Diffractive Parton Distributions Research Articles

Incoherent diffractive production of jets in electron DIS off nuclei at high energy

We study incoherent diffractive production of two and three jets in electron-nucleus deep inelastic scattering (DIS) at small xBj using the color dipole picture and the effective theory of the color glass condensate (CGC). We consider color fluctuations in the CGC weight-function as the source of the nuclear break-up and the associated momentum transfer |t|. We focus on the regime in which the two jets are almost back-to-back in transverse space and have transverse momenta P⊥ much larger than both the momentum transfer and the saturation scale Qs. The cross section for producing such a hard dijet is parametrically dominated by large size fluctuations in the projectile wave-function that scatter strongly and for which a third, semihard, jet appears in the final state. The 2+1 jets cross section can be written in a factorized form in terms of incoherent quark and gluon diffractive transverse momentum distributions (DTMDs) when the third jet is explicit, or incoherent diffractive parton distribution functions (DPDFs) when the third jet is integrated over. We find that the DPDFs and the corresponding cross section saturate logarithmically when |t|≪Qs2, while they fall like 1/|t|2 in the regime Qs2≪|t|≪P⊥2. We further show that there is no angular correlation between the hard jet momentum and the momentum transfer. For typical EIC kinematics the 2 jets and 2+1 jets cross sections are of the same order. Published by the American Physical Society 2024

Determination of diffractive PDFs from a global QCD analysis of inclusive diffractive DIS and dijet cross-section measurements at HERA

We present an updated set of {\tt SKMHS} diffractive parton distribution functions (PDFs). In addition to the diffractive deep-inelastic scattering (diffractive DIS) data sets, the recent diffractive dijet cross sections measurements by the H1 experiment from the HERA collider are added to the data sample. The new set of diffractive PDFs, entitled {\tt SKMHS23} and {\tt SKMHS23-dijet}, are presented at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. Since the gluons directly contribute to jet production through the boson-gluon fusion process, the data on diffractive dijet production in inclusive DIS help to constrain the gluon density, allowing for the determination of both the quark and gluon densities with better accuracy. The NLO and NNLO theory predictions calculated using both {\tt SKMHS23} and {\tt SKMHS23-dijet} are compared to the analyzed data showing excellent agreements. The effect arising from the inclusion of diffractive dijet data and higher order QCD corrections on the extracted diffractive PDFs and data/theory agreements are clearly examined and discussed.

Global QCD analysis of diffractive parton distribution function considering higher twist corrections within the xFitter framework

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 structure-function $F_2^D$ is also examined. For the contribution of heavy flavors, we utilize the Thorne-Roberts general mass variable number scheme. We show that for those corrections, in particular, the twist-4 contribution allows to include the high-$\beta$ region and leads to a better description of the diffractive DIS data sets. We find that the inclusion of the subleading Reggeon exchange significantly improves the description of the diffractive DIS cross-section measurements. The resulting sets are in good agreement with all diffractive DIS data analyzed, which cover a wider kinematical range than in previous fits. The {\tt SKMHS22} diffractive PDFs sets presented in this work are available via the {\tt LHAPDF} interface. We also make suggestions for future research in this area.

How large is the diffractive contribution to inclusive dijet photoproduction in ultraperipheral collisions at the LHC?

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 diffraction. At the same time, using looser $p_T$ cuts, e.g., $p_{T1} > 10$ GeV and $p_{T i\neq 1} > 5-7$ GeV, we find that $(d\sigma_{\rm diff}/dx_A)/(d\sigma_{\rm inc}/dx_A)$ can reach $10-20$% at $x \approx 5 \times 10^{-4}$. Also, applying our framework to proton-proton UPCs at $\sqrt{s_{NN}}=13$ TeV, we find that the ratio of the diffractive and inclusive cross sections of dijet photoproduction $(d\sigma_{\rm diff}/dx_p)/(d\sigma_{\rm inc}/dx_p)$ is as large as $10-15$% for $x_p \sim 5 \times 10^{-4}$. An account of the contribution of Pomeron-Pomeron scattering, which is not included in our analysis, should make this ratio somewhat larger.

Matching of fracture functions for SIDIS in target fragmentation region

In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of ΛQCD, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than ΛQCD but much smaller than Q which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.

Measurement of single-diffractive dijet production in proton\u2013proton collisions at sqrt{s} = 8,text {Te}text {V} with the CMS and TOTEM experiments

