Diffractive Cross Sections Research Articles

Predictions for diffraction at the LHC compared to experimental results

Diffractive proton-proton cross sections at the lhc, as well as the total and total-inelastic proton-proton cross sections, are predicted in a simple model obeying all unitarity constraints. The model has been implemented in the pythia8-mbr event genera- tor for single diffraction, double diffraction, and central diffraction processes. Predictions of the model are compared to recent LHC results. The pythia8-mbr option includes a full simulation of the hadronization of the implemented diffrac- tion dissociation processes: single, double, and central diffraction. In the original mbr simulation used in cdf, the hadronization of the final state(s) was based on a data-driven phenomenological model of multiplicities and pt distributions calibrated using S ¯ ppS and Fermilab fixed-target results. Later, the model was successfully tested against Tevatron mb and diffraction data. However, only π ± and π 0 particles were produced in the final state, with multiplicities obeying a statistical model of a modified Gamma distribution function that provided good fits to experimental data (8). This model could not be used to predict specific-particle final states. In the pythia8-mbr implementation, hadronization is performed by PYTHIA8 tuned to reproduce final-state distributions in agreement with mbr's, with hadronization done in the pythia8 framework. Thus, all final-state particles are now automatically produced, greatly enhancing the horizon of applicability of tpythia8-mbr.

Nuclear and Coulomb interactions in coherent fragmentation of relativistic nuclei in a photoemulsion

The role of the nuclear and Coulomb interactions in coherent fragmentation of relativistic nuclei is discussed with the cluster-model analysis of the experimental data on the fragmentation of 7Li (P = 3A GeV/c) via the 3H + 4He channel in photoemulsion used as an example. The calculated electromagnetic contribution of ∼10% to the cross section is not in conflict with the photoemulsion data and the upper estimate of ∼40% derived from the earlier measurements of total cross sections for fragmentation of light nuclei using the counter technique. The observed irregularities in the differential cross section for 7Li fragmentation with a separated Coulomb peak at a very small momentum transfer Q are ascribed to the overlap of nuclear diffraction patterns arising from light (C, N, O) and heavy (Ag, Br) photoemulsion nuclei. The predicted diffraction cross sections in the inelastic channel drastically differ from the usual shape of nuclear diffraction in an elastic channel. For pure targets, they have a shape of oscillations with a few peaks of comparable intensity and show strong dependence on the form of the surface nuclear density and radii of the intranuclear cluster and target nucleus. The probability for two-body clustering in 7Li is estimated at about 0.7.

Asymptotic regime for hadron-hadron diffractive collisions at ultrahigh energies

Using the pre-LHC and LHC data for $\ensuremath{\pi}p$ and $pp$ diffractive collisions, we study the ultrahigh-energy asymptotic regime in the framework of the black disk picture. The black disk picture, being constrained by the $s$-channel unitarity condition and the $t$-channel analyticity, gives rather definite predictions for diffractive processes increasing with the energy. To deal with the data, we consider the Dakhno-Nikonov eikonal model, which predicts a growth of the ${ln}^{2}s$ type for total and elastic cross sections and ($\ensuremath{\tau}={\mathbf{q}}_{\ensuremath{\perp}}^{2}{ln}^{2}s$) scaling for diffractive scattering and diffractive dissociation of hadrons. According to the calculations, ultrahigh-energy asymptotic characteristics of diffractive and total cross sections are universal, and this results in the asymptotic equality of cross sections for all types of hadrons. We estimate the energy scale of the asymptotics in different processes. The manifestation of the asymptotic regime in hadron fragmentation reactions is discussed.

Interpretation of the measurements of total, elastic, and diffractive cross sections at LHC

Recently at LHC one has obtained measurements of the total, elastic and diffractive cross sections in pp collisions at very high energy. The total cross section is in good agreement with predictions based on a leading behavior \sigma_{tot} (s) \propto (\ln s/s_0)^2, on the other hand the elastic cross section is lower than most expectations and the diffractive cross section is higher. It is remarkable that the ratio (\sigma_{el} + \sigma_{diff})/\sigma_{tot} calculated combining the results of the TOTEM and ALICE detectors is 0.495^{+0.05}_{-0.06}, very close to the maximum theoretically allowed value of 1/2 known as the Miettinen Pumplin bound. In this work we discuss these results using the frameworks of single and multi--channel eikonal models, and outline the main difficulties for a consistent interpretation of the data.

