Proton Structure Function Research Articles

Contact interaction study of proton parton distributions

Using a symmetry-preserving formulation of a vector×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ imes \\,$$\\end{document}vector contact interaction (SCI) and treating the proton as a quark + interacting-diquark bound state, whose structure is obtained by solving a Poincaré-covariant Faddeev equation, we provide a comprehensive, coherent set of predictions for unpolarised and polarised proton parton distribution functions (DFs): valence, glue, and four-flavour separated sea. The results enable many themes to be addressed, including: the asymmetry of antimatter in the proton; the neutron:proton structure function ratio; helicity retention in hard scattering processes; the charm quark momentum fraction; the sign and size of the polarised gluon DF; and the origin of the proton spin. In all cases where sound analyses of data are available, SCI predictions are semiquantitatively in agreement with the results. Those mismatches which exist are typically attributable to the momentum-independence of the underlying interaction. Judiciously interpreted, the SCI delivers a sound and insightful explanation of proton structure as expressed in DFs.

The EMC effect for few-nucleon bound systems in light-front Hamiltonian dynamics

The light-front formalism for a covariant description of the European Muon Collaboration (EMC) effect, already applied to He3, is formally extended to any nucleus, and used for actually calculating the 3H and He4 cases. The realistic and accurate nuclear description of few-nucleon bound systems, obtained with both phenomenological and chiral potentials, has been properly combined with the Poincaré covariance and macroscopic locality, automatically satisfying both number of particles and momentum sum rule. While retaining the on-mass-shell nucleon structure functions, one is then able to predict a sizable EMC effect for He4, as already observed for He3. Moreover, the impact on the EMC effect of both i) the short-range correlations, such as those generated by modern nuclear interactions, and ii) the ratio between the neutron and proton structure functions has been studied. The short-range correlations generated by retaining only the standard nuclear degrees of freedom act on the depth of the minimum in the EMC ratio, while the uncertainties linked to the ratio of neutron to proton structure functions are found to be very small. These light-front results facilitate ascribing deviations from experimental data due to genuine QCD effects, not included in a standard nuclear description, and initiating unbiased investigations.

Analysis of the gluon distribution with next-to-leading order splitting function at small-x* *Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030301), the National Natural Science Foundation of China (12375073), the Major Project of Basic and Applied Basic Research in Guangdong Province (2020B0301030008), the Basic Research Program (Natural Science) of Guizhou Province, China(QKHJC-ZK[2023]YB027), and the Education

An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is presented. We first obtain simplified forms of the LO and NLO splitting functions in the small-x limit. With these approximated splitting functions, we obtain the analytical gluon distribution using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data; however, the NLO results considering the "ladder" structure of gluon emission are slightly better than the LO results. These results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x region. In addition, we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon distribution. The differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.

Investigation of proton structure function F2p at HERA in light of an analytical solution to the Balitsky–Kovchegov equation

In this paper, the proton structure function F2p(x,Q2) at small-x is investigated using an analytical solution to the Balitsky–Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function F2p(x,Q2) is computed by applying the analytical expression for the scattering amplitude N(k, Y) derived from the BK solution. At transverse momentum k and total rapidity Y, the scattering amplitude N(k, Y) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density xg(x, Q 2) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of F2p(x,Q2) in the kinematic region of 10−5 ≤ x ≤ 10−2 and 2.5 GeV2 ≤ Q 2 ≤ 60 GeV2. Our predicted results for F2p(x,Q2) within the specified kinematic region are in good agreement with the recent high-precision data for F2p(x,Q2) from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.

