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 function F ₂ in the range 3.5 × 10^?5 ≤ x ≤ 4 × 10^?3 and 1.5 GeV² ≤ Q ² ≤ 15 GeV² at the ep collider HERA operating at a centre-of-mass energy of ${sqrt s} = 300 {? GeV}$. The rise of F ₂ with decreasing x observed in the previous HERA measurements persists in this lower x and Q ² range. The Q ² evolution of F ₂, even at the lowest Q ² and x measured, is consistent with perturbative QCD.     

A measurement of the photon structure function F 2γ at an average Q 2 of 12 GeV2/ c 4

The hadronic photon structure functionF ₂ ^γ has been measured in theQ ² range from 4 to 30 GeV²/c ⁴ and down tox values of order 0.001, using data taken with the DELPHI detector at LEP between 1991 and 1993. A comparison is made with severalF ₂ ^γ parameterizations with special emphasis on their lowx behaviour. A result on theQ ² evolution ofF ₂ ^γ is presented.     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

Measurement of the proton structure functionF2 from the 1993 HERA data

The ZEUS detector has been used to measure the proton structure functionF ₂. During 1993 HERA collided 26.7 GeV electrons on 820 GeV protons. The data sample corresponds to an integrated luminosity of 0.54 pb^–1, representing a twenty fold increase in statistics compared to that of 1992. Results are presented for 7Q ²<>⁴ GeV² andx values as low as 3×10^–4. The rapid rise inF ₂ asx decreases observed previously is now studied in greater detail and persists forQ ² values up to 500 GeV².supported by Worldlab, Lausanne, Switzerland     

Solutions of independent DGLAP evolution equations for the gluon distribution and singlet structure functions in the next-to-leading order at low x

We present a set of independent formulas to extract the gluon distribution and the singlet structure function from its derivatives with respect to lnQ ² in the next-to-leading order of perturbation theory at low x based on a hard Pomeron exchange. In this approach, both singlet quarks and gluons have the same high-energy behavior at small x. This approach requires the QCD input parameterizations for independent DGLAP evolutions, which we calculated numerically and compared with the MRST, GRV, and DL models. The Pomeron has a hard nature. Its evolution gives a good fit to the experimental data. The values obtained are in the range 10⁻⁴ ≤ x ≤ 10⁻² at Q ² = 20 GeV². The text was submitted by the author in English.     

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.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Elastic J/ψ production at HERA

Cross sections for elastic production of J/ψ mesons in photoproduction and electroproduction are measured in electron proton collisions at HERA using an integrated luminosity of 55 pb^-1. Results are presented for photon virtualities Q² up to 80 GeV². The dependence on the photon-proton centre of mass energy W_γp is analysed in the range 40≤W_γp≤305 GeV in photoproduction and 40≤W_γp≤160 GeV in electroproduction. The W_γp dependences of the cross sections do not change significantly with Q² and can be described by models based on perturbative QCD. Within such models, the data show a high sensitivity to the gluon density of the proton in the domain of low Bjorken x and low Q². Differential cross sections dσ/dt, where t is the squared four-momentum transfer at the proton vertex, are measured in the range |t|<1.2 GeV² as functions of W_γp and Q². Effective Pomeron trajectories are determined for photoproduction and electroproduction. The J/ψ production and decay angular distributions are consistent with s-channel helicity conservation. The ratio of the cross sections for longitudinally and transversely polarised photons is measured as a function of Q² and is found to be described by perturbative QCD based models.     

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.     

On the possibility of measuringF L (x,Q 2) at HERA using radiative events

It is shown that a significant measurement of the longitudinal structure functionF _L (x, Q ²) can be performed at HERA, forQ ²=2 GeV² andQ ²=5 GeV² and forx around 10^?4, using radiative events with hard photon emission collinear to the incident lepton beam, under the present running conditions and with an integrated luminosity of 10 pb^?1. The influence of experimental conditions is discussed.     

Indirect determination of the ratio R=σL/σT at small x from HERA data

The value of the deep inelastic scattering cross-section ratio R=σ _L /σ _T is found in the range 10⁻⁴⩽x⩽10⁻² from F ₂ and dF ₂/d ln Q ² HERA data using very simple relations based on perturbative QCD. Zh. éksp. Teor. Fiz. 112, 32–36 (July 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Lithium ion conductivity of Li5+xBaxLa3?xTa2O12 (x?=?0–2) with garnet-related structure in dependence of the barium content

