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.     

Dijet production in diffractive deep inelastic scattering at HERA

The production of dijets in diffractive deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 61 pb^-1. The dijet cross section has been measured for virtualities of the exchanged virtual photon, 5 < Q² < 100 GeV², and γ^*p centre-of-mass energies, 100 < W < 250 GeV. The jets, identified using the inclusive k_T algorithm in the γ^*p frame, were required to have a transverse energy E^* _T,jet > 4 GeV and the jet with the highest transverse energy was required to have E^* _T,jet > 5 GeV. All jets were required to be in the pseudorapidity range -3.5<η^* _jet<0. The differential cross sections are compared to leading-order predictions and next-to-leading-order QCD calculations based on recent diffractive parton densities extracted from inclusive diffractive deep inelastic scattering data.     

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.     

Diffractive photoproduction of D*±(2010) at HERA

Diffractive photoproduction of D^*±(2010) mesons was measured with the ZEUS detector at the ep collider HERA, using an integrated luminosity of 78.6 pb^-1. The D^* mesons were reconstructed in the kinematic range: transverse momentum p_T(D^*) > 1.9 GeV and pseudorapidity |η(D^*)|<1.6, using the decay D^*+→D⁰π⁺ _s followed by D⁰→K^-π⁺(+c.c.). Diffractive events were identified by a large gap in pseudorapidity between the produced hadronic state and the outgoing proton. Cross sections are reported for photon–proton centre-of-mass energies in the range 130 < W < 300 GeV and for photon virtualities Q² < 1 GeV², in two ranges of the Pomeron fractional momentum x_IP<0.035 and x_IP<0.01. The relative contribution of diffractive events to the inclusive D^*±(2010) photoproduction cross section is about 6%. The data are in agreement with perturbative QCD calculations based on various parameterisations of diffractive parton distribution functions. The results are consistent with diffractive QCD factorisation.     

Measurement of the Q and energy dependence of diffractive interactions at HERA

Diffractive dissociation of virtual photons, , has been studied in ep interactions with the ZEUS detector at HERA. The data cover photon virtualities 0.17 < Q ² < 0.70 GeV² and 3 < Q ² < 80 GeV² with 3 < M_X < 38 GeV, where M_X is the mass of the hadronic final state. Diffractive events were selected by two methods: the first required the detection of the scattered proton in the ZEUS leading proton spectrometer (LPS); the second was based on the distribution of M_X. The integrated luminosities of the low- and high-Q² samples used in the LPS-based analysis are 0.9 pb^-1 and 3.3 pb^-1, respectively. The sample used for the M_X-based analysis corresponds to an integrated luminosity of 6.2 pb^-1. The dependence of the diffractive cross section on W, the virtual photon-proton centre-of-mass energy, and on Q² is studied. In the low-Q² range, the energy dependence is compatible with Regge theory and is used to determine the intercept of the Pomeron trajectory. The W dependence of the diffractive cross section exhibits no significant change from the low-Q² to the high-Q² region. In the low-Q² range, little Q² dependence is found, a significantly different behaviour from the rapidly falling cross section measured for Q ² > 3 GeV². The ratio of the diffractive to the virtual photon-proton total cross section is studied as a function of W and Q². Comparisons are made with a model based on perturbative QCD. Received: 27 March 2002 / Published online: 9 August 2002     

Dissociation of virtual photons in events with a leading proton at HERA

The ZEUS detector has been used to study dissociation of virtual photons in events with a leading proton, , in e ⁺ p collisions at HERA. The data cover photon virtualities in two ranges, 0.03 < Q ² < 0.60 GeV² and 2 < Q ² < 100 GeV², with M _X > 1.5 GeV, where M _X is the mass of the hadronic final state, X. Events were required to have a leading proton, detected in the ZEUS leading proton spectrometer, carrying at least 90% of the incoming proton energy. The cross section is presented as a function of t, the squared four-momentum transfer at the proton vertex, , the azimuthal angle between the positron scattering plane and the proton scattering plane, and Q ². The data are presented in terms of the diffractive structure function, . A next-to-leading-order QCD fit to the higher-Q ² data set and to previously published diffractive charm production data is presented.Received: 10 August 2004, Revised: 4 October 2004, Published online: 9 November 2004     

On the rise of the proton structure function F2 towards low x

A measurement of the derivative (∂ lnF₂/∂ lnx)_Q²≡−λ(x,Q²) of the proton structure function F₂ is presented in the low x domain of deeply inelastic positron–proton scattering. For 5×10⁻⁵x0.01 and Q²1.5 GeV², λ(x,Q²) is found to be independent of x and to increase linearly with lnQ².     

A measurement of the proton structure function F2(x,Q2)

A measurement of the proton structure function F₂(x, Q²) is reported for momentum transfers squared Q² between 4.5 GeV² and 1600 GeV² and for Bjorken x between 1.8 × 10⁻¹⁴ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F₂ increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q² dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the “diffractive” contribution to F₂.     

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.     