Exclusive diffractive photon bremsstrahlung at the LHC

We calculate differential distributions for the $p p \to p p \gamma$ reaction at the LHC energy $\sqrt{s} = 14$ TeV. We consider diffractive classical bremsstrahlung mechanisms including effects of non point-like nature of protons. In addition, we take into account (vector meson)-pomeron, photon-pion as well as photon-pomeron exchange processes for the first time in the literature. Predictions for the total cross section and several observables related to these processes e.g. differential distributions in pseudorapidities and transverse momenta of photons or protons are shown and discussed. The integrated diffractive bremsstrahlung cross section ($E_{\gamma}>100$ GeV) is only of the order of $\mu$b. We try to identify regions of the phase space where one of the mechanisms dominates. The classical bremsstrahlung dominates at large forward/backward photon pseudorapidities, close to the pseudorapidities of scattered protons. In contrast, the photon-pomeron (pomeron-photon) mechanism dominates at midrapidities but the related cross section is rather small. In comparison the virtual-omega rescattering mechanism contributes at smaller angles of photons (larger photon rapidities). Photons in the forward/backward region can be measured by the Zero Degree Calorimeters (ZDCs) installed in experiments at the LHC while the midrapidity photons are difficult to measure (small cross section, small photon transverse momenta). Protons could be measured by ALFA detector (ATLAS) or TOTEM detector at CMS. The exclusivity could be checked with the help of main central detectors.

Exclusivepp→ppπ0reaction at high energies

The amplitudes for the $pp\ensuremath{\rightarrow}pp{\ensuremath{\pi}}^{0}$ process applicable at high energy are discussed in detail. Both diffractive bremsstrahlung (Drell-Hiida-Deck-type model), photon-photon and photon-omega exchange mechanisms are included in the calculation. Large cross sections of the order of mb are predicted. The corresponding differential cross sections in rapidities and transverse momenta of outgoing protons and pions as well as relative azimuthal angle between outgoing protons are calculated for RHIC and LHC energies. The hadronic bremsstrahlung contributions dominate at large (forward, backward) pion rapidities. The diffractive nonresonant background contributes at small ${\ensuremath{\pi}}^{0}p$ invariant mass and could be therefore misinterpreted as the Roper resonance. We predict strong dependence of the slope in $t$ (squared four-momentum transfer between ingoing and outgoing proton) on the mass of the supplementary excited ${\ensuremath{\pi}}^{0}p$ system. At high energies and midrapidities, the photon-photon contribution dominates over the diffractive components, however, the corresponding cross section is rather small. The photon-odderon and odderon-photon contributions are included in addition and first estimates (upper limits) of their contributions to rapidity and transverse momentum distribution of neutral pions are presented. We suggest a search for the odderon contribution at midrapidity and at ${p}_{\ensuremath{\perp},{\ensuremath{\pi}}^{0}}\ensuremath{\sim}0.5\text{ }\text{ }\mathrm{GeV}$. Our predictions are ready for verification at RHIC and LHC. The bremsstrahlung mechanisms discussed here contribute also to the $pp\ensuremath{\rightarrow}p(n{\ensuremath{\pi}}^{+})$ reaction. Both channels give a sizable contribution to the low-mass single diffractive cross section and must be included in extrapolating the measured experimental single diffractive cross section.

Diffractive gauge bosons production beyond QCD factorization

We discuss single diffractive gauge boson $({\ensuremath{\gamma}}^{*},{W}^{\ifmmode\pm\else\textpm\fi{}},Z)$ production in proton-proton collisions at different (Large Hadron Collider and Relativistic Heavy Ion Collider) energies within the color dipole approach. The calculations are performed for gauge bosons produced at forward rapidities. The diffractive cross section is predicted as a function of the fractional momentum and invariant mass of the lepton pair. We found a dramatic breakdown of the diffractive QCD factorization caused by an interplay of hard and soft interactions. Data from the CDF experiment on diffractive production of $W$ and $Z$ are well explained in a parameter-free way.

Running coupling and pomeron loop effects on inclusive and diffractive DIS cross sections

Within the framework of a (1+1)-dimensional model which mimics high-energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic γ ∗ h scattering cross sections. We analyze the cases of both fixed and running coupling within the mean-field approximation, in which the evolution of the scattering amplitude is described by the Balitsky–Kovchegov equation, and also through the pomeron loop equations, which include in the evolution the gluon number fluctuations. In the diffractive case, similarly to the inclusive one, suppression of the diffusive scaling, as a consequence of the inclusion of the running of the coupling, is observed.