The Importance of the Structure of Federal Executive Authorities in Public Administration

The paper shows that the current system of federal executive authorities, being an abstract category, is implemented only through the functioning of a specific structure of these bodies. As a set of real subjects, this structure materializes the management strategy embedded in the system of federal executive authorities, which, however, does not arise chaotically, but is formed in the process of development of the system of bodies and their corresponding structure. The paper examines the dynamics of the system and structure of the central executive bodies in the USSR and federal executive authorities in the Russian Federation. The author has analyzed the advantages and disadvantages of corresponding systems and structures that existed in post-Soviet Russia before 2004, as well as structures functioning currently. The information problems of the modern model of federal executive bodies, types and features of communication channels peculiar to the system under consideration have been analyzed. It is argued that the nature of information links between the elements of the system structure determines the degree of stability of the structure itself and, as a result, the entire mechanism of public administration, i.e., the probability of their preservation or destruction. It is concluded that the importance of the structure of federal executive authorities is explained not only in optimizing management activities, but also in forming such a configuration of information communication channels in a specific system of executive bodies that stabilizes the functioning of the entire mechanism of public administration.

Self-consistent description of HERA data at low Q2 and soft hadron production at LHC

Using the analytical expression for transverse momentum dependent (TMD) gluon density in a proton, a self-consistent simultaneous description of low Q2 data on proton structure function F2(x,Q2), reduced cross section for the electron-proton deep inelastic scattering at HERA and soft hadron production in pp collisions at the LHC is achieved in the framework of color dipole approach and modified quark-gluon string model.

Twist decomposition of non-linear effects in Balitsky–Kovchegov evolution of proton structure functions

Effects of non-linear small-x evolution of the gluon distribution given by the Balitsky–Kovchegov equation are analyzed within the collinear approximation framework. We perform a twist decomposition of the proton structure functions F2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_2$$\\end{document} and FL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_{\ extrm{L}}$$\\end{document} obtained from the Balitsky–Kovchegov equation using the Mellin representation of the scattering cross-sections at high energies. In both the structure functions we find strong corrections coming from the non-linear effects in the gluon evolution at twist 2, and strongly suppressed higher twist effects. This implies that unitarization effects of high energy scattering amplitudes are mostly the leading twist effect. Furthermore we consider the double logarithmic limit of the Balitsky–Kovchegov equation for the collinear gluon distribution, and compare the result to the Gribov–Levin–Ryskin equation. We find that these two equations differ by two powers of the hard scale logarithm for the large scales.

Geant4 Electron–Proton Integral Inelastic Cross Section Models

Electron-proton integral inelastic cross section is calculated based on the proton structure function formalism. The cross section is compared with the GEANT4 CHIPS model calculations utilizing the equivalent photon method.

Proton Structure Functions at Next-to-Leading Order in the Dipole Picture with Massive Quarks.

We predict heavy quark production cross sections in deep inelastic scattering at high energy by applying the color glass condensate effective theory. We demonstrate that, when the calculation is performed consistently at next-to-leading order accuracy with massive quarks, it becomes possible, for the first time in the dipole picture with perturbatively calculated center-of-mass energy evolution, to simultaneously describe both the light and heavy quark production data at small x_{Bj}. Furthermore, we show how the heavy quark cross section data provides additional strong constraints on the extracted nonperturbative initial condition for the small-x_{Bj} evolution equations.

Resonant contributions to polarized proton structure functions

Nucleon resonance contributions to the polarized proton ${g}_{1}$ and ${g}_{2}$ structure functions are computed from resonance electroexcitation amplitudes extracted from CLAS exclusive meson electroproduction data. Including resonances in the mass range up to 1.75 GeV, and taking into account the interference between excited states, we compare the resonant contributions with the polarized proton structure function and polarization asymmetry data from Jefferson Lab 6 GeV measurements. All resonance-like structure observed in the polarized structure functions and asymmetries can be attributed to the resonant contributions, confirming their essential role in the behavior of ${g}_{1}$ and ${g}_{2}$ in the resonant region over the entire range ${Q}^{2}<7.5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$ covered by the measurements. Comparing the resonance contributions with the ${g}_{1}$ and ${g}_{2}$ structure functions computed from parton distribution functions extrapolated from the deep-inelastic region, we also quantify the degree to which quark-hadron duality holds for ${g}_{1}$ and ${g}_{2}$ and their moments.

Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD

We present a simultaneous extraction of the moments of ${F}_{2}$ and ${F}_{L}$ structure functions of the proton for a range of photon virtuality, ${Q}^{2}$. This is achieved by computing the forward Compton amplitude on the lattice utilizing the second-order Feynman-Hellmann theorem. Our calculations are performed on configurations with two different lattice spacings and volumes, all at the $SU(3)$ symmetric point. We find the moments of ${F}_{2}$ and ${F}_{L}$ in good agreement with experiment. Power corrections turn out to be significant. This is the first time the ${Q}^{2}$ dependence of the lowest moment of ${F}_{2}$ has been quantified.

Parametrization of the nuclear structure function

In this paper, the parametrization of the nuclear structure function which is directly constrained by the dynamics of QCD in its high-energy limit is considered. This simple parameterization of the nuclear structure function is obtained from the proton experimental data by relying on a Froissart-bounded parametrization of the proton structure function. This phenomenological model describes high-energy QCD in the presence of saturation effects. Numerical calculations and comparison with available data from NMC, EMC and E665 Collaborations demonstrate that the suggested method by N.Armesto, C.A.Salgado and U.A. Wiedemann (ASW model) provides reliable ratio of nuclear structure functions $F_{2}^{A}/AF^{p}_{2}$ at low $x$ for light and heavy nuclei. The magnitude of nuclear shadowing is predicted for various kinematic regions and can be applied as well in analysis of ultra-high energy processes by future experiments at electron-ion colliders.

Functional Interaction of the Cruciate Ligaments, Posteromedial and Posterolateral Capsule, Oblique Popliteal Ligament, and Other Structures in Preventing Abnormal Knee Hyperextension

Background: The ligaments and soft tissue capsular structures of the knee joint that provide a resisting force to prevent abnormal knee hyperextension have not been determined. This knowledge is required for the diagnosis and treatment of knee hyperextension abnormalities. Purpose: To determine the resisting moment of knee ligament and capsular structures that resist knee hyperextension. Hypothesis: The combined posteromedial and posterolateral capsular structures function to provide a major restraint to prevent abnormal knee hyperextension. The anterior and posterior cruciate ligaments resist knee hyperextension but function as secondary restraints. Study Design: Descriptive laboratory study. Methods: A 6 degrees of freedom robotic system determined intact laxity limits in 24 cadaveric knees from 0° to 100° of knee flexion for anteroposterior limits at ±135 N, abduction-adduction limits at ±7 N·m, and external-internal limits at ±5 N·m. One loading method (n = 14 knees) used a static loading sequence with knee hyperextension to 27-N·m torque while maintaining all other degrees of freedom at zero load during sequential soft tissue cutting. The second method (n = 10 knees) used a cyclic loading sequence to decrease viscoelastic effects with soft tissue cutting at 0° of extension, followed by knee hyperextension to 27-N·m torque and cycled back to 0°. Selective soft tissue cuttings were performed of the following: oblique popliteal ligament, fabellofibular ligament, posterolateral capsule, posteromedial capsule with posterior oblique ligament, cruciate ligaments, lateral collateral ligament, popliteus, anterolateral ligament and iliotibial band, and superficial plus deep medial collateral ligaments. The sequential loss in the restraining moment with sectioning provides the function of that structure in resisting knee hyperextension. Results: The median resisting force to knee hyperextension, in descending order, was the posteromedial capsule and posterior oblique ligament (21.7%), posterorolateral ligament and fabellofibular ligament (17.1%), anterior and posterior cruciate ligaments (13% and 12.9%, respectively), superior and deep medial collateral ligament (9.6%), oblique popliteal ligament (7.7%), and lateral collateral ligament (5.4%). The combined posterior capsular structures provided 54.7% and the anterior and posterior cruciate ligaments 25.3% of the total resisting moment to prevent knee hyperextension. Conclusion: Diagnosis of abnormal knee hyperextension involves a combination of multiple ligament and soft tissue structures without 1 primary restraint. The posteromedial and posterolateral capsular structures provided the major resisting moment to prevent knee hyperextension. The cruciate ligaments produced a lesser resisting moment to knee hyperextension. Clinical Relevance: This is the first study to comprehensively measure all of the knee ligaments and capsular structures providing a resisting moment to abnormal knee hyperextension. These data are required for diagnostic and treatment strategies on the pathomechanics of abnormal knee hyperextension in patients after injury or developmental cases.

