We find very small $R=σ_{L}/σ_{T}$ and abnormally large higher twist effects in production of longitudinally polarized D-wave vector mesons.
We discuss the contribution of diffractive $Q \bar Q$ production to the longitudinal double-spin asymmetry in polarized deep--inelastic $lp$ scattering. We show the strong dependence of the $A_{ll}$ asymmetry on the pomeron spin structure.
Diffractive deep inelastic events with a large rapidity gap are analyzed by using a Regge model for the pomeron flux and a gluonic content for the pomeron. Contrary to the expectations, the simplest assumption for the pomeron trajectory gives the best agreement with the data on the ratio of diffractive to the total number of events. In this case the main properties of the model are described by an analytic expression.
Recent experimental data on diffractive deep inelastic scattering collected by the H1 and ZEUS Collaborations at HERA are analysed in a model with a non-linear trajectory in the pomeron flux. The $t$ dependence of the diffractive structure function $F_2^{D(4)}$ is predicted. The normalization of the pomeron flux and the (weak) $Q^2$ dependence of the pomeron structure function are revised as well.
The diffractive open charm production is computed in perturbative QCD formalism and in the Regge approach. The results are compared with recent data on charm diffractive structure function measured at DESY-HERA. Our results demonstrate that this observable can be useful to discriminate the QCD dynamics.
We present the first study of the QCD corrections to the color-singlet (CS) $J/ψ$ production in deeply inelastic $ep$ scattering at HERA. The $K$-factor ranges from $0.85$ to $2.38$ in the kinematic regions we study. In low transverse momentum regions, the $K$-factors is even smaller, and close to 1, which indicates good convergence of the perturbative expansion. With the QCD corrections, the CS cross section is still below the data. At least at QCD next-to-leading order, the color-octet mechanism is necessary to describe the data.
The QCD analysis of deep inelastic diffractive scattering is performed assuming the dominance of the "soft" pomeron exchange and simple, physically motivated parametrization of parton distributions in a pomeron. Results of the analysis are compared with the recent data obtained by the H1 collaboration at HERA. Both the LO and NLO approximations are considered and the theoretical predictions concerning the quantity $R=F_L^D/F_T^D$ for diffractive structure functions are presented.
A brief review on the status of unpolarized parton densities and the determination of the QCD scale $Λ_{\rm QCD}$ from deep-inelastic scattering data is presented.
We consider the production of charm by real and virtual photons. Special attention is paid to diffractive charm production, which provides information on the gluonic content of the Pomeron. Our calculations are based on the gluon distributions of the CKMT-model, which is shown to lead to agreement with the data on open charm production in deep inelastic scattering. We compare predictions for diffractive charm production of different models for the distribution of gluons in the Pomeron. Experiments at HERA should be able to discriminate between them. Predictions for beauty production in diffrac…
The charm contribution to the structure functions of diffractive deep inelastic scattering is considered here within the context of the Ingelman-Schlein model. Numerical estimations of this contribution are made from parametrizations of the HERA data. Influence of the Pomeron flux factor is analized as well as the effect of the shape of the initial parton distribution employed in the calculations. The obtained results indicate that the charm contribution to diffractive deep inelastic process might be large enough to be measured in the HERA experiments.
We analyse the dissociation of a photon in diffractive deep inelastic scattering in the kinematic regime where the diffractive mass is much bigger than the photon virtuality. We consider the dominant q\bar{q}g component keeping track of the transverse momentum of the gluon which can be measured as a final-state jet. We show that the diffractive gluon-jet production cross-section is strongly sensitive to unitarity constraints. In particular, in a model with parton saturation, this cross-section is sensitive to the scale at which unitarity effects become important, the saturation scale. We argue…
We successfully describe the HERA-data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $ep$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of $Q^2$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.
In this paper we propose the study of the diffractive quarkonium photoproduction in $pp$ collisions at LHC energies to probe the photon flux associated to a ultrarelativistic proton. The total photon distribution is expected to be given in terms of the elastic and inelastic components. Distinctly from the elastic photon component which can be determined from the elastic form factors, the magnitude of the inelastic component still is an open question. We consider the current parametrizations for the photon distribution of a proton and estimate the rapidity distributions and total cross sections…
The nucleon structure functions probed in deep-inelastic scattering at large virtualities form an important tool to test Quantum Chromdynamics (QCD) through precision measurements of the strong coupling constant $α_s(M_Z^2)$ and the different parton distribution functions. The exact knowledge of these quantities is also of importance for all precision measurements at hadron colliders. During the last two decades very significant progress has been made in performing precision calculations. We review the theoretical status reached for both unpolarized and polarized lepton-hadron scattering based…
Following recent progresses in the understanding of high-energy scattering in QCD, we derive the first phenomenological consequences of Pomeron loops, in the context of both inclusive and diffractive deep inelastic scattering. In particular, we discuss diffusive scaling, a new scaling law that emerges for sufficiently high energies and up to very large values of $Q^2,$ well above the proton saturation momentum.
