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.
A new method of extracting diffractive parton distributions is presented which avoids the use of Regge theory ansatz and is in much closer relation with the factorisation theorem for diffractive hard processes.
A new method of extracting diffractive parton distributions is presented which avoids the use of Regge theory ansatz and is in much closer relation with the factorization theorem for diffarctive hard processes.
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.
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 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.
We study the consequences of high-energy collider data on the best fits to total, elastic, inelastic, and single-diffractive cross sections for $pp$ and $p \bar{p}$ scattering using different unitarisation schemes. We find that the data are well fitted both by eikonal and U-matrix schemes, but that diffractive data prefer the U-matrix. Both schemes may be generalised by means of an additional parameter; however, this yields only marginal improvements to the fits. We provide estimates for $ρ$, the ratio of the real part to the imaginary part of the elastic amplitude, for the different fits. We …
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…
We use diffractive parton distributions obtained from fits to the diffractive structure function measured at HERA to predict cross sections for single diffractive Higgs production at the LHC. The dominant background processes are also considered. Although some 5% - 15% of Higgs events are predicted to be diffractive in this model, the ratio of signal to background is not significantly improved.
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.
The most recent H1 and ZEUS data for diffractive structure functions are analyzed under three different theoretical approaches. This includes the Pomeron Structure Function (PSF) framework, Bartels-Ellis-Kowalski-Wusthoff (BEKW) color dipole approach and the Golec-Biernat-Wusthoff (GBW) saturation model. The models are shown to successfully fit the set of combined data. Conceptual differences between the models are discussed and, as an example, the prediction for the longitudinal diffractive structure function is presented.
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 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…
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
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 …
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 sc…
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.
We describe new QCD fits to diffractive proton structure functions measured at HERA, and we use these parton densities to predict the shape of the dijet mass fraction at the Tevatron and look for the existence of exclusive events in the dijet channel.
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 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…
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…
We discuss two different models for the impact parameter dependent dipole cross section: one based on DGLAP evolution and the other inspired by the Balitsky-Kovchegov equation. The parameters are determined from fits to data on the total gamma* p cross section measured at HERA. The impact parameter dependent saturation scale is extracted. Predictions are then confronted with HERA data on exclusive diffractive vector meson production and deeply virtual Compton scattering. Finally, predictions are given for the cross sections of exclusive photoproduced J/psi and Upsilon mesons, and Z^0 bosons, e…
We review elastic and diffractive scattering of protons (called also "forward physics") with emphasis on the LHC data, especially those deviating from the expectations based on extrapolations from earlier measurements at the ISR, Fermilab and thus triggering searches for new ideas, models and theories. We list these new data and provide a brief introduction of available theoretical approaches, mainly those based on analyticity, crossing symmetry and unitarity, particularly the Regge-pole model realizing these concepts. Fits to the data are presented and tensions between theoretical predictions…
We extract diffractive parton densities from diffractive, deep inelastic (DIS) ep data from the ZEUS experiment. Then we use these fits to predict the diffractive production of jets and of W's and Z's in p\bar p collisions at the Tevatron. Although the DIS data require a hard quark density in the pomeron, we find fairly low rates for the Tevatron processes (a few percent of the inclusive cross section). This results from the combined effects of Q^{2} evolution and of a normalization of the parton densities to the data. The calculated rates for W production are generally consistent with the pre…
In this paper we present a combined analysis of the H1 data on leading baryon and diffractive structure functions from DIS, which are handled as two components of the same semi-inclusive process. The available structure function data are analyzed in a series of fits in which three main exchanges are taking into account: pomeron, reggeon and pion. For each of these contributions, Regge factorization of the correspondent structure function is assumed. By this procedure, we extract information about the interface between the diffractive, pomeron-dominated, region and the leading proton spectrum, …
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.
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…
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.
Recent results on diffraction at HERA, from the H1 and ZEUS Collaborations, and at Tevatron, from the CDF and D0 Collaborations, are reviewed. The measurement of the diffractive structure function at HERA is presented, and the pomeron structure function is extracted from QCD fits. Diffractive dijet production is given as an example analysis of the diffractive final state. These analysis are consistent with a leading gluon partonic structure for the pomeron. Hard single diffraction, double diffraction and double pomeron exchange processes are studied at the Tevatron and complement the studies p…
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 new QCD fits to diffractive cross sections measured at HERA and we use the parton densities derived from these fits to predict the shape of the dijet mass fraction in double Pomeron exchange at the Tevatron. We discuss the existence of exclusive events in this dijet channel and some prospects are given for the LHC.