Test of the TMD gluon density in a proton with the longitudinal structure function FL(x,Q2)

We investigate the dependence of the deep inelastic proton structure function FL(x,Q2) on different forms of the transverse momentum dependent (TMD, or unintegrated) gluon distribution. We present a comparison of theoretical results with the latest experimental data taken by the H1 and ZEUS Collaborations at HERA. We demonstrate that these data, despite of having quite large uncertainties, can test different kinds of the gluon TMD in a proton. Moreover, different phenomenological models at low x could be tested by future experiments on deep inelastic scattering.

Comparison of empirical structural vulnerability rapid prediction models considering typical earthquakes

The damage caused by different destructive earthquakes to various building structures has diverse characteristics. To understand the failure mode and vulnerability mechanism of various structures under a typical destructive earthquake, a relatively accurate rapid prediction model suitable for the vulnerability of various specific structures is constructed. In the present study, four distinct structural typologies of the Wenchuan earthquake (Dujiangyan city) and Jiuzhaigou earthquake (Jiuzhaigou county) in China are examined, and the failure characteristics and damage mechanism are studied. A rapid vulnerability prediction method based on multidimensional parameters is proposed. The model is verified using the established structural vulnerability database (8,553 buildings). The comparison models of rapid vulnerability prediction of various typical structures (surface, function, and matrix) are developed. A new method for the rapid prediction of regional group structure vulnerability based on resultant peak acceleration parameters is proposed, and a quantitative relationship model based on resultant peak acceleration and macrointensity level is constructed. The traditional vulnerability index calculation model is modified and improved, and a new fragility rapid prediction model of regional typical structural groups based on the revised average earthquake damage index parameter is obtained. Using the verification of the empirical structure seismic damage sample database of field inspection, the established multidimensional vulnerability rapid prediction model of typical structures has greater stability and reliability.

One-to-One Correspondence of Soft and Hard Pomeron with the Color Dipole Picture of the Gluon Density at Low x

The correspondence between the gluon density behavior of the color dipole picture (CDP) and the two-Pomeron approach at low x deep inelastic scattering is considered. For photon virtualities of {{Q}^{2}} gtrsim 10 GeV2, the results for the parametrization and CDP models are defined by the CDP asymptotic limit and are compatible with the soft and hard-Pomeron approach. These results show that the hard-Pomeron trajectory does not guarantee converging towards the asymptotic representation at low and large {{Q}^{2}} ({{Q}^{2}} lesssim 100 GeV2) values in a wide range of the virtual-photon–proton energy squared. The gluon distributions can be obtained directly in terms of the proton structure functions and the running coupling and compared with the results from the M. Gluck, P. Jimenez-Delgado and E. Reya (GJR) and A. Martin, W. Stirling, R. Thorne, and G. Watt (MSTW) parametrizations.

Beyond DGLAP improved saturation model

We present a modification of the DGLAP improved saturation model with respect to the nonlinear correction (NLC). The GLR-MQ improved saturation model is considered by employing the parametrization of proton structure function due to the Laplace transforms method, which preserves its behavior success in the low and high Q^{2} regions. We show that the geometric scaling holds for the GLR-MQ improved model in a wide kinematic region rQ_{s}. These results are comparable with other models in a wide kinematic region rQ_{s}. The behavior of the dipole cross sections, with respect to the GLR-MQ improved saturation model, are comparable with the Color Glass Condensate (CGC) model. The model describes the dipole cross sections in the inclusive and diffractive processes. We also compare the nonlinear corrections to the impact-parameter dependent saturation (IP-Sat) model with the impact-parameter dependent color glass condensate (b-CGC) dipole model. Finally, we consider the linear and nonlinear corrections to the IP Non-Sat model. These results provide a benchmark for further investigation of QCD at small x in future experiments such as the Large Hadron Collider and Future Circular Collider projects.