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     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure functionF ₂ in the range 3.5×10⁻⁵≤x≤4×10⁻³ and 1.5 GeV²≤Q ²≤15GeV² at theep collider HERA operating at a centre-of-mass energy of √s=300GeV. The rise ofF ₂ with decreasingx observed in the previous HERA measurements persists in this lowerx andQ ² range. TheQ ² evolution ofF ₂, even at the lowestQ ² andx measured, is consistent with perturbative QCD. supported by EU HCM contract ERB-CHRX-CT93-0376     

Measurement of isolated photon production in deep-inelastic scattering at HERA

The production of isolated photons in deep-inelastic scattering ep→eγX is measured with the H1 detector at HERA. The measurement is performed in the kinematic range of negative four-momentum transfer squared 4<Q²<150 GeV² and a mass of the hadronic system W_X>50 GeV. The analysis is based on a total integrated luminosity of 227 pb^-1. The production cross section of isolated photons with a transverse energy in the range 3<E_T ^γ<10 GeV and pseudorapidity range -1.2<η^γ<1.8 is measured as a function of E_T ^γ, η^γ and Q². Isolated photon cross sections are also measured for events with no jets or at least one hadronic jet. The measurements are compared with predictions from Monte Carlo generators modelling the photon radiation from the quark and the electron lines, as well as with calculations at leading and next to leading order in the strong coupling. The predictions significantly underestimate the measured cross sections.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

Quasielastic versus inelastic and deep inelastic lepton scattering in nuclei at x > 1

We have made a thorough investigation of the nuclear structure function W_2A in the region of 0.8 < x < 1.5 and Q² < 20 GeV², separating the quasielastic and inelastic plus deep inelastic contributions. The agreement with present experimental data is good giving support to the results for both channels. Predictions are made in yet unexplored regions of x and Q² to assert the weight of the quasielastic or inelastic channels. We find that at Q² < 4 GeV² the structure function is dominated by the quasielastic contributions for x < 1.5, while for values of Q² > 15 GeV² and the range of x studied the inelastic channels are over one order of magnitude bigger than the quasielastic one. The potential of the structure function at x > 1 as a source of information on nuclear correlations is stressed once more.     

Longitudinal spin structure of the nucleon at COMPASS (SPS CERN)

We present new results on longitudinal inclusive double-spin asymmetry A _1,p (x) in deep-inelastic muon-proton scattering and proton spin-dependent structure function g ₁ ^p (x, Q ²). New COMPASS data on longitudinal polarised NH₃ target were collected during the year 2011 with beam of positive muons with energy E = 200 GeV. Kinematical threshold Q ² ≥ 1 (GeV/c)² and the fractional energy 0.1 < y < 0.9 allow us to cover low x region down to 0.025.     

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).     

Proton diffusion in the superprotonic phase of [(NH4)1 − xRbx]3H(SO4)2 as studied by 1H spin-lattice relaxation

Proton diffusion in [(NH₄)_1 ? xRb_x]₃H(SO₄)₂ (0 < x < 1) has been studied by means of ¹H spin-lattice relaxation times, T₁. The relaxation times were measured at 200.13 MHz in the range of 296–490 K and at 19.65 MHz in the range of 300–470 K. In the high-temperature phase (phase I), translational diffusion of the acidic protons relaxes both the acidic protons and the ammonium protons. Spin diffusion averages the relaxation rate of the two kinds of protons, whereas proton exchange between them are slow. The spin-lattice relaxation times in phase I were analyzed theoretically, and parameters of proton diffusion were obtained. The mean residence time of the acidic protons increases with increase in x for [(NH₄)_1 ? xRb_x]₃H(SO₄)₂ (0 ≤ x ≤ 0.54). Rb₃H(SO₄)₂ does not obey this trend. The results of NMR well explain the macroscopic proton conductivity.     

Perturbative QCD results on pion production in <Emphasis Type="Italic">pp,pA</Emphasis> and <Emphasis Type="Italic">AA</Emphasis> collisions

We summarize new pQCD results on pion production in proton–proton (pp), proton–nucleus (pA) and nucleus–nucleus (AA) collisions. Our calculation introduces intrinsic parton transverse momentum (k_T) and is performed effectively at next-to-leading order (NLO), applying a K factor extracted for jet events. Two different factorization scales, Q = p_Tjet/2 and p_Tjet are used. Experimental data in pA collisions imply a preference for the latter choice at NLO level. We display our results at CERN SPS for AA collisions.     

Deep-inelastic scattering in κ factorization and the anatomy of the differential gluon structure function of the proton

The differential gluon structure function of the proton, ?(x, Q ²), introduced by Fadin, Kuraev, and Lipatov in 1975 is extensively used in small-x QCD. We report here the first determination of ?(x, Q ²) from experimental data on the small-x proton structure function F _2p (x, Q ²). We give convenient parametrizations for ?(x, Q ²) based partly on the available DGLAP evolution fits (GRV, CTEQ, and MRS) to parton distribution functions and on realistic extrapolations into the soft region. We discuss the impact of soft gluons on various observables. The x dependence of the so-determined ?(x, Q ²) varies strongly with Q ² and does not exhibit simple Regge properties. Nonetheless, the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F _2p (x, Q ²) by the soft and hard Regge components with intercepts Δ_soft=0 and Δ_hard ～ 0.4.