High-energy strong interactions: from ‘hard’ to ‘soft’

We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’ interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the data, these Monte Carlos need an additional infrared cutoff k _min with a value k _min∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k _min. Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small x, we demonstrate that this effective cutoff k _min is actually due to the strong absorption of low k _t partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k _t , and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging.     

Determining the inelastic proton–proton cross section at the large hadron collider using minimum bias events

In this paper a new method is described for determining the non-diffractive part of the inelastic proton–proton cross section, at the LHC centre of mass energy of 14 TeV. The method is based on counting the number of inelastic proton–proton interactions in the collision regions. According to a preliminary investigation, this measurement will be best suited for the initial low luminosity phase of the LHC. Knowledge of the proton–proton luminosity is likely to dominate the measurement uncertainty. PACS 13.85.Hd     

Measurement of the total photoabsorption cross section on a proton in the energy range 600–1500 MeV at the GRAAL

The total photoabsorption cross section on a free proton was measured at the GRAAL facility in the energy range E _γ = 600−1500 MeV. The large-aperture LAGRANγE detector and a liquid hydrogen target were used in the experiment performed with a back-scattered Compton gamma beam. To improve the accuracy, two alternative methods were employed. First, a subtraction method of using empty-target measurements allowed the cross section σ _tot to be evaluated directly because of a low level of the electromagnetic background. Second, an algorithm for evaluating σ _tot on the basis of summing the dominating partial cross sections was developed. Experimental results obtained for σ _tot by the two methods are compared with existing data. The article was translated by the authors. Published in Russian in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 76–83.     

Early LHC measurements to check predictions for central exclusive production

We show how the early data runs of the LHC can provide valuable checks of the different components of the formalism used to predict the cross sections of central exclusive processes. The ‘soft’ rapidity gap survival factor can be studied in electroweak processes, such as W+gaps events, for which the bare amplitude is well known. The generalised gluon distribution, in the appropriate kinematic region, can be probed by exclusive Υ production. The perturbative QCD effects, especially the Sudakov-like factor, can be probed by exclusive two- and three-jet production. We discuss the possible role of enhanced absorptive corrections that would violate the soft–hard factorisation implied in the usual formalism, and we suggest ways that the LHC may explore their presence.     

Survival probabilities for high mass diffraction

Based on the calculation of survival probabilities, we suggest a procedure to assess the value of G_3P, the triple pomeron ‘bare’ coupling constant, by comparing the large rapidity gap single high mass diffraction data in proton–proton scattering and J/Ψ photo and DIS production. For p–p scattering the calculation in a three amplitude rescattering eikonal model predicts the survival probability to be an order of magnitude smaller than for the two amplitude case. The calculations of the survival probabilities for photo and DIS J/Ψ production are made in a dedicated model. In this process we show that, even though its survival probability is considerably larger than in p–p scattering, its value is below unity and cannot be neglected in the data analysis. We argue that, regardless of the uncertainties in the suggested procedures, the outcome is important, both with regards to a realistic estimate of G_3P and to the survival probabilities relevant to LHC experiments. PACS 13.85-t; 13.85.Hd; 11.55.-m; 11.55.Bq     

Drell–Yan diffraction: breakdown of QCD factorization

We consider the diffractive Drell–Yan process in proton–(anti)proton collisions at high energies in the color dipole approach. The calculations are performed at forward rapidities of the leptonic pair. The effect of eikonalization of the universal “bare” dipole–target elastic amplitude in the saturation regime takes into account the principal part of the gap survival probability. We present predictions for the total and differential cross sections of the single-diffractive lepton-pair production at RHIC and LHC energies. We analyze implications of the QCD factorization breakdown in the diffractive Drell–Yan process, which is caused by a specific interplay of the soft and hard interactions, resulting in rather unusual properties of the corresponding observables.     

Theoretical expectations for σtot at the large hadron collider

In this note, we summarize and compare various model predictions forpp total cross-section σ _tot ^pp , giving an estimate of the range of predictions for the total cross-section, σ _tot ^pp expected at the LHC. We concentrate on the results for σ _tot ^pp obtained in a particular QCD based model of the energy dependence of the total cross-section, including the effect of soft gluon radiation. We obtain the range of predictions in this model by exploring the allowed range of model parameters. We further give a handy parametrisation of these results which incidentally spans the range of various other available predictions at the LHC as well     

K*0 and φ meson production in proton–nucleus interactions at ?s=41.6\textGeV\sqrt{s}=41.6\text{GeV}

The inclusive production cross sections of the strange vector mesons K^*0, K̄^*0, and φ have been measured in interactions of 920 GeV protons with C, Ti, and W targets with the HERA-B detector at the HERA storage ring. Differential cross sections as a function of rapidity and transverse momentum have been measured in the central rapidity region and for transverse momenta up to p_T = 3.5 GeV/c. The atomic number dependence is parametrised as σ_pA=σ_pN*A^α, where σ_pN is the proton–nucleon cross section. Within the phase space accessible, α(K^*0)=0.86±0.03, α(K̄^*0)=0.87±0.03, and α(φ)=0.96±0.02. The total proton–nucleon cross sections, determined by extrapolating the differential measurements to full phase space, are σ_pN→K*0=(5.06±0.54) mb, σ_pN→K̄*0=(4.02±0.45) mb, and σ_pN→φ=(1.17±0.11) mb. For all resonances the Cronin effect is observed; compared to the measurements of Cronin et al. for K^± mesons, the measured values of α for φ mesons coincide with those of K⁺ mesons for all transverse momenta, while the enhancement for K^*0/K̄^*0 mesons is smaller.     