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.
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…
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…
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 $Q^2$.
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 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.
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…
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.
We have compared polarized parton densities determined in the NLO QCD fits to polarized structure functions and spin asymmetries. We consider models of such distributions based on MRST 99 and MRST 2001 fits to non-polarized data. Simple power law corrections corresponding to higher twists are taken into account and their importance is analyzed. The role of positivity conditions for parton densities and their influence on the values of $χ^{2}$ is discussed.
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…
A detailed comparison of HERA data at low Bjorken-$x$ and low four-momentum-transfer squared, $Q^2$, with predictions based on $\ln{Q^2}$ evolution (DGLAP) in perturbative Quantum Chromo Dynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, $F_{\rm L}$. This additional term, $F_{\rm L}~A_{\rm L}^{\rm HT}/Q^2$, improves the description of the reduced cross sections significantly. The resulting predictions for $F_{\rm L}$ suggest that further corrections …
Dipole models based on various saturation scenarios provide reasonable fits to small-x DIS inclusive, diffractive and exclusive data from HERA. Proton un-integrated gluon distributions extracted from such fits are employed in a $k_\bot$-factorization framework to calculate inclusive gluon distributions at various energies. The n-particle multiplicity distribution predicted in the Glasma flux tube approach shows good agreement with data over a wide range of energies. Hadron inclusive transverse momentum distributions expressed in terms of the saturation scale demonstrate universal behavior over…
We performed the combine fits of SLAC, BCDMS and NMC data at NLO level. The data are fitted very well with different parametrizations of higher twist contributions. The theory-based parametrizations lead to the low values of QCD parameter Λ^{f=4}_{\overfull{MS}} \sim 140 \pm 21 MeV (or α_s(M^2_Z)= 0.103 \pm 0.002).
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 improved next-to-next-to-leading order (NNLO) QCD analysis of the experimental data of the CCFR collaboration for the $xF_3$ structure function is made. Theoretical ambiguities of the NNLO fits are estimated by means of the Padé resummation technique, which was applied both in the expanded and non-expanded forms. The NNLO and the new N$^3$LO $α_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account the target mas corrections and the twist-4 $1/Q^2$-terms. Our NNLO results for $α_s(M_Z)$ values, extracted from the CCFR $xF_3$ data, are $α_s(M_…
Soft pomeron fits reproduce all zero-Q2 data for light quarks, but run into problems at HERA for heavy mesons and for high Q2, and at the Tevatron for W diffractive production. I review the basic properties of the soft pomeron, and outline the possibilities which have been considered to account for the new data.
The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA are analysed in terms of perturbative QCD in the perspective of the QCD extrapolation to the Tevatron and the LHC. It is shown that both data sets can be well described by a QCD analysis in which point-like parton distributions, evolving according to the next-leading DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. For present data from H1 and ZEUS the gluon distributions are found to be quite different and we give the corresponding sets of quark and gluon parton …
The common view that structure functions measured in deep inelastic lepton scattering are determined by the probability of finding quarks and gluons in the target is not correct in gauge theory. We show that gluon exchange between the fast, outgoing partons and target spectators, which is usually assumed to be an irrelevant gauge artifact, affects the leading twist structure functions in a profound way. This observation removes the apparent contradiction between the projectile (eikonal) and target (parton model) views of diffractive and small x_{Bjorken} phenomena. The diffractive scattering o…
We analyse the possibilities for the study of inclusive diffraction offered by future electron--proton/nucleus colliders in the TeV regime, the Large Hadron-electron Collider as an upgrade of the HL-LHC and the Future Circular Collider in electron-hadron mode. Compared to $ep$ collisions at HERA, we find an extension of the available kinematic range in $x$ by a factor of order $20$ and of the maximum $Q^2$ by a factor of order $100$ for LHeC, while the FCC version would extend the coverage by a further order of magnitude both in $x$ and $Q^2$. This translates into a range of available momentum…
