Proton–proton interaction in constituent quarks model at LHC energies

In this paper we consider soft processes at LHC energies in the framework of the constituent quark model. We show that this rather naive model is able to describe all available soft process data at lower energies and to predict the behavior of the total cross section, the elastic and diffractive cross sections at LHC energy. It turns out that the “input” pomeron that has been used in this approach has parameters that are close to the so called “hard” pomeron with rather large intercept Δ≈0.12 and small value of the slope α^′ _P≈0.08 GeV^-2. We show that the elastic amplitude has a minimum at impact parameter b=0 and a maximum at b≈2 GeV^-1. Such a behavior is the result of overlapping of the parton clouds that belong to the different quarks in the hadron.     

Unitarisation and black-disk limit at the LHC in the presence of a hard pomeron

Recent models of soft diffraction include a hard pomeron pole besides the usual soft term. Such models violate the black-disk limit around Tevatron energies, so that they need to be supplemented by a unitarisation scheme. Two standard schemes are considered in this Letter, and we show that they lead to an uncertainty at the LHC much larger than previously estimated. We also examine the signature of unitarisation on various small-t observables, the slope in t of the elastic cross section, or the ratio of the real to imaginary parts of the scattering amplitude, and show that the existence of a unitarised hard pomeron in soft scattering may be confirmed by LHC data.     

Saturation in diffractive deep inelastic eA scattering

In this paper, we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio σ^diff/σ^tot and predict the x_ℙ and β behavior of the nuclear diffractive structure function F_2,A^D(3)(Q²,β,x_ℙ). Moreover, we analyze the ratio R^diff_A1,A2(Q²,β,x_ℙ)=F_2,A1^D(3)/F_2,A2^D(3), which probes the nuclear dependence of the structure of the pomeron. We show that saturation physics predicts that approximately 37% of the events observed at eRHIC should be diffractive.     

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     

Diffractive deep-inelastic scattering with a leading proton at HERA

The cross section for the diffractive deep-inelastic scattering process ep→eXp is measured, with the leading final state proton detected in the H1 Forward Proton Spectrometer. The data analysed cover the range x_IP<0.1 in fractional proton longitudinal momentum loss, 0.08<|t|<0.5 GeV^-2 in squared four-momentum transfer at the proton vertex, 2<Q²<50 GeV² in photon virtuality and 0.004<β=x/x_IP<1, where x is the Bjorken scaling variable. For , the differential cross section has a dependence of approximately dσ/dt∝e^6t, independently of x_IP, β and Q² within uncertainties. The cross section is also measured triple differentially in x_IP, β and Q². The x_IP dependence is interpreted in terms of an effective pomeron trajectory with intercept α_IP(0)=1.114±0.018(stat.)±0.012(syst.)^+0.040 _-0.020(model) and a sub-leading exchange. The data are in good agreement with an H1 measurement for which the event selection is based on a large gap in the rapidity distribution of the final state hadrons, after accounting for proton dissociation contributions in the latter. Within uncertainties, the dependence of the cross section on x and Q² can thus be factorised from the dependences on all studied variables which characterise the proton vertex, for both the pomeron and the sub-leading exchange.     

On the determination of double diffraction dissociation cross section at HERA

The excitation of the proton into undetected multiparticle states (double diffraction dissociation) is an important background to single diffractive deep-inelastic processesep→e′p′ρ ⁰,e′p′J/ψ,e′p′X at HERA. We present estimates of the admixture of the double diffraction dissociation events in all diffractive events. We find that in theJ/ψ photoproduction, electroproduction of theρ ⁰ at largeQ ² and diffraction dissociation of real and virtual photons into high mass statesX the contamination of the double diffraction dissociation can be as large as ∼30%, thus affecting substantially the experimental tests of the pomeron exchange in deep inelastic scattering at HERA. We discuss a possibility of tagging the double diffraction dissociation by neutrons observed in the forward neutron calorimeter. We present evaluations of the spectra of neutrons and efficiency of neutron tagging based on the experimental data for diffractive processes in the protonproton collisions.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

Electromagnetic polarizabilities of the nucleon and properties of the σ-meson pole contribution

The t-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, (α - β)^t, can be quantitatively understood in terms of a σ-meson pole in the complex t-plane of the invariant scattering amplitude A ₁(s, t) with properties of the σ-meson as given by the quark-level Nambu-Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the complex t-plane where the properties of the σ-meson are taken from the ππ → σ → ππ, γγ → σ → ππ and Nˉ → σ → ππ reactions. This equivalence may be understood as a sum rule where the properties of the σ-meson as predicted by the NJL model are related to the f ₀(600) particle observed in the three reactions. In the following, we describe details of the derivation of (α - β)^t making use of predictions of the quark-level NJL model for the σ-meson mass. An erratum to this article is available at .     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

Target-mass and finite <Emphasis Type="Italic">t</Emphasis> corrections to diffractive deep-inelastic scattering

The quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering given in a previous paper (Blümlein et al. in Nucl. Phys. B 755:112–136, 2006) is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. We consider the off-cone twist-2 light-cone operators to derive the target-mass and finite t corrections to diffractive deep-inelastic scattering and deep-inelastic scattering. The corrections turn out to be at most proportional to x|t|/Q ², xM ²/Q ², x=x _BJ or x _ℙ, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson-exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit t,M ²→0 one obtains the results of (Blümlein and Robaschik in Phys. Lett. B 517:222, 2001) and (Blümlein and Robaschik in Phys. Rev. D 65:096002, 2002).     

