The current analysis aims to present the results of a QCD analysis of diffractive parton distribution functions (diffractive PDFs) at next-to-leading order (NLO) accuracy in perturbative QCD. In this new determination of diffractive PDFs, we use all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) datasets from H1 and ZEUS Collaborations at HERA including the most recent H1/ZEUS combined measurements. In this analysis, we consider the heavy quark contributions to the diffractive DIS in the so-called framework of {\tt FONLL} general mass variable flavor number scheme (GM-VFNS). The uncertainties on the diffractive PDFs are calculated using the standard "Hessian error propagation" which served to provide a more realistic estimate of the uncertainties. This analysis are enriched, for the first time, by including the nonperturbative higher twist (HT) effects in the calculation of diffractive DIS cross sections which are particularly important at large-$x$ and low $Q^{2}$ regions. Then, the stability and reliability of the extracted diffractive PDFs are investigated upon inclusion of HT effects. We discuss the novel aspects of the approach used in this QCD fit, namely, optimized and flexible parameterizations of diffractive PDFs, the inclusion of HT effects, and considering the recent H1/ZEUS combined dataset. Finally, we present the extracted diffractive PDFs with and without the presence of HT effects, and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted datasets. We show that the inclusion of HT effects in diffractive DIS can improve the description of the data which leads, in general, to a very good agreement between data and theory predictions.
The data on the diffractive deep inelastic scattering (DDIS) at HERA exhibit a strong excess, up to about 100%, above the twist-two NLO DGLAP description at low $Q^2$ and at large energy. I show, that complementing the DGLAP fit by twist 4 and 6 components of the saturation model leads to a good description of data at low $Q^2$ and conclude that the DDIS at HERA provides the first evidence of higher twist effects in DIS.
We present {\tt SKMHS22}, a new set of diffractive parton distribution functions (PDFs) and their uncertainties at next-to-leading-order accuracy in perturbative QCD within the {\tt xFitter} framework. We describe all available diffractive DIS data sets from HERA and the most recent high-precision H1/ZEUS combined measurements considering three different scenarios. First, we extract the diffractive PDFs considering the standard twist-2 contribution. Then, we include the twist-4 correction from the longitudinal virtual photons. Finally, the contribution of subleading Reggeon exchange to the str…
HERA data on diffractive DIS show deviations from twist 2 DGLAP predictions below $Q^2\sim 5$ GeV$^2$ at low pomeron $ξ$, which may reach up to 100%. These deviations are consistent with higher twists effects extracted from the saturation model. It is a first direct evidence for the higher twists in DIS. This finding affects determination of the diffractive parton densities that are used for the predictions at the LHC.
Diffractive parton distributions of the proton are determined from fits to diffractive data from HERA. In addition to the twist--2 contribution, the twist--4 contribution from longitudinally polarised virtual photons is considered, which is important in the region of small diffractive masses. A new prediction for the longitudinal diffractive structure function is presented which differs significantly from that obtained in the pure twist--2 analyses.
We study a twist decomposition of diffractive structure functions in the diffractive deep inelastic scattering at HERA. At low $Q^2$ and at large energy the data exhibit a strong deviation from the twist-2 NLO DGLAP description. It is found that this deviation in consistent with higher twist effects. We conclude that the DDIS at HERA provides the first, strong evidence of higher twist effects in DIS.
We make predictions for the diffractive longitudinal structure function F_L^D to be measured at HERA, based on DGLAP fits of diffractive parton distributions with twist--4 contribution. This contribution describes diffractive qqbar production from longitudinal photons and significantly changes predictions for F_L^D obtained in pure DGLAP analyses.
We determine diffractive parton distributions of the proton from DGLAP based fits to HERA data including the twist--4 contribution from longitudinal polarized virtual photons, which is known to be important in the region of large beta. The biggest impact of this contribution is on the diffractive gluon distribution and on the diffractive longitudinal structure function to be determined from HERA data.