Phenomenological analysis connecting proton–proton and antiproton–proton elastic scattering

Based on the behavior of the elastic scattering data, we introduce an almost model-independent parameterization for the imaginary part of the scattering amplitude, with the energy and momentum transfer dependences inferred on an empirical basis and selected by rigorous theorems and bounds from axiomatic quantum field theory. The corresponding real part is analytically evaluated by means of dispersion relations, allowing connections between particle–particle and particle–antiparticle scattering. Simultaneous fits to proton–proton and antiproton–proton experimental data in the forward direction and also including data beyond the forward direction lead to a predictive formalism in both energy and momentum transfer. We compare our extrapolations with predictions from some popular models and discuss the applicability of the results in the normalization of elastic rates that can be extracted from present and future accelerator experiments (Tevatron, RHIC and LHC). PACS 13.85.Dz, 13.85.-t     

Limiting fragmentation in hadron–hadron collisions at high energies

Limiting fragmentation in proton–proton, deuteron–nucleus and nucleus–nucleus collisions is analyzed in the framework of the Balitsky–Kovchegov equation in high energy QCD. Good agreement with experimental data is obtained for a wide range of energies. Further detailed tests of limiting fragmentation at RHIC and the LHC will provide insight into the evolution equations for high energy QCD.     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Diffraction at the LHC – antishadow scattering?

Numerical predictions for the global characteristics of proton–proton interactions are given for the LHC energy. Possibilities for the discovery of the antishadow scattering mode and its physical implications are discussed. Received: 18 August 2000 / Revised version: 9 July 2001 / Published online: 7 September 2001     

Measurement of the total photon proton cross section and its decomposition at 200 GeV centre of mass energy

We present a new measurement of the total photoproduction cross section performed with the H1 detector at HERA. For an average centre of mass energy of 200 GeV a value of σ _tot ^λp =165±2±11μb has been obtained. A detailed analysis of the data in adequate kinematic regions enabled a decomposition of the total cross section in its elastic, single diffractive dissociation and remaining non-diffractive parts, based on safe assumptions on the double diffractive dissociation contribution. Supported by the Bundesministerium für Forschung und Technologie, FRG under contract numbers 6AC17P, 6AC47P, 6DO57I, 6HH17P, 6HH27I, 6HD17I, 6HD27I, 6KI17P, 6MP17I, and 6WT87P     

Soft processes at the LHC,II: soft–hard factorisation breaking and gap survival

We calculate the probability that the rapidity gaps in diffractive processes survive both eikonal and enhanced rescattering. We present arguments that enhanced rescattering, which violates soft–hard factorisation, is not very strong. Accounting for NLO effects, there is no reason to expect that the black-disc regime is reached at the LHC. We discuss the predictions for the survival of the rapidity gaps for exclusive Higgs production at the LHC.     

How can the odderon be detected at RHIC and LHC?

The odderon remains an elusive object, 33 years after its invention. The odderon is now a fundamental object in QCD and it has to be found experimentally if QCD is right. In the present paper, we show how to find it at RHIC and LHC. The most spectacular signature of the odderon is the predicted difference between the differential cross-sections for proton–proton and antiproton–proton at high s and moderate t. This experiment can be done by using the STAR detector at RHIC and by combining these future data with the already present UA4/2 data. The odderon could also be found by the ATLAS experiment at LHC by performing a high-precision measurement of the real part of the hadron elastic scattering amplitude at small t.     

Large contribution of virtual Delbrück scattering to the emission of photons by relativistic nuclei in nucleus–nucleus and electron–nucleus collisions

Delbrück scattering is the elastic scattering of a photon in the Coulomb field of a nucleus via a virtual electron loop. The contribution of this virtual subprocess to the emission of a photon in the collision of ultra-relativistic nuclei, Z₁Z₂→Z₁Z₂γ, is considered. We identify the incoming virtual photon as being generated by one of the relativistic nuclei involved in the binary collision and the scattered photon as being emitted in the process. The energy and angular distributions of the photons are calculated. The discussed process has no infrared divergence. The total cross section obtained is 14 barn for Au–Au collisions at the RHIC collider and 50 barn for Pb–Pb collisions at the LHC collider. These cross sections are considerably larger than those for ordinary tree-level nuclear bremsstrahlung in the considered photon energy range, m_e⪡E_γ⪡m_eγ, where γ is the Lorentz factor of the nucleus. Finally, photon emission in electron–nucleus collisions, eZ→eZγ, is discussed in the context of the eRHIC option.     

<Emphasis Type="Italic">γ</Emphasis>–hadron correlation measurements to study jets fragmentation with ALICE at LHC

The possibility to study the fragmentation function of jets with energies below 50 GeV, which cannot be reconstructed in the heavy-ion environment, is explored. We propose to measure the imbalance distribution between prompt photon and charged hadrons with the ALICE experiment at LHC. In the present article, the case of proton–proton collisions at  TeV is examined with Monte-Carlo simulations. Performances for prompt photon identification and rejection of the π ⁰ decay photons are presented. We find that the measurement in proton–proton is meaningful with respect to statistical and systematic errors for photon energies larger than 20 GeV.