Combined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelastic ep scattering at HERA

A combination of the inclusive diffractive cross section measurements made by the H1 and ZEUS Collaborations at HERA is presented. The analysis uses samples of diffractive deep inelastic ep scattering data at a centre-of-mass energy sqrt(s) = 318 GeV where leading protons are detected by dedicated spectrometers. Correlations of systematic uncertainties are taken into account, resulting in an improved precision of the cross section measurement which reaches 6% for the most precise points. The combined data cover the range 2.5 < Q2 < 200 GeV2 in photon virtuality, 0.00035 < xIP < 0.09 in proton fractional momentum loss, 0.09 < |t| < 0.55 GeV2 in squared four-momentum transfer at the proton vertex and 0.0018 < beta < 0.816 in beta = x/xIP, where x is the Bjorken scaling variable.

Diffractive Higgs production by AdS Pomeron fusion

The double diffractive Higgs production at central rapidity is formulated in terms of the fusion of two AdS gravitons/Pomerons first introduced by Brower, Polchinski, Strassler and Tan in elastic scattering. Here we propose a simple self-consistent holographic framework capable of providing phenomenologically compelling estimates of diffractive cross sections at the LHC. As in the traditional weak coupling approach, we anticipate that several phenomenological parameters must be tested and calibrated through factorization for a self-consistent description of other diffractive process such as total cross sections, deep inelastic scattering and heavy quark production in the central region.

Inclusive measurement of diffractive deep-inelastic scattering at HERA

The diffractive process ep \rightarrow eXY, where Y denotes a proton or its low mass excitation with MY < 1.6 GeV, is studied with the H1 experiment at HERA. The analysis is restricted to the phase space region of the photon virtuality 3 \leq Q2 \leq 1600 GeV2, the square of the four-momentum transfer at the proton vertex |t| < 1.0 GeV2 and the longitudinal momentum fraction of the incident proton carried by the colourless exchange xIP < 0.05. Triple differential cross sections are measured as a function of xIP, Q2 and beta = x/xIP where x is the Bjorken scaling variable. These measurements are made after selecting diffractive events by demanding a large empty rapidity interval separating the final state hadronic systems X and Y . High statistics measurements covering the data taking periods 1999-2000 and 2004-2007 are combined with previously published results in order to provide a single set of diffractive cross sections from the H1 experiment using the large rapidity gap selection method. The combined data represent a factor between three and thirty increase in statistics with respect to the previously published results. The measurements are compared with predictions from NLO QCD calculations based on diffractive parton densities and from a dipole model. The proton vertex factorisation hypothesis is tested.

Orbital currents, anapoles, and magnetic quadrupoles in CuO

We show that orbital currents in a CuO${}_{2}$ plane, if present, should be described by two independent parity- and time-reversal-odd order parameters, a toroidal dipole (anapole) and a magnetic quadrupole. Based on this, we derive the resonant x-ray diffraction cross section for monoclinic CuO at the antiferromagnetic wave vector and show that the two order parameters can be disentangled. From our analysis, we examine a recent claim of detecting anapoles in CuO.

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.

Inclusive Diffraction at HERA

Results are reported on measurements of diffractive cross sections in deep-inelastic scattering (DIS) and photoproduction at HERA. The cross sections are compared for processes with a leading proton in the final state and with a large gap in the rapidity distribution of the final state hadrons. The cross section dependences on the proton fractional longitudinal momentum loss x P and the squared four-momentum transfer at the proton vertex t are interpreted in terms of an effective pomeron trajectory and a sub-leading exchange. The hypothesis of proton vertex factorisation is tested. The longitudinal structure function is extracted from the diffractive cross sections measured at different proton beam energies. The cross sections of diffractive dijet production are compared with QCD predictions at next-to-leading order (NLO) based on parton distribution functions obtained from diffractive inclusive DIS data. Combined NLO QCD fits to the inclusive and dijet DIS data are performed to determine diffractive quark singlet and gluon densities with a better precision. The ratio of the diffractive dijet cross sections in photoproduction and DIS is compared with NLO QCD predictions to test QCD collinear factorisation.