We study a twist decomposition of diffractive structure functions in the diffractive deep inelastic scattering (DDIS) at HERA. At low Q2 and at large energy the data exhibit a strong excess, up to about 100%, above the twist 2 NLO DGLAP description. The excess in consistent with higher twist effects. It is found, that complementing the DGLAP fit by twist 4 and 6 components of the GBW saturation model leads to a good description of data at low Q2. We conclude that the DDIS at HERA provides the first, strong evidence of higher twist effects in DIS.
In this letter we report the direct perturbative QCD evaluation of twist-4 effects in diffractive DIS. They are large and have a strong impact on the $Q^2$ dependence of diffractive structure functions at large $β$. Based on the AGK rules, we comment on the possible contribution from diffractive higher twists to $\propto {1 \over Q^{2}}$ corrections to proton structure function at small $x$. These corrections to the longitudinal structure function $F_{L}$ may be particularly large.
Diffractive production of heavy flavors is calculated within the light-cone dipole approach. Novel leading twist mechanisms are proposed, which involve both short and long transverse distances inside the incoming hadron. Nevertheless, the diffractive cross section turns out to be sensitive to the primordial transverse momenta of projectile gluons, rather than to the hadronic size. Our calculations agree with the available data for diffractive production of charm and beauty, and with the observed weak variation of the diffraction-to-inclusive cross section ratios as function of the hard scale.
A quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering is given. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region. Evolution equations of the diffractive hadronic matrix elements are derived at the level of the twist-2 contributions and are compared to those of inclusive deep-inelastic forward scattering (DIS). The diffractive parton densities are obtained as projections of two-variable parton distributions. We also comment on the higher twist contributions …
We review diffractive deep inelastic scattering (DIS) in the light of the collinear factorization theorem. This theorem allows to define diffractive parton distributions in the leading twist approach. Due to its selective final states, diffractive DIS offers interesting insight into the form of the diffractive parton distributions which we explore with the help of the saturation model. We find Regge-like factorization with the correct energy dependence measured at HERA. A remarkable feature of diffractive DIS is the dominance of the twist-4 contribution for small diffractive masses. We quantif…
Within the kt-factorization approach, we evaluate the impact factor of the transition gamma* -> rhoT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. More generally, relying on these equations and on the invariance under rotation on the light-cone of the factorized amplitude, the non-perturbative Distribution Amplitudes can be reduced to a minimal set. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson. We prove the equival…
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.
We use several diverse parameterizations of diffractive parton distributions, extracted in leading twist QCD analyses of the HERA diffractive deep inelastic scattering (DIS) data, to make predictions for leading twist nuclear shadowing of nuclear quark and gluon distributions in DIS on nuclei. We find that the HERA diffractive data are sufficiently precise to allow us to predict large nuclear shadowing for gluons and quarks, unambiguously. We performed detailed studies of nuclear shadowing for up and charm sea quarks and gluons within several scenarios of shadowing and diffractive slopes, as w…
We describe the twist-2 contributions to inclusive unpolarized and polarized deep-inelastic diffractive scattering in an operator approach. The representation refers to the observed large rapidity gap but does not require reference to a pomeron picture. We discuss both the case of vanishing target mass $M$ and momentum transfer $t$ as well as the effects at finite $t$ and $M$, which lead to modifications at large $β$ and low values of $Q^2$.
