Origin of the Q 2-dependence of the DIS structure functions

We consider in detail Q ²-dependence of the DIS structure functions. Very often this dependence is claimed to be originated by the Q ²-dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q ²-dependent intercepts. We demonstrate that the DGLAP parametrization α _s = α _s (Q ²) is an approximation valid in the region of large x (where 2pq can be approximated by Q ²) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so α _s should be replaced by an effective coupling which is independent of Q ² at small x. As a consequence, intercepts of the structure functions are independent of Q ² . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q ² , even when the coupling does not depend on it. We also consider the structure functions at small Q ² and give a comment on power-Q ² corrections to the structure functions at large and small Q ² .     

Total cross sections and nucleon structure functions in the gargamelle SPS neutrino/antineutrino experiment

Total neutrino and antineutrino cross sections in the energy range 15 to 150 GeV, and the nucleon structure functions, F₂(x, Q²) and xF₃(x, Q²) in the Q² range 0.5 to 50 (GeV/c)² have been measured using a data sample of 3000 neutrino and 3800 antineutrino events. The structure functions show a weak Q² dependence at different x values.     

Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Model for nucleon gluon and sea quark structure functions at allx and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon gluon and sea quark structure functions at allx, and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =1.25 GeV² andA ²=0.01 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ².     

Color-conductivity in nuclei and the EMC-effect

We advocate that gluons and quarks of sufficiently short wavelengths are delocalized in nuclei. This hypothesis leads us to structure functions measured in μ-nucleus scattering, which depend at fixedx only on the ratio of the resolving power 1/Q and the radius of the nucleusR _A, whereA denotes the mass number of the nucleus. Thus we suggest that the structure functionF ₂(x, Q ²,A) per nucleon of an isoscalar nucleusA scales essentially as \(F_2 (x,Q^2 ,A) = \tilde F_2 (x,R_A^2 \cdot Q^2 )\) with a universal function \(\tilde F_2\) . The ratio of the so obtained structure functions of iron to deuterium agrees rather well with the one measured recently by the European Muon Collaboration. This observation implies that nuclei are “color-insulators” at lowQ ², but “color conductors” at largeQ ².     

Spin Structure of the Nucleon at Low Q 2 Region

The spin structure of the nucleon can play a key testing ground for the Quantum Chromo-Dynamics(QCD) at wide kinematic ranges from smaller to large four momentum transfer Q ². It is far more challenging to understand the QCD at small Q ² region due to the non-perturbative nature. Jefferson Lab has been one of the major experimental facilities for the spin structure with its polarized electron beams and various polarized targets. A few QCD sum rules have been compared with the measured spin structure functions g ₁ and g ₂ at low Q ² and the most surprising results have been obtained for the spin polarizabilities, γ ₀ and δ _LT .     

Tests of scaling of the proton electromagnetic structure functions

Deep-inelastic structure functions W₁ and W₂ have been extracted from electron-proton scattering cross sections that were measured in recent experiments at SLAC. The structure functions display deviations from scaling in the variable ω in the kinetic range 1.5 ? ω ? 3.0 and 2 ? Q² ? 15 GeV².     

Event-by-event search for charged-neutral fluctuations in Pb-Pb collisions at 158 A⋅GeV

We analyse the proton electromagnetic form factor ratioR(Q ² ) =QF ₂ (Q ² )/F ₁ (Q ² ) as a function of momentum transferQ ² within perturbative QCD. We find that the prediction for (R(Q ² ) at large momentum transferQ depends on the exclusive quark wave functions, which are unknown. For a wide range of wave functions we find thatQF ₂ F ₁ ～ const. at large momentum transfer, which is in agreement with recent JLAB data.     

F L structure function and heavy quark contributions

In this paper we obtain the heavy-quark contribution to the longitudinal structure functions F _L (x, Q ²). Since F _L structure functions contains rather large heavy flavor contributions in the small x region, we need to use the massive operator matrix elements, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q ²?>?>?m ². The method of QCD analysis, based on the Jacobi polynomials method, is also described. Our results for longitudinal structure function are in good agreement with the available experimental data.     

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.     

On the Q 2 dependence of nuclear structure functions

The recent high statistics NMC data on the Tin to Carbon structure function ratio seems to indicate, for the first time, a significant Q ² dependence, especially at small values of Bjorken x, x < 0.05, and Q ² > 1 GeV². A purely log(Q ²)-type dependence of the structure functions, which is consistent with the free nucleon data, yields a fairly flat ratio with little or no Q ² dependence. In view of this seeming contradiction, we re-examine the applicability of such a model to nuclear structure functions in such a kinematical regime. We find that the model is consistent with all data, within experimental errors, without any need for introducing additional Q ² dependences or higher twist contributions. The model correctly reproduces the Q ² dependence of the Carbon structure function as well. We also critically examine the Q ² dependence of the corresponding spin dependent structure functions.     

Structure functions of nuclei for all x and Q 2

We propose a modified version of the quark cluster model to describe the structure functions of nuclei over the complete kinematical region of the variables x = Q ²/2m _N ν and Q ². The model accounts for shadowing effects at very small x and anti-shadowing in the region 0.1 ≤ x ≤ 0.3. The experimental observation that the ratio of structure functions F ₂ ^A /F ₂ ^D is less than unity in the region x ? 0.5 is related to the influence of multiquark clusters. The model agrees with all available data on nuclear structure fuctions for a large variety of nuclei, and can be used to make predictions for kinematical regions not yet studied experimentally.     

Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.     

Higher order QCD contributions to electron structure functions

We study deep inelastice ⁺ e ^? scattering with untagged throughgoing target electrons. The corresponding electron structure functions are not trivially related to photon structure functions. Both can be calculated in QCD perturbation theory but the first ones can be measured more easily. In studying next-to-leading log contributions to electron structure functions we find that the leading logQ ² approximation completely fails at present energies. This is due to different scales λ andm _e . A modified leading-log approximation is introduced. Higher order corrections to this approximation are small away fromx=0 or 1.     

Twist-4 gluon recombination corrections for deep inelastic structure functions

We calculate twist-4 coefficient functions for the deep inelastic structure function F₂(x,Q²) associated to 4-gluon operator matrix elements for general values of the Bjorken variable x and study the numerical effect on the slope ∂F₂(x,Q²)/∂logQ². It is shown that these contributions diminish the strongly rising twist-2 terms towards small values of x.     

Quark masses and specific scaling in deep-inelastic processes

Within an operator-product expansion, the problem of the quark-mass dependence of the heavy-flavor contribution to the structure function F ₂ in the current-fragmentation region is considered at high values of the momentum transfer squared Q ². A linear combination of the structure functions F ₂ ^c and F ₂ is found that possesses a specific scaling property for Q ² → ∞ at small fixed values of the Bjorken variable x. A lower bound on the ratio F ₂ ^c /F ₂ is calculated and is compared with data obtained at the HERA collider.     

Evaluation of fully integrated γ v p → π+π− p cross sections in the resonance region at photon virtualities 5 < Q 2 < 12 GeV2

Evaluation of fully integrated double pion electroproduction cross sections of protons was carried out at 1.4 < W < 2.0 GeV, 5 < Q ² < 12 GeV². The cross-section evaluation was obtained from an approach based on extrapolation of the double pion component of inclusive structure functions F ₁ and F ₂ from photon virtualities Q ² < 5 GeV² towards 5 < Q ² < 12 GeV². Q ²-parameterization compatible with restrictions from the Operator Product Expansion was used to conduct the extrapolation. The results will be used to extract double pion electroproduction cross sections of protons in future experiments with the new CLAS12 detector.