IMPROVEMENT OF FINANCIAL ACTIVITIES OF SMALL ENTERPRISES

The key points of the financial activity of small business development are justified. It is noted that entrepreneurship in the field of small business is determined by the activity of business entities, which is characterized by both features that are characteristic of business structures in general, and specific features that determine the peculiarities of such functioning of business entities in the sphere of the implementation of business tasks and goals. It was determined that the success of small business is determined by the conditions of the environment in which business structures function. It is clarified that such conditions should include economic, legal, socio-cultural, demographic, technological, natural-geographic and organizational conditions. It has been proven that ensuring the existence of all enterprises depends on its financial resources. The sources of formation of financial resources are the main feature of their classification. In practice, own and involved groups of sources of formation are distinguished. FG "Iryna – O.T" was chosen to evaluate the structure of sources of small enterprises. This is a farm, the main activity of which is grain and technical crops. During the studied period, the amount of financial resources is increasing. Having evaluated the financial management of the FG "Iryna – O.T" using various indicators, we came to the conclusion that the FG under study is profitable and financially independent. Having evaluated the formation, placement and efficiency of the use of financial resources, they came to the conclusion that the FG "Iryna – O.T" had a good financial condition, as evidenced by the relevant indicators: the amount of net profit increased by 469.8 thousand hryvnias; liquidity indicators of the FG indicate the liquid balance of the enterprise; the state of the FG in 2020–2022 is characterized as financially stable; the financial independence of the FG is high, which indicates a good state of financial resources; profitability indicators of FG had positive values. In general, FG "Iryna – O.T" has positive indicators of filling financial resources, their volume increases over the years, however, the FG has become completely independent of obligations and avoids a crisis situation associated with a lack of funds to pay debts. Farms are an important component of the market of economic relations between the world and Ukraine. In the conditions of hostilities, farmers and private peasant farms provided food for the local population and internally displaced persons, thus proving the stability and possibility of ensuring the existence of small producers.

Аспекти мовленнєвожанрової організації „неприродних” наративів (на матеріалі української та російської мов)

The article reveals the mechanisms allowing the author’s intention to destruct the structural-content organization of speech genres and influence the formation and perception of an artistic narrative. The research gives ground to outline a set of devices to make the communicative sense of artistic narratives odd, which is explained by the author’s creation of „unnatural” ontology of the narrated world; to outline various ways of semantic destruction of speech acts, and intentional breaches of the pragmatic conditions of the effective speech-genre structures creation and functioning. The result of these devices use is the formation of the ontological, perceptional, behavioural, mental and some other types of textual (discursive, narrative) absurd. Mechanisms of creating intentional and/or nonintentional „unnatural” speech acts as constituents of artistic narratives are active sources of forming unusual communicative senses of aesthetic nature.

Production of e+e− in proton-lead collision: Photon-photon fusion

We analyze the photon-initiated processes for production of $ e ^ + e ^- $ pairs in proton-nucleus collisions at LHC energy, taking into account both elastic processes and proton dissociations in the low-mass region (LMR) and intermediate-mass region (IMR) as defined by the ALICE collaboration. The calculations are performed within the $k_{\rm T}$-factorisation approach, including transverse momenta of intermediate photons. We discuss several differential distributions in invariant mass of both the leptons $M_{ll}$, pair rapidity $Y_{ll}$ and transverse momenta of the lepton pair $p_{t,ll}$. In addition, we present the two-dimensional distributions in $\log_{10} x_{Bj}$ and $\log_{10} Q^{2}$ and ($\log_{10} W,\log_{10} Q^{2}$) the arguments of the deep-inelastic structure functions. All presented results were obtained with modern parametrizations of proton structure functions. Limiting to small invariant masses of dielectrons one tests structure functions in the nonperturbative region of small $Q^2$ and/or small $W$. We quantify difference for different parametrizations from the literature.