We use the Glauber-Gribov multiple scattering formalism and the theory of leading twist nuclear shadowing to develop a method for the calculation of leading twist hard coherent diffraction in hadron-nucleus processes. We demonstrate that soft multiple rescatterings lead to the factorization breaking of hard diffraction in proton-nucleus scattering, which is larger than in hadron-nucleon scattering. At the LHC and RHIC kinematics, we compare the hard diffractive to e.m.~mechanisms of hard coherent production of two jets in proton-nucleus scattering. We study the x_{\Pomeron}, βand A-dependence …
We present a precise comparison of the results of the dipole models with the newest data from HERA on the diffractive open charm production. We found good agreement with the data on the diffractive open charm production both for the the gluon distributions from the considered dipole models and the DGLAP fits to HERA data from our earlier analysis for diffractive parton distributions with higher twist. We also show that exclusive diffractive charm production can practically be neglected
The large rapidity gap events, observed at HERA, have changed considerably our physical picture of deep inelastic scattering during the past years. We review the present theoretical understanding of diffractive DIS with emphasis on the close relation to inclusive DIS. This includes success and limitations of the leading twist description, the connection between diffractive and inclusive parton distributions in the semiclassical approach, the colour structure of the proton and comparison with data. The progress report concludes with a list of open questions.
With the imminent construction of an electron-ion collider in the USA, both saturation physics and nuclear shadowing physics will be important for the same processes for the first time. In particular for exclusive production of vector mesons, such as the J/$ψ$. In this paper we investigate the underlying assumptions commonly made when phenomenologically investigating this process from a shadowing and saturation perspective respectively. We use the bSat model which is commonly used to describe saturation physics, and a calculation by M.G. Ryskin which is commonly used when describing nuclear sh…
Initial- and final-state rescattering, neglected in the parton model, have a profound effect in QCD hard-scattering reactions, predicting single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and ano…
A quantum field theoretic treatment of inclusive deep--inelastic diffractive scattering is given. The process can be described in the general framework of non--forward scattering processes using the light--cone expansion in the generalized Bjorken region. Target mass and finite $t$ corrections of the diffractive hadronic tensor are derived at the level of the twist--2 contributions both for the unpolarized and the polarized case. They modify the expressions contributing in the limit $t, M^2 \to 0$ for larger values of $β$ or/and $t$ in the region of low $Q^2$. The different diffractive structu…
The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA is analyzed in terms of both Regge phenomenology and perturbative QCD evolution. A new method determines the values of the Regge intercepts in ``hard'' diffraction, confirming a higher value of the Pomeron intercept than for soft physics. The data are well described by a QCD analysis in which point-like parton distributions, evolving according to the DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. The gluon distributions are found to be quite different for H1 and…
Exclusive and semi-exclusive processes, the diffractive dissociation of hadrons into jets, and hard diffractive processes such as vector meson leptoproduction provide new testing grounds for QCD and essential information on the structure of light-cone wavefunctions of hadrons, particularly the pion distribution amplitude. I review the basic features of the leading-twist QCD predictions and the problems and challenges of studying QCD at the amplitude level. The application of the light-cone formalism to the exclusive semi-leptonic decay of heavy hadrons is also discussed.
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…
Factorization of short- and long-distance interactions is severely broken in hard diffractive hadronic collisions. Interaction with the spectator partons leads to an interplay between soft and hard scales, which results in a leading twist behavior of the cross section, on the contrary to the higher twist predicted by factorization. This feature is explicitly demonstrated for diffractive radiation of abelian (Drell-Yan, gauge bosons, Higgs) and non-abelian (heavy flavors) particles
We derive a full set, and determine the twist, of helicity amplitudes for diffractive production of light to heavy vector mesons in deep inelastic scattering. For large $Q^{2}$ all helicity amplitudes but the double-flip are calculable in perturbative QCD and are proportional to the gluon structure function of the proton at a similar hard scale. We find a substantial breaking of the $s$-channel helicity conservation which must persist also in real photoproduction.
Initial- and final-state interactions from gluon-exchange, normally neglected in the parton model have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, and nuclear shadowing and antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency.
The cross section for coherent nuclear processes in which an incident meson or photon dissociates diffractively into two jets of high relative transverse momentum (between about 1 and 3 GeV/c) is found to be proportional in QCD to $A^2$ in a wide kinematical region. The leading correction to this is a significant positive term $\propto A^{7/3}$ caused by nuclear multiple-scattering. We find also that shadowing of hard diffractive processes reappears as a leading twist effect in the TeV energy range.