Measurements are presented of the single-diffractive dijet cross section and the diffractive cross section as a function of the proton fractional momentum loss xi and the four-momentum transfer squared t. Both processes {text{ p }{}{}} {text{ p }{}{}} rightarrow {text{ p }{}{}} {text{ X }} and {text{ p }{}{}} {text{ p }{}{}} rightarrow {text{ X }} {text{ p }{}{}} , i.e. with the proton scattering to either side of the interaction point, are measured, where {text{ X }} includes at least two jets; the results of the two processes are averaged. The analyses are based on data collected simultaneously with the CMS and TOTEM detectors at the LHC in proton–proton collisions at sqrt{s} = 8,text {Te}text {V} during a dedicated run with beta ^{*} = 90,text {m} at low instantaneous luminosity and correspond to an integrated luminosity of 37.5{,text {nb}^{-1}} . The single-diffractive dijet cross section sigma ^{{text{ p }{}{}} {text{ X }}}_{mathrm {jj}}, in the kinematic region xi < 0.1, 0.03< |t | < 1,text {Ge}text {V} ^2, with at least two jets with transverse momentum p_{mathrm {T}} > 40,text {Ge}text {V} , and pseudorapidity |eta | < 4.4, is 21.7 pm 0.9,text {(stat)} ,^{+3.0}_{-3.3},text {(syst)} pm 0.9,text {(lumi)} ,text {nb} . The ratio of the single-diffractive to inclusive dijet yields, normalised per unit of xi , is presented as a function of x, the longitudinal momentum fraction of the proton carried by the struck parton. The ratio in the kinematic region defined above, for x values in the range -2.9 le log _{10} x le -1.6, is R = (sigma ^{{text{ p }{}{}} {text{ X }}}_{mathrm {jj}}/Delta xi )/sigma _{mathrm {jj}} = 0.025 pm 0.001,text {(stat)} pm 0.003,text {(syst)} , where sigma ^{{text{ p }{}{}} {text{ X }}}_{mathrm {jj}} and sigma _{mathrm {jj}} are the single-diffractive and inclusive dijet cross sections, respectively. The results are compared with predictions from models of diffractive and nondiffractive interactions. Monte Carlo predictions based on the HERA diffractive parton distribution functions agree well with the data when corrected for the effect of soft rescattering between the spectator partons.

Diffractive gamma gamma production in pp collisions at the LHC

In this letter we estimate the contribution of the double diffractive processes for the diphoton production in pp collisions at the large hadron collider (LHC). The acceptance of the central and forward LHC detectors is taken into account and predictions for the invariant mass, rapidity and, transverse momentum distributions are presented. A comparison with the predictions for the light-by-light (LbL) scattering and exclusive diphoton production is performed. We demonstrate that the events associated to double diffractive processes can be separated and its study can be used to constrain the behavior of the diffractive parton distribution functions.

Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions

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.

Phenomenology of diffractive DIS in the framework of fracture functions and determination of diffractive parton distribution functions

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, a QCD framework designed to provide a statistically sound representation of diffractive DIS processes. Heavy quark contributions to the diffractive DIS are considered within the framework of the FONLL general mass variable flavor number scheme (GM-VFNS) and the "Hessian approach" is used to determine the uncertainties of diffractive PDFs. We discuss the novel aspects of the approach used in the present analysis, namely an optimized and flexible parametrization of the diffractive PDFs as well as a strategy based on the fully factorization theorem for diffractive hard processes. We then present the diffractive PDFs, and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted data sets. We find that the systematic inclusion of higher-order QCD corrections could improves the description of the data. We compare the extracted sets of diffractive PDFs based on the fracture functions approach to other recent sets of diffractive PDFs, finding in general very good agreements.

Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD

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, 40 single-differential and four double-differential distributions for six measurements at HERA by the H1 and ZEUS collaborations are calculated. In the studied kinematical range, the NNLO corrections are found to be sizeable and positive. The NNLO predictions typically exceed the data, while the kinematical shape of the data is described better at NNLO than at next-to-leading order (NLO). A significant reduction of the scale uncertainty is achieved in comparison to NLO predictions. Our results use the currently available NLO diffractive parton distributions, and the discrepancy in normalisation highlights the need for a consistent determination of these distributions at NNLO accuracy.

First global next-to-leading order determination of diffractive parton distribution functions and their uncertainties within the xFitter framework

We present 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 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 the inclusion of high-precision data from H1/ZEUS combined inclusive diffractive cross sections measurements. We study the impact of the H1/ZEUS combined data by producing a variety of determinations based on reduced data sets. We find that these data sets have a significant impact on the diffractive PDFs with some substantial reductions in uncertainties. The predictions based on the extracted diffractive PDFs are compared to the analyzed diffractive DIS data and with other determinations of the diffractive PDFs.

Single-diffractive production of charmed mesons at the LHC within the kt-factorization approach

We discuss the single-diffractive production of cc pairs and charmed mesons at the LHC. For a first time we propose a kt-factorization approach to the diffractive processes. The transverse momentum dependent diffractive parton distributions are obtained from standard (collinear) diffractive parton distributions used in the literature. In this calculation the transverse momentum of the pomeron is neglected with respect to transverse momentum of partons entering the hard process. We also perform a first evaluation of the cross sections at the LHC using the diffractive transverse momentum dependent parton distributions. The results of the new approach are compared with those of the standard collinear one. Significantly larger cross sections are obtained in the kt-factorization approach in which some parts of higher-order effects is effectively included. The differences between corresponding differential distributions are discussed. Finally, we present a feasibility study of the process at the LHC using proton tagging technique. The analysis suggests that the measurement of single-diffractive charm production is possible using ATLAS and CMS/TOTEM detectors.