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced inep interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function ofx , the momentum fraction lost by the proton, of , the momentum fraction of the struck quark with respect tox , and ofQ ² in the range 6.3·10^–4x <>^–2, 0.1<0.8 and=">Q ²<100>². The dependence is consistent with the formx wherea=1.30±0.08(stat) _–0.14 ^+0.08 (sys) in all bins of andQ ². In the measuredQ ² range, the diffractive structure function approximately scales withQ ² at fixed . In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.supported by Worldlab, Lausanne, Switzerland     

Diffractive resonance production and f-dominance of the pomeron

A model for predicting diffractive production of meson resonances is presented. From a study of the s and t dependence of the available cross section and density matrix data, we deduce that the assumption of f, f′ dominance of the pomeron is violated. Relative to elastic scattering, where f, f′ dominance works well, the pomeron component in these inelastic processes appears to be about one half as strong in amplitude.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k _ring(t) ∝ t ^-δ and k _eq(t) ∝ t ^1-δ for times less than the longest polymer relaxation time. Here δ is an effective exponent which approaches δ = 5/4 for very long Rouse chains. Our present analysis also suggests a “sub-leading” term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) ∼ 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we “exponentiate” to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.     

Glue in the pomeron from nonlinear k ⊥ factorization

We derive the nonlinear k _⊥ factorization for the spectrum of jets in high-mass diffractive deep inelastic scattering as a function of three hard scales—the virtuality of the photon Q ², the transverse momentum of the jet, and the saturation scale Q _A . In contrast to all other hard reactions studied so far, we encounter a clash between the two definitions of the glue in the pomeron from the inclusive spectrum of leading quarks and the small-β evolution of the diffractive cross section. This clash casts a further shadow on customary applications of the familiar collinear factorization to a pQCD analysis of diffractive deep inelastic scattering. The text was submitted by the authors in English.     

Pressure variation of Luttinger liquid parameters in single wall carbon nanotubes networks

We measure electrical transport on networks of single wall nanotube of different origin as a function of temperature T, voltage V and pressure P. We observe Luttinger liquid (LL) behavior, a conductance ∝T^α and a dynamic conductance ∝V^α. We observe a sample dependent P variation of the α parameters, interpreted as Fermi level changes due to pressure induced charge transfer. We show how, through standard four-leads and crossed configuration methods, it is possible to determine α_bulk and α_end, respectively. We study and discuss the pressure and doping level dependences of the number of channels N, the LL parameter g and the intra-rope tube-tube coupling constant U within a phenomenological model.     

Structure of light neutron-rich nuclei and mechanism of elastic proton scattering

Differential cross sections for elastic p ⁶He, p ⁸Li, and p ⁹Li scattering at two energies of 70 and 700 MeV per nucleon were calculated within the Glauber theory of multiple diffractive scattering. Threeparticle wave functions (α-n-n for ⁶He, α-t-n for ⁸Li, and ⁷Li-n-n for ⁹Li) were used for realistic potentials of intercluster interactions. The sensitivity of elastic scattering to proton-nucleus interaction and to the structure of nuclei was explored. In particular, the dependence of the differential cross section on the contribution of higher order collisions, on scattering on the core and peripheral nucleons, and on the contribution of small wave-function components and their asymptotic behavior was determined. A comparison with available experimental data and with the results of calculations within different formalisms was performed.     

Properties of neutral charmed mesons in <Emphasis Type="Italic">pA</Emphasis> interactions at 70 GeV

The results of data handling for the E-184 experiment involving the irradiation of the active target, consisting of carbon, silicon, and lead plates by a 70-GeV proton beam are presented. When the two-prong neutral charmed meson decay signal was selected and the cross section for charm production at a near-threshold energy was estimated (σ(c $ \bar c $ \bar c ) = 7.1 ± 2.4(stat.) ± 1.4(syst.) μb/nucleon), some properties of D ⁰ and $ \bar D^0 $ \bar D^0 were investigated. These include the atomic-weight dependence of the cross section on the target mass number (its A dependence); the differential cross sections dσ/dp _t ² and dσ/dx _F; and the dependence of the parameter α on x _F, p _t ², and p _lab. The experimental results are compared with the predictions of the FRITIOF7.02 program.     

Universal magnetoluminescence kinetics in magnetically frozen 2D electron systems

The kinetics of recombination of electrons and acceptor-bound holes in AlGaAs-GaAs heterostructure obey a single-exponential decay in the liquid phase of 2D electrons, whereas localization gives rise to a broad spectrum of recombination rates, especially in the magnetic freeze-out regime. This results in a power-law dependence I(t)∝(τ/t)^α in the tail of the recombination kinetics, with the universal exponent α=(1−ν)⁻¹ at ν<1 for all the samples examined experimentally in this work. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 118–122 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.