We derive an expression for diffractive F_2 structure function which should be valid at small x for quasi-elastic scattering on a hadron and for quasi-elastic scattering on a large nucleus. This expression includes multiple rescatterings of the quark-antiquark pair produced by the virtual photon off the sources of color charge in a quasi-classical approximation. We find that there is a relation between such diffractive production and inclusive processes. In the former, one averages over all colors of sources before squaring the amplitude, and in the latter one first squares the amplitude and t…
A complete set of asymptotic three particle light cone distribution amplitudes of twist 3 and 4 for a transversely polarized massive vector meson built out of massless current quarks is constructed. The method used is based on a modified conformal projectors technique which allows to handle kinematical corrections due to a finite hadron mass. Consequences of our finding for the ρ-meson hard diffractive electroproduction and γρπform factor are discussed. Our results may imply a breakdown of OPE for some exclusive processes beyond the leading twist level.
Diffractive photoproduction of $η_c$ is an important process to study the effect of Odderon, whose existence is still not confirmed in experiment. A detailed interpretation of Odderon in QCD, i.e., in terms of gluons is also unclear.Taking charm quarks as heavy quarks, we can use NRQCD and take $η_c$ as a $c\bar c$ bound state. Hence, in the production of $η_c$a free $c\bar c$ pair is first produced and this pair is transformed into $η_c$ subsequently.In the forward region of the kinematics, the $c\bar c$ pair interacts with initial hadron through exchanges of soft gluons. This interaction can…
The nuclear option at THERA provides an ideal and unique opportunity to investigate the black body limit (BBL) of high energy Deep Inelastic Scattering of highly virtual photons off heavy nuclear targets and thereby probe QCD in a new regime. At high enough energies, whichever hadronic configuration the photon fluctuates into, the interaction at a given impact parameter with the heavy nuclear target will eventually reach its geometrical limit corresponding to the scattering from a black disk. An attractive feature of the BBL regime for a large nucleus is that the interaction is strong although…
Using next-to-leading order (NLO) perturbative QCD, we calculate the diffractive contribution to inclusive dijet photoproduction in Pb-Pb ultraperipheral collisions (UPCs) at the LHC and find that it does not exceed $5-10$% in small-$x_A$ bins in the ATLAS kinematics at $\sqrt{s_{NN}}=5.02$ TeV. Its smallness is a result of the restricted kinematics ($p_{T1} > 20$ GeV and $x_A > 0.001$), the large nuclear suppression of nuclear diffractive parton distribution functions predicted in the leading twist model of nuclear shadowing, and additional suppression due to QCD factorization breaking in dif…
In this work the production of vector mesons in diffractive DIS is analyzed, with an emphasis on the impact of the internal spin structure of a vector meson upon its virtual photoproduction rate. We derived the full sets of s-channel helicity conserving and violating amplitudes for pure S and D wave vector mesons and found a striking difference between S and D wave vector meson production. First, in the case of helicity conserving amplitudes, D wave vector mesons were found to exhibit dramatically different Q^2-behavior due to abnormally large higher twist contributions. Besides, we found that…
Hadronic diffractive processes characterised by a hard scale (hard diffraction) contain a nontrivial interplay of hard and soft, nonperturbative interactions, which breaks down factorisation of short and long distances. On the contrary to the expectations based on the factorization hypothesis, assuming that hard diffraction is a higher twist, these processes should be classified as a leading twist. We overview various implications of this important observation for diffractive radiation of Abelian (Drell-Yan, gauge bosons, Higgs boson) and non-Abelian (heavy flavors) particles, as well as direc…
Measurements of the diffractive structure function $F_2^{D(3)}(x_{\PO}, β, Q^2)$, describing the process $ep \to eXY$, are presented in the two kinematic regions $0.4 \leq Q^2 \leq 5$, ${\rm GeV}^2$, $0.001 \leq β\leq 0.65$, and $200 \leq β\leq 800 {\rm GeV^2}$, $0.4 \leq β\leq 0.9$, both with $\xpom < 0.05$, $M_{_Y} < 1.6 {\rm GeV}$ and $|t| < 1.0 {\rm GeV^2}$. Together with published measurements at intermediate $Q^2$, the data are compared with models based on QCD and Regge phenomenology. The diffractive trajectory is found to have an intercept larger than that describing soft hadronic data…
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…