The geometric scaling property observed in the HERA data at small x, that the deep inelastic scattering (DIS) total cross-section is a function of only the variable Q^2*x^λ, has been argued to be a manifestation of the saturation regime of QCD and of the saturation scale Q^2_s(x) x^{-λ}. We show that this implies a similar scaling in the context of diffractive DIS and we observe, for several diffractive observables, that the experimental data from HERA confirm the expectations of this scaling.
We perform a novel type of analysis of diffractive deep-inelastic scattering data, in which the input parton distributions of the Pomeron are parameterised using the perturbative QCD expressions. In particular, we treat individually the components of the Pomeron of different size. We are able to describe simultaneously both the recent ZEUS and H1 diffractive data. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks.
In the framework of Anisotropic Chromo Dynamics, a non-perturbative model of QCD based on magnetic condensation in the vacuum, we develope a picture of the Pomeron. Within this model we are able to calculate the diffractive contribution to deep inelastic scattering in the small Bjorken x region, actually probed at Hera. We calculate the diffractive structure function of the proton and make the comparison with the experimental data of Zeus and H1 collaborations. Good agreement with the experimental data, both for the diffractive structure function $F_2^D$ and for the ''structure function'' of t…
Inspired by a recent study of Iancu, Mueller and Triantafyllopoulos [1] and earlier papers by Golec-Biernat and Wusthoff [2,3], we propose semi-inclusive diffractive deep inelastic scattering (SIDDIS) to investigate the gluon tomography in the nucleon and nuclei at small-$x$. The relevant diffractive quark and gluon parton distribution functions (DPDF) can be computed in terms of the color dipole S-matrices in the fundamental and adjoint representations, respectively. Novel correlations from the gluon tomography in the dipole S-matrix can be experimentally studied through the DPDFs in these pr…
Predictions for deep Virtual Compton Scattering are obtained in a two-component dipole model of diffraction. The model automatically includes hard and soft components and implicitly allows for ``hadronic'' contributions via large dipoles. It is also applicable to real Compton Scattering, which provides an important constraint.
We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($γ^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector $\r$ and the dipole impact parameter $\b$. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $γ^{(*)}$-h collisi…
Shadowing effects in deep-inelastic lepton-nucleus scattering probe the mass spectrum of diffractive leptoproduction from individual nucleons. We explore this relationship using current experimental information on both processes. In recent data from the NMC and E665 collaboration, taken at small x << 0.1 and Q^2 < 1 GeV^2, shadowing is dominated by the diffractive excitation and coherent interaction of low mass vector mesons. If shadowing is explored at small x << 0.1 but large Q^2 >> 1 GeV^2 as discussed at HERA, the situation is different. Here dominant contributions come from the coherent i…
In the context of both inclusive and diffractive deep inelastic scattering, we derive the first phenomenological consequences of the inclusion of Pomeron loops in the QCD evolution equations towards high energy. We discuss the transition between the well-known geometric scaling regime and the new diffusive scaling, that emerges for sufficiently high energies and up to very large values of Q^2, well above the proton saturation momentum.
Polarized inclusive deep-inelastic scattering is formulated in the light cone expansion. The QCD evolution of the leading twist distribution functions is derived. It is shown that the twist--2 contribution to the structure functions g_2^{D(3)} is obtained via g_1^{D(3)} by a Wandzura--Wilczek relation.
In this paper we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio $σ^{diff}/σ^{tot}$ and predict the $x_{\pom}$ and $β$ behavior of the nuclear diffractive structure function $F_{2,A}^{D(3)}(Q^2, β, x_{IP})$. Moreover, we analyze the ratio $R^{diff}_{A1,A2}(Q^2, β, x_{IP}) = F_{2,A1} ^{D(3)}/F_{2,A2} ^{D(3)}$, which probes the nuclear dependence of the structure of the Pomeron. We show that saturation physics predicts that approximately 37 % of the events observed at eRHIC should be diffractive.
We present the microscopic QCD evaluation of the secondary reggeon contribution to diffractive DIS. It is shown that the interference between Pomeron and Reggeon enters in the maximal possible way. In the region of large $β\simeq 1$ it is shown, that the structure functions of the Reggeon and Pomeron as well as the Reggeon-Pomeron interference SF have a universal $\sim (1-β)^2$ behaviour.
We present a QCD-based model where rescattering between final state partons in deep inelastic scattering leads to events with large rapidity gaps and a leading proton. In the framework of this model the amplitude for multiple gluon exchanges is calculated in the eikonal approximation to all orders in perturbation theory. Both large and small invariant mass M_X limits are considered. The model successfully describes the precise HERA data on the diffractive deep inelastic cross section in the whole available kinematical range and gives new insight into the density of gluons at very small momentu…
We propose a new description of inclusive diffraction in deep inelastic scattering (DIS). The diffractive structure functions are expressed in the dipole picture and contain heavy-quark contributions. The dipole scattering amplitude, a saturation model fitted on inclusive DIS data, features a saturation scale Q_s(x) larger than 1 GeV for x=10^{-5}. The q\bar{q}g contribution to the diffractive final state is modeled in such a way that both the large-Q^2 and small-beta limits are implemented. In the regime xpom<0.01 in which saturation is expected to be relevant, we obtain a parameter-free desc…
Misprints and numerical coefficients corrected, a bit of phenomenology and one figure added. The case for the linear evolution of the unitarized structure functions made stronger.
