Narrow Results

A representation of Pomeron amplitude derived asymptotically in the framework of the geometrical diffraction picture is shown to be consistent with the gross feature of the experimental data of the differential cross-section of pp and scattering in the low energy region over a wide range of momentum transfer. It is found that the most peripheral part of the diffraction interaction is characterized by a mass parameter of 0.4–0.5 GeV indicating the dominance of the two-pion states.

We discuss the shape of the interaction region of the elastically scattered protons stipulated by the high-energy Pomeron exchange which turns out to be very similar with the shape of the static string representing the confining QCD flux tube. This similarity disappears when we enter the LHC energy region, which corresponds to many-Pomeron exchanges. Reversing the argument we conjecture a modified relationship between the width and the length of the confining string at very large lengths.

Anticipating forthcoming publication by the TOTEM collaboration of low-$\left|t\right|$ elastic scattering data at $\sqrt{s}$ = 13 and 2.76 TeV, hereby we emphasize the correlation between two prominent structures seen upon the otherwise exponential diffraction cone, namely a “break” staying fixed around $t\approx -$0.1 GeV² and a dip moving with energy logarithmically inwards; while at the ISR, the two structures are separated by a distance of about 1 GeV², at the LHC, the dip comes close to the periphery of the “break”, thus affecting its parametrization. An unbiased disentangling and identification of the “break” at the LHC should account for this correlation.

The presence of Odderon at high energy has been in question for quite some time. We have confronted the Odderon description to the available data especially for pp and scattering including the most recent measurements by UA4/2, E710, CDF and E811 Collaborations. The Odderon in perturbative and nonperturbative QCD has also been discussed along with some phenomenological approaches. A comparison of the Odderon description with other models has also been made for data including the measurements from cosmic ray, which corresponds to the LHC energy of 14 TeV. Our study especially focuses on the measurements at RHIC and LHC and the presence or otherwise of Odderon.

Starting from the viewpoint that the constituent quark has its own structure and incorporating the hypothesis of maximum nonperturbative strong interaction reaction (MNSIR), which should be obeyed in high energy strong soft processes, we modified the field theory for soft Pomeron (ℙ) of Landshoff and Nachtmann and proposed a new structure model for the soft Pomeron ℙ and Reggeon ℝ. In this model a pair of constituent quarks coming from colliding hadron in strong soft processes are first disaggregated into a valance quark with a nonperturbative gluon cloud G wrapped about, or, according to the case, into a nonperturbative gluon wrapped by spinor cloud. Corresponding to such mechanism, the relevant structure of soft Pomeron ℙ or Region ℝ is represented by the sum of a series of cut ladder diagrams. In the multi-Regge region, where the energy of the system is very large and the momentum transfer |t| is very small, and in the approximation where only the leading order of log s is preserved, we calculated the scattering amplitude and its total cross-section from the sum of such ladder diagrams. The Regge-behavior factor in the form of an exponential power law of s does arise. We also get compact formulas for the trajectories of soft ℙ and ℝ. As example of application, an alternative mechanism of J/Ψ nonquarkonic-hadron decay is proposed.

Based on IS model, the cross-sections of associated η_c and γ diffractive production in collision are calculated. Under the framework of NRQCD factorization formalism for quarkonia production, the dominant contribution to associated η_c and γ production comes from color octet subprocess, the color octet matrix element of is related to that of of J/ψ by the heavy quark spin symmetry. Because the value of color octet matrix element of of J/ψ is determined by the large P_TJ/ψ production data, the prediction of η_c and γ is more reliable. The ratio of diffractive to inclusive cross-sections is independent of the values of color octet matrix elements, which is sensitive to the gluon factor of the Pomeron and renormalized Pomeron flux factors. So experimental measurement of this ratio can give us more information of the nature of Pomeron and test the assumption of diffractive hard scattering factorization.

In this work, we perform a comparison of the use of distinct gluon propagators with the experimental data in diffractive processes, pp elastic scattering and light meson photo-production. The gluon propagators are calculated through nonperturbative methods, being justified their use in this class of events, due to the smallness of the momentum transfer. Our results are not able to select the best choice for the modified gluon propagator among the analyzed ones. This shows that the application of this procedure in this class of high energy processes, although giving a reasonable fit to the experimental data, should be taken with same caution.

A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze pp and scattering. The main emphasis is on the delicate and nontrivial dynamics in the dip-bump region, near t = -1 GeV². The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the C-even and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the nonlinearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross-sections and the inelastic cross-section are calculated. Predictions for the LHC energy region, where most of the existing models will be either confirmed or ruled out, are presented.

I give a brief introduction to central exclusive production in hadron–hadron collisions, the subject of this special issue of the International Journal of Modern Physics A.

Selected results from the study of Double Pomeron Exchange with the Split Field Magnet detector at the CERN Intersecting Storage Rings are presented. This concerns various general features of central pionic systems as well as the spectroscopy in the π⁺π^- channel, emphasizing the production properties of the f₂(1270) meson. This summary refers to a series of publications over a time span of 17 years based on the work of the CCHK^1,2 and ABCDHW^3–7 collaborations at the CERN ISR.