We present a first study of gluonic twist-four corrections to the deep inelastic structure function F_2 at small x and small Q^2. The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution equations of the gluonic twist-four operators that are expected to be dominant at small x. We first review the analytical results which are presently available and define the framework of our calculation. In the second part we discuss the connection with DIS diffractive dissociation which can be used to estimate the size of some of the twist-four corrections. In …
We describe the most recent data on the diffractive structure functions from the H1 and ZEUS Collaborations at HERA using four models. First, a Pomeron Structure Function (PSF) model, in which the Pomeron is considered as an object with parton distribution functions. Then, the Bartels Ellis Kowalski Wusthoff (BEKW) approach is discussed, assuming the simplest perturbative description of the Pomeron using a two-gluon ladder. A third approach, the Bialas Peschanski (BP) model, based on the dipole formalism is then described. Finally, we discuss the Golec-Biernat-Wüsthoff (GBW) saturation model w…
We extract the leading twist-2 and subleading twist-3 Distribution Amplitudes (DAs) of the rho meson using the HERA data on diffractive rho photoproduction. We do so using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. We find that our extracted twist-2 DA is not much model dependent and is consistent with QCD Sum Rules and lattice predictions. The extracted twist-3 DA is more model dependent but is still consistent with the Sum Rules prediction.
We quantify perturbative and non-perturbative QCD effects in the exclusive $J/ψ$-photoproduction cross section, and in the shrinkage of the differential cross section with respect to momentum transfer, $t$. We predict that in the high energy THERA region there will always be a significant contribution to this process that rises quickly with energy. This implies that the taming of the rise of the cross section with energy, due to both the expansion of spatially-small fluctuations in the photon and to higher twist effects, is rather gradual.
The goal of this study is to determine a set of diffractive parton distribution function (diffractive PDFs) from a QCD analysis of all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) data sets from HERA $ep$ collider, including the most recent H1 and ZUES combined inclusive diffractive cross section measurements. This extraction of diffractive PDFs, referred to as {\tt HK19-DPDF}, is performed at next-to-leading (NLO) and next-to-next-to-leading (NNLO) in perturbative QCD. This new determination of diffractive PDFs is based on the fracture functions methodology…
We report on a successful extraction of the twist-2 and twist-3 Distribution Amplitudes (DAs) of the rho meson using the HERA data on diffractive rho photoproduction. We extract these DAs using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. All our extracted DAs are consistent with Sum Rules and lattice predictions.
The low $x$ limit of deep inelastic electron proton scattering is considered using methods of perturbative QCD. In the first part we investigate the phenomenological consequences of the resummation of leading logarithms in $1/x$ given by the BFKL pomeron. We apply the BFKL pomeron to the inclusive structure function $F_2$, to the diffractive production of vector mesons at large momentum transfer, to inclusive photon diffractive dissociation in DIS and to quark-antiquark production with large transverse momenta in DIS diffractive dissociation. For the last process we perform extensive numerical…
We present {\tt GKG18-DPDFs}, a next-to-leading order (NLO) QCD analysis of diffractive parton distribution functions (diffractive PDFs) and their uncertainties. This is the first global set of diffractive PDFs determined within the {\tt xFitter} framework. This analysis is motivated by all available and most up-to-date data on inclusive diffractive deep inelastic scattering (diffractive DIS). Heavy quark contributions are considered within the framework of the Thorne-Roberts (TR) general mass variable flavor number scheme (GM-VFNS). We form a mutually consistent set of diffractive PDFs due to…
Some of the most difficult theoretical challenges of QCD occur at the interface of the perturbative and nonperturbative regimes. Exclusive and semi-exclusive processes, the diffractive dissociation of hadrons into jets, and hard diffractive processes such as vector meson leptoproduction provide new testing grounds for QCD and essential information on the structure of light-cone wavefunctions of hadrons, particularly the pion distribution amplitude. I review the basic features of the leading-twist QCD predictions and the problems and challenges of studying QCD at the amplitude level.
