Longitudinal Structure Function FL Research Articles

Decoupling of the structure functions in momentum space based on the Laplace transformation

Using Laplace transform techniques, we describe the determination of the longitudinal structure function FL(x,Q2), at the leading-order approximation in momentum space, from the structure function F2(x,Q2) and its derivative with respect to lnQ2 in a kinematical region of low values of the Bjorken variable x. Since the x dependence of F2(x,Q2) and its evolution with Q2 are determined much better by the data than FL(x,Q2), this method provides both a direct check on FL(x,Q2) where measured, and a way of extending FL(x,Q2) into regions of x and Q2 where there are currently no data. In our calculations, we ultilize the Block-Durand-Ha parametrization for the structure function F2(x,Q2) [M. M. Block , .]. We find that the Laplace transform method in momentum space provides correct behaviors of the extracted longitudinal structure function FL(x,Q2) and that our obtained results are in line with data from the H1 Collaboration and other results for FL(x,Q2) obtained using Mellin transform method. Published by the American Physical Society 2024

Longitudinal structure function FL at low Q2 and low x with model for higher twist: An update

A reanalysis of the model for the longitudinal structure function FL(x,Q2) at low x and low Q2 was undertaken, in view of the advent of the EIC. The model is based on the photon-gluon fusion mechanism suitably extrapolated to the region of low Q2. It includes the kinematic constraint FL∼Q4 as Q2→ 0 and higher twist contribution which vanishes as Q2→∞. Revised model was critically updated and compared to the presently available data.

Longitudinal Structure Function FL at Small x Extracted from the Berger–Block–Tan Parametrization of F2

The longitudinal structure function FL(x,Q2) is extracted at low values of the Bjorken variable x from the Berger-Block-Tan parametrization of F2(x,Q2). The obtained FL(x,Q2) does not violate the high-energy asymptotic Froissart boundary and is in a reasonable good agreement with the available experimental data.

Absence of π2 terms in physical anomalous dimensions in DIS: Verification and resulting predictions

We study the higher-order corrections to structure functions in inclusive deep-inelastic scattering (DIS) in massless perturbative QCD, in the context of the conjectured absence of even-n values of the Riemann zeta-function ζn, i.e., of powers of π2, in Euclidean physical quantities. We provide substantial additional support for this conjecture by demonstrating that it holds, as far as it can be tested by the results of diagram computations, for the physical anomalous dimensions of structure functions at the fourth and fifth order in the strong coupling constant αs. The conjecture is then employed to predict hitherto unknown ζ4 and ζ6 contributions to the anomalous dimensions for parton distributions and to the coefficient functions for the longitudinal structure function FL.

Geometric Scaling Analysis of Deep Inelastic Scattering Data Including Heavy Quarks**Supported by the National Natural Science Foundation of China under Grant Nos 11305040, 11375071 and 11447203, the Education Department of Guizhou Province Innovation Talent Fund under Grant No [2015]5508, the Education Department of Guizhou Province Innovation Team Fund under Grant No [2014]35, the Guizhou Province Science Technology Foundation under Grant

An analytic massive total cross section of photon-proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton–hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton–hadron cross section, which plays a significant role in the description of the photoproduction region.

Analysis of the Longitudinal Structure Function FL from the Non-linear Regge Gluon Density Behavior at Low-x

The longitudinal structure function with shadowing correction according to the nonlinear effects of the gluon density behavior at low x is considered. The solution of the GLR-MQ evolution equation for the gluon density shows that the FLg (x, Q2) behavior can be tamed by the singularity at low x values. Comparing our results with H1 data at R=4GeV−1 shows that at very low x this behavior is completely tamed by taking shadowing correction into account.

Longitudinal structure function FL of proton from Regge-like behaviour of gluon distribution function up to next-to-next-to-leading order at small-x

The behaviour of the longitudinal structure function FL with respect to the Bjorken variable x and Q2, the squared four-momentum transfer between lepton and nucleon, in the next-to-next-to-leading order (NNLO) at small x is presented using the Regge-like behaviour of the gluon distribution function. Here we have calculated \( t \left(=\ln \frac{Q^{2}}{\Lambda^{2}}\right)\) - and x -evolutions of the FL structure function using the gluon distribution function obtained as a result of solution of the DGLAP evolution equation at small x . We have also studied the behaviour of the DIS cross section ratio R in this kinematical region. The calculated results are compared with recent H1, ZEUS data and DL model results, CT10 parameterization. The results obtained can be explained within the framework of perturbative quantum chromodynamics i.e., the evolution of the structure function FL increases towards low values of x .

Longitudinal Structure Function F L of Proton from Regge Like Behaviour of Structure Function at Small-x

The evolutions of longitudinal structure function FL from quantum chromodynamics (QCD) evolution equation in next-to-leading order at small-x is presented using the Regge like behaviour of the structure function. The proposed simple analytical expression for FL structure function provides the t- and x-evolution equations to study the behaviour of FL structure function at small-x. The calculated results are compared with the data of H1, ZEUS collaborations and results of Block model, Donnachie–Landshoff model. Our calculated results can be described within the framework of perturbative QCD.

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

Self-similarity based model of proton structure function at small x was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region 6.2 × 10−7 ≤ x ≤ 10−2 and 0.045 ≤ Q2 ≤ 120 GeV2. We use momentum sum rule to pin down the corresponding self-similarity-based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function FL(x, Q2) for Altarelli—Martinelli equation in QCD and is compared with the recent HERA data.

Solution of Evolution Equation for Longitudinal Structure Function