The stoichiometry range and lithium ion conductivity of Li_5+x Ba _x La_3−x Ta₂O₁₂ (x = 0, 0.25, 0.50, 1.00, 1.25, 1.50, 1.75, 2.00) with garnet-like structure were studied. The powder X-ray diffraction data of Li_5+x Ba _x La_3−x Ta₂O₁₂ indicated that single phase oxides with garnet-like structure exist over the compositional range 0 ≤ x ≤ 1.25; while for x = 1.5, 1.75 and 2.00, the presence of second phase in addition to the major garnet like phase was observed. The cubic lattice parameter increases with increasing x and reaches a maximum at x = 1.25 then decreases slightly with further increase in x in Li_5+x Ba _x La_3−x Ta₂O₁₂. The impedance plots of Li_5+x Ba _x La_3−x Ta₂O₁₂ samples obtained at 33 °C indicated a minimum grain-boundary resistance (R _gb) contribution to the total resistance (R _b + R _gb) at x = 1.0. The total (bulk + grain boundary) ionic conductivity increases with increasing lithium and barium content and reaches a maximum at x = 1.25 and then decreases with further increase in x in Li_5+x Ba _x La_3−x Ta₂O₁₂. Scanning electron microscope investigations revealed that Li_6.25Ba_1.25La_1.75Ta₂O₁₂ is much more dense, and the grains are more regular in shape. Among the investigated compounds, Li_6.25Ba_1.25La_1.75Ta₂O₁₂ exhibits the highest total (bulk + grain boundary) and bulk ionic conductivity of 5.0 × 10⁻⁵ and 7.4 × 10⁻⁵ S/cm at 33 °C, respectively.     

Dielectric spectroscopy of PbZr1 ? xTixO3 solid solutions (0.495 ≤ x ≤ 0.51) in a temperature range of 100–300 K at frequencies from 1 × 10?2 to 2 × 107 Hz

The behavior of the relative permittivity ɛ/ɛ₀ of PbZr_{1 − x} Ti _x O₃ (PZT) solid solutions (0.495 ≤ x ≤ 0.51) in the temperature range of 100–300 K at frequencies from 1 × 10⁻² to 2 × 10⁷ Hz was investigated. Diffuse, strongly relaxing maxima at T = 230−260 K (x = 0.495−0.505) and 150–160 K (x = 0.510) were observed in the PZT studied. The relaxation processes are well described by the Vogel-Fulcher law, and the dielectric spectra are approximated by the Cole-Cole formula.     

Precision measurement of structure function ratios for6Li,12C and40Ca

The structure function ratiosF ₂ ^C /F ₂ ^Li ,F ₂ ^Ca /F ₂ ^Li andF ₂ ^Ca /F ₂ ^C were measured in deep inelastic muonnucleus scattering at an incident muon energy of 90 GeV, covering the kinematic range 0.0085<x<0.6 and 0.8<Q ²<17GeV². The sensitivity of the nuclear structure functions to the size and mean density of the target nucleus is discussed.Supported by Bundesministerium für Forschung und Technologie     

The BFKL-Regge factorization and F2b , F2c , FL at HERA: physics implications of nodal properties of the BFKL eigenfunctions

The asymptotic freedom is known to split the leading-log BFKL pomeron into a series of isolated poles in the complex angular momentum plane. One of our earlier findings was that the subleading hard BFKL exchanges decouple from such experimentally important observables as small-x charm F ₂ ^c , beauty F ₂ ^b and the longitudinal structure functions of the proton at moderately large Q ². For instance, we predicted precocious BFKL asymptotics of F ₂ ^c (x, Q ²) with intercept of the rightmost BFKL pole a _IP(0) − 1 = Δ_IP ≈ 0.4. On the other hand, the small-x open beauty photo- and electro-production probes the vacuum exchange for much smaller color dipoles which entails significant subleading vacuum pole corrections to the small-x behavior. In view of the accumulation of the experimental data on small-x F ₂ ^c and F ₂ ^b we extend our 1999 predictions to the kinematical domain covered by new HERA measurements. Our parameter-free results agree well with the determination of F ₂ ^c , F _L and published H1 results F ₂ ^b on but slightly overshoot the very recent (2008, preliminary) H1 results on F ₂ ^b .     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Low temperature photoconductivity of Pb1?xSnxTe?In? films at millimeter wavelengths

Photoconductivity of single crystal Pb_1−xSn_xTe〈In〉, (0.24≤x≤0.25), films at 4.2K in the wavelength region 4÷5 mm and magnetic fields up to 8 T was studied. Preparation technology of the films with high photoconductivity (P_FEP ≤ 10⁻¹² W×Hz^1/2) and photoresponsiveness (τ ≤ 10⁻⁶ s), as well as the measurements procedure are described in the paper. Also the mechanism of photoconductivity is discussed.     

Approximate fixed-ρ solution of ‘sea-quark’ evolution equation at small-x and HERA

We found an approximate simple solution of sea-quark evolution equation in terms ofρ(=√ln(x ₀/x)/ln[ln(Q ²/Λ²)/(Q ₀ ² /Λ²)]) andζ(≡ln[ln(Q ²Λ²)/ln(Q ₀ ² /Λ²)]) in the small-x region whenρ is fixed and compared with HERA data. Agreement with data is found for largeQ ² and smallρ. Comparison with double asymptotic scaling prediction is made. We found a critical value ofρ. More data are needed to confirm this point.     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.