We investigate the influence of higher twist corrections to deep inelastic structure functions in the low-$Q^2$ and small-$x$ HERA region. We review the general features of the lowest-order QCD diagrams which contribute to twist-4 at small-$x$, in particular the sign structure of longitudinal and transverse structure functions which offers the possibility of strong cancellations in $F_2$. For a numerical analysis we perform a twist analysis of the saturation model which has been very successful both in describing the structure function and the DIS diffractive cross section at HERA. As the main…
Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced diffractively. There are different fracture functions for a process in different kinematic regions. We take the production of a lepton pair combined with a diffractively produced particle in hadron collisions to discuss this. Those fracture functions can be factorized further if there are large energy scales involved. They can be factorized with twist-2 parton …
A new NLO DGLAP QCD fit to recent inclusive diffractive DIS data from the H1 collaboration is presented. Diffractive parton distributions are extracted, including their experimental and theoretical uncertainties. The parton distributions are used for comparisons with recent diffractive final state data from HERA and the TEVATRON.
Initial-state and final-state interactions, which are conventionally neglected in the parton model, have a profound effect in QCD hard-scattering reactions. These effects, which arise from gluon exchange between the active and spectator quarks, cause leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, and the breakdown of the Lam-Tung relation in Drell-Yan reactions. Diffractive deep inelastic scattering also leads to nuclear shadowing and non-universal antishadowing of nuclear structure functions through multiple scattering reacti…
The diffractive dissociation of a hadron at high energies, by either Coulomb or Pomeron exchange, has a natural description in QCD as the materialization of the projectile's light-cone wavefunctions; in particular, the diffractive dissociation of a meson, baryon, or photon into high transverse momentum jets measures the shape and other features of the projectile's distribution amplitude. Diffractive dissociation can thus test fundamental properties of QCD, including color transparency and intrinsic charm. All of these effects have an impact on exclusive decays of $B$ mesons and the study of $C…
ZEUS inclusive diffractive cross-section measurements have been used in a next-to-leading-order QCD analysis to extract the diffractive parton distribution functions. Data on diffractive dijet production in deep inelastic scattering have also been used to constrain the gluon density. Predictions based on the extracted parton densities are able to describe measurements of dijet photoproduction.
We investigate the leading twist quark generalized transverse momentum distributions (GTMDs) at nonzero skewness in a light-front quark-diquark model for the nucleon motivated by soft-wall AdS/QCD. The boost-invariant longitudinal coordinate, $σ=\frac{1}{2} b^- P^+$, is identified as the Fourier conjugate of the skewness. The Fourier transform of the GTMDs with respect to the skewness variable $ξ$ can be employed to provide the Wigner distributions in the boost-invariant longitudinal position space $σ$, the coordinate conjugate to light-front time, $τ=t+z/c$. The Wigner distributions in the lo…
The cross section for deep inelastic lepton-proton scattering (DIS) $\ell p \to \ell' X$ includes a diffractive deep inelastic (DDIS) contribution $\ell p \to \ell' p' X$, in which the proton remains intact with a large longitudinal momentum fraction $x_F$ greater than 0.9 and small transverse momentum. The DDIS events, which can be identified with Pomeron exchange in the $t$-channel, account for approximately $10\%$ of all of the DIS events. Thus, when one measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS events as a contribution to the DIS cross section, whether…
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.