It is proposed, that color-singlet gluon-clusters can be formed in hadrons as a consequence of self-organized criticality (SOC) in systems of interacting soft gluons, and that the properties of such spatiotemporal complexities can be probed experimentally by examing inelastic diffractive scattering. Theoretical arguments and experimental evidences supporting the proposed picture are presented --- together with the result of a systematic analysis of the existing data for inelastic diffractive scattering processes performed at different incident energies, and/or by using different beam-particles…
Diffractive hard scattering is interpreted as the effect of soft gluon exchanges between the emerging energetic quarks and the nucleon's color field, resulting in an overall color singlet exchange. Summing multiple gluon exchanges to all orders leads to exponentiation and an amplitude in analytic form. Numerical evaluation reproduces the precise HERA data and gives new insights on the density of gluons in the proton.
We investigate a simplified version of the ACOT prescription for calculating deeply inelastic scattering from Q^2 values near the squared mass M_H^2 of a heavy quark to Q^2 much larger than M_H^2.
We discuss recent theoretical results on diffractive deeply inelastic scattering, focusing on the partonic picture of diffraction in configuration space and the predictions for the beta behavior and the scaling violation.
We give an overview of jet physics in deeply inelastic scattering at HERA. The problem of jet definitions, the scale dependence of jet cross sections and some applications are discussed. (Talk presented at the Workshop on Deeply Inelastic Scattering and QCD, Paris, April 1995. To appear in the proceedings.)
We examine diffractive proton-proton scattering. Using a functional integral approach we derive the scattering amplitudes, which are governed by the expectation value of lightlike Wegner-Wilson loops. This expectation value is then evaluated using a cumulant expansion and the model of the stochastic vacuum. From the scattering amplitudes we calculate total and differential cross sections for high centre of mass energy and small momentum transfer and compare with experiments.
We survey the current phenomenological status of semi-inclusive deep inelastic scattering at moderate hard scales and in the limit of very large transverse momentum. As the transverse momentum becomes comparable to or larger than the overall hard scale, the differential cross sections should be calculable with fixed order pQCD methods, while small transverse momentum (TMD factorization) approximations should eventually break down. We find large disagreement between HERMES and COMPASS data and fixed order calculations done with modern parton densities, even in regions of kinematics where such c…
The "triple-Regge" analysis of subleading Reggeon contributions to the diffractive structure function in DIS at HERA is presented. The recently published data allow to estimate the only free parameter of the analysis related to the ratio of the RRP and PPP couplings. The large value of this ratio is prefered which is in agreement with analyses of soft hadronic interactions. The role of the subleading Reggeons as well as pions for the fast forward neutron production in diffractive processes is estimated. The forward piN state production is also discussed.
We argue that the difference between the structure functions corresponding to deep inelastic scattering with and without heavy quarks in the current fragmentation region scales at high Q^2 and fixed (low) x.
The small-$t$ behaviour of the deep inelastic diffractive dissociation cross section in the triple Regge region is investigated, using the BFKL approximation in perturbative QCD. We show that the cross section is finite at $t=0$, but the diffusion in $\ln{k_t^2}$ leads to a large contribution of small momenta at the triple Pomeron vertex. We study the dependence upon the total energy and the invariant mass. At $t=0$, there is a decoupling of the three BFKL singularities which is a consequence of the conservation of the conformal dimension. For large invariant masses, the four gluon state in th…
The $t$-dependence and the $(M_x^2/s)$-dependence of the double differential cross-sections for inelastic diffractive scattering off proton-target are discussed. Here $t$ stands for the four-momentum-transfer squared, $M_x$ for the missing mass, and $\sqrt{s}$ for the total c.m.s. energy. It is shown, that the space-time properties of the color-singlet gluon-clusters due to SOC, discussed in Part I, lead to simple analytical formulae for $d^2σ/dt d(M_x^2/s)$ and for $dσ/dt$, and that the obtained results are in good agreement with the existing data. Further experiments are suggested.
We propose a partonic picture for high-mass diffractive dissociation events in onium-nucleus scattering, which leads to simple and robust predictions for the distribution of the sizes of gaps in diffractive dissociation of virtual photons off nuclei at very high energies. We show that the obtained probability distribution can formally be identified to the distribution of the decay time of the most recent common ancestor of a set of objects generated near the edge of a branching random walk, and explain the physical origin of this appealing correspondence. We then use the fact that the diffract…
The Sivers function is extracted from HERMES data on single spin asymmetries in semi-inclusive deeply inelastic scattering. The result is used for making predictions for the Sivers effect in the Drell-Yan process.