Measurement of the diffractive longitudinal structure function $F_{L}^{D}$ at HERA

First measurements are presented of the diffractive cross section $\sigma_{ep \rightarrow eXY}$ at centre-of-mass energies $\sqrt{s}$ of 225 and 252 GeV, together with a precise new measurement at $\sqrt{s}$ of 319 GeV, using data taken with the H1 detector in the years 2006 and 2007. Together with previous H1 data at $\sqrt{s}$ of 301 GeV, the measurements are used to extract the diffractive longitudinal structure function F_L^D in the range of photon virtualities 4.0 <= Q^2 <= 44.0 GeV^2 and fractional proton longitudinal momentum loss 5 10^{-4} <= x_{IP} <= 3 10^{-3}. The measured F_L^D is compared with leading twist predictions based on diffractive parton densities extracted in NLO QCD fits to previous measurements of diffractive Deep-Inelastic Scattering and with a model which additionally includes a higher twist contribution derived from a colour dipole approach. The ratio of the diffractive cross section induced by longitudinally polarised photons to that for transversely polarised photons is extracted and compared with the analogous quantity for inclusive Deep-Inelastic Scattering.

HERA-data in the light of small x evolution with state of the art NLO input

Both total and diffractive cross sections from HERA are successfully confronted with JIMWLK evolution equations in the asymptotic pseudo-scaling region. We present a consistent, simultaneous description of both types of cross sections that includes NLO corrections in the form of running coupling and energy conservation corrections. The inclusion of energy conservation corrections allows to match all available data with x below .02 i.e. up to Q^2 of 1200 GeV^2. We discuss the effects of quark masses including charm, contrast asymptotic and pre-asymptotic fit strategies, and survey non-perturbative uncertainties related to impact parameter dependence.

Neutrino production of single pions: Dipole description

The light-cone distribution amplitudes for the axial current are derived within the instanton vacuum model (IVM), which incorporates nonperturbative effects including spontaneous chiral symmetry breaking. This allows to extend applicability of the dipole approach, usually used in the perturbative domain, down to $Q^{2}\to0$, where partially conserved axial current (PCAC) imposes a relation between the neutrino-production cross section and the one induced by pions. A dramatic breakdown of the Adler relation (AR) for diffractive neutrino-production of pions, caused by absorptive corrections, was revealed recently in arXiv:1105.1711. Indeed, comparing with the cross section predicted by the dipole phenomenology at $Q^{2}\to0$ on a proton target we confirmed the sizable deviation from the value given by the AR, as was estimated in arXiv:1105.1711 within a simplified two-channel model. The dipole approach also confirms that in the black-disc limit, where the absorptive corrections maximize, the diffractive cross section ceases, on the contrary to the expectation based on PCAC.

Inclusive and diffractive DIS at low x from HERA to the EIC

We describe a model for low x DIS off nucleons and nuclei which provides initial conditions for QCD evolution that satisfy unitarity at low-x. We discuss it's extension to the perturbative regime and it's predictions for several DIS observables. We emphasize the well-known connection between rise of the diffractive cross section at high energies and nuclear shadowing.

QCD rescattering mechanism for diffractive deep inelastic scattering

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 momentum fractions in the proton.

Total and diffractive cross sections in enhanced Pomeron scheme

For the first time, a systematic analysis of the high energy behavior of total and diffractive proton-proton cross sections is performed within the Reggeon field theory framework, based on the resummation of all significant contributions of enhanced Pomeron diagrams to all orders with respect to the triple-Pomeron coupling. The importance of different classes of enhanced graphs is investigated, and it is demonstrated that absorptive corrections due to ``net''-like enhanced diagrams and due to Pomeron ``loops'' are both significant and none of those classes can be neglected at high energies. A comparison with other approaches based on partial resummations of enhanced diagrams is performed. In particular, important differences are found concerning the predicted high energy behavior of total and single high mass diffraction proton-proton cross sections, with our values of ${\ensuremath{\sigma}}_{pp}^{\mathrm{tot}}$ at $\sqrt{s}=14\text{ }\text{ }\mathrm{TeV}$ being some 25%--40% higher and with the energy rise of ${\ensuremath{\sigma}}_{\mathrm{HM}}^{\mathrm{SD}}$ saturating well below the LHC energy. The main causes for those differences are analyzed and explained.