The CERN Intersecting Storage Rings, with from 22 GeV to 63 GeV and , allowed the first observations of p + p → p + X + p with two leading protons (x_F > 0.95) or two rapidity gaps Δy > 3. Studies of the central hadronic system (X) were made to search for glueballs, finding f₀ and f₂ resonances, and to advance our understanding of hadronic diffraction. I review the experiments, not including those at the Split Field Magnet (SFM) facility covered elsewhere in this volume. Some double pomeron exchange studies at the CERN Collider are also covered.

The LHC detectors have incomplete angular coverage in the forward direction, for example in the region 6 ≲ |η| ≲ 8, which can be improved with the addition of simple scintillation counters around the beam pipes about 50 m to 120 m from the intersection point. These counters detect showers created by particles hitting the beam pipes and nearby material. The absence of signals in these counters in low pileup conditions is an indication of a forward rapidity gap as a signature of diffraction. In addition, they can be used to detect hadrons from low mass diffractive excitations of the proton, not accompanied by a leading proton but adjacent to a rapidity gap over (e.g.) 3 ≲ |η| ≲ 6. Such a set of forward shower counters, originally used at CDF, was used in CMS (FSC) for high-β* running with TOTEM during LHC Run-1. During LS1 the CMS FSC system is being upgraded for future low pileup runs. A similar system, called HERSCHEL is being installed in LHCb. ALICE is implementing scintillation counters, ADA and ADC, with 4.5 ≲ |η| ≲ 6.4.

In 1970, on purely theoretical grounds, all total hadronic total cross-sections were predicted to increase without limit for higher and higher energies. This was contrary to the conventional belief at that time. In 1978, an accurate phenomenological model was formulated for the case of proton–proton and antiproton-proton interactions. The parameters for this model were slightly improved in 1984 using the additional available experimental data. Since then, for 30 years these parameters have not changed. This development, including especially the difficult task of formulating this phenomenological model and the comparison of the predictions of this model with later experimental results, is summarized.

A brief summary is reported on measurements of soft and hard diffractive processes by the ATLAS, CMS and TOTEM collaborations at a center of mass energy of 7 TeV.

We analyze the recent results of next-to-next-to-leading (NNLO) singlet BFKL eigenvalue in $N=4$ SYM written in terms of harmonic sums. The nested harmonic sums building known NNLO BFKL eigenvalue for specific values of the conformal spin have poles at negative integers. We sort the harmonic sums according to the complexity with respect to their weight and depth and use their pole decomposition in terms of the reflection identities to find the most complicated terms of NNLO BFKL eigenvalue for an arbitrary value of the conformal spin. The obtained result is compatible with the Bethe–Salpeter approach to the BFKL evolution.

The central exclusive production of charged hadron pairs in pp collisions at a center-of-mass energy of 13TeV is examined, based on data collected in a special high-${\beta }^{*}$ run of the LHC. Events are selected by requiring both scattered protons detected in the TOTEM Roman pots, exactly two oppositely charged identified particles in the CMS silicon tracker, and the energy–momentum balance of these four particles. The nonresonant continuum processes are studied with the invariant mass of the centrally produced two-pion system in the resonance-free region, $m<0.7$GeV or $m>1.8$GeV. Differential cross sections as functions of the azimuthal angle between the surviving protons, squared four-momenta, and two-hadron invariant mass are measured in a wide region of scattered protons with transverse momentum between 0.2 and 0.8GeV and for pion rapidities $|y|<2$. A rich structure of interactions related to double pomeron exchange emerges. The parabolic minimum in the distribution of the two-proton azimuthal angle is observed for the first time. It can be understood as an effect of additional pomeron exchanges between the protons, and of the interference between the bare and the rescattered amplitudes. After model tuning, various physical quantities related to the pomeron cross section, proton–pomeron and hadron–pomeron form factors, trajectory slopes and intercepts, as well as coefficients of diffractive eigenstates of the proton are determined.

We review the elastic and diffractive scatterings of protons (called also the “forward physics”) with emphasis on the LHC data, especially those deviating from the expectations based on extrapolations from earlier measurements at the ISR and 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 and the data that may indicate the way to further progress are in the focus of our paper.

Photoproduction of ϕ, γp → ϕ + p, is revisited in a model with Pomeron and hadron degrees of freedom. The scattering equation is written such that the final state interaction is included at the one-loop level of hadrons. We find a parameter set to reproduce the bump-like structure near the threshold in a way consistent with other meson production data.

At high energies the Pomeron plays a crucial part in describing the soft interactions. In the light of LHC (Large Hadron Collider) data we perform a detailed analysis of proton-proton ($pp$) and antiproton-proton ($\bar{p}p$) forward scattering data in order to determine the intercept and the slope of the soft Pomeron trajectory. This analysis is performed based on Regge theory using Born-level amplitudes. We investigate the role of the proton-Pomeron vertex form and of the nearest $t$-channel singularity. We give predictions for the total cross section and the ratio of the real part to the imaginary part of the elastic amplitude in $pp$ collisions at LHC and cosmic-ray energies.

Central exclusive production at hadron colliders is characterised by the hadronic state produced at or close to midrapidity, and by the two forward scattered protons, or remnants thereof. No particles are produced between the midrapidity system and the forward going beam particles, and such events can hence be identified experimentally by a double-gap topology. At LHC energies, central exclusive production in proton—proton collisions is dominated by pomeron—pomeron fusion. The models to describe such reactions are reviewed, and the ongoing efforts in the ALICE Collaboration to analyse double-gap events taken in Run 2 at the LHC are presented.