Single-diffractive Drell\u2013Yan pair production at the LHC

We present predictions for single-diffractive low-mass Drell–Yan pair production in pp collisions at the LHC at sqrt{s}=13 TeV. Predictions are obtained adopting a factorised form for the relevant cross sections and are based on a new set of diffractive parton distributions resulting from the QCD analysis of combined HERA leading proton data. We discuss a number of observables useful to characterise the expected factorisation breaking effects.

Dijet production in s=7 TeV pp collisions with large rapidity gaps at the ATLAS experiment

A $6.8 \ {\rm nb^{-1}}$ sample of $pp$ collision data collected under low-luminosity conditions at $\sqrt{s} = 7$ TeV by the ATLAS detector at the Large Hadron Collider is used to study diffractive dijet production. Events containing at least two jets with $p_\mathrm{T} > 20$ GeV are selected and analysed in terms of variables which discriminate between diffractive and non-diffractive processes. Cross sections are measured differentially in $\Delta\eta^F$, the size of the observable forward region of pseudorapidity which is devoid of hadronic activity, and in an estimator, $\tilde{\xi}$, of the fractional momentum loss of the proton assuming single diffractive dissociation ($pp \rightarrow pX$). Model comparisons indicate a dominant non-diffractive contribution up to moderately large $\Delta\eta^F$ and small $\tilde{\xi}$, with a diffractive contribution which is significant at the highest $\Delta\eta^F$ and the lowest $\tilde{\xi}$. The rapidity-gap survival probability is estimated from comparisons of the data in this latter region with predictions based on diffractive parton distribution functions.

Diffractive production of heavy mesons at the LHC

We discuss diffractive production of heavy mesons at the LHC. In addition to standard collinear approach, for a first time we propose a k t -factorization approach to the diffractive processes. The unintegrated (transverse momentum dependent) diffractive parton distributions in proton are calculated with the help of the Kimber-Martin-Ryskin prescription where collinear diffractive PDFs are used as input. Some correlation observables, like azimuthal angle correlation between c and c , and cc pair transverse momentum distribution were obtained for the first time. The results of the new approach are compared with those of the standard collinear one. Significantly larger cross sections are obtained in the k t -factorization approach where some part of higher-order effects is effectively included.

Diffractive dijet production with a leading proton in ep collisions at HERA

The cross section of the diffractive process e + p → e + Xp is measured at a centre-of-mass energy of 318 GeV, where the system X contains at least two jets and the leading final state proton p is detected in the H1 Very Forward Proton Spectrometer. The measurement is performed in photoproduction with photon virtualities Q 2 < 2 GeV2 and in deep-inelastic scattering with 4 GeV2 < Q 2 < 80 GeV2. The results are compared to next- to-leading order QCD calculations based on diffractive parton distribution functions as extracted from measurements of inclusive cross sections in diffractive deep-inelastic scattering.

A global analysis of diffractive events at HERA

We extract diffractive parton distribution functions (DPDFs) and diffractive structure functions from the most recent H1 and ZEUS diffractive deep inelastic scattering data obtained by various methods. We consider the Pomeron as an object with PDF, evolving according to the next-to-leading order DGLAP equations within the framework of the ‘fixed flavour number scheme’. Having performed a global fit analysis, we achieve a very good description of all available measurements by introducing a new set of quark distribution forms for the Pomeron. We predict longitudinal and charm proton diffractive structure function as well. Our results are compared with other analyses from the literature.

Measurement of dijet production in diffractive deep-inelastic scattering with a leading proton at HERA

The cross section of diffractive deep-inelastic scattering ep \rightarrow eXp is measured, where the system X contains at least two jets and the leading final state proton is detected in the H1 Forward Proton Spectrometer. The measurement is performed for fractional proton longitudinal momentum loss xIP < 0.1 and covers the range 0.1 < |t| < 0.7 GeV2 in squared four-momentum transfer at the proton vertex and 4 < Q2 < 110 GeV2 in photon virtuality. The differential cross sections extrapolated to |t| < 1 GeV2 are in agreement with next-toleading order QCD predictions based on diffractive parton distribution functions extracted from measurements of inclusive and dijet cross sections in diffractive deep-inelastic scattering. The data are also compared with leading order Monte Carlo models.

Heavy quark production inγPinteractions at hadronic colliders

The diffractive heavy quark cross sections are estimated considering photon-Pomeron ($\gamma \pom$) interactions in hadron - hadron at RHIC, Tevatron, and CERN LHC energies. We assume the validity of the hard diffractive factorization and calculate the charm and bottom total cross sections and rapidity distributions using the diffractive parton distribution functions of the Pomeron obtained by the H1 Collaboration at DESY-HERA. Moreover, we compare our predictions with those obtained using the dipole model. We verify that this process is a good test of the different mechanisms for diffractive heavy quark production at hadron - hadron colliders.

The study of heavy contribution in diffractive parton distribution functions

In this paper we give a brief introduction to the description of QCD analysis in order to determine the diffractive parton distribution functions (DPDFs) at the next-to-leading order (NLO) approximation. We focus on key features of analysis for all available diffractive HERA data and outline challenges for considering heavy quark contributions within the framework of the fixed flavour number scheme (FFNS) which is in full agreement with the diffractive heavy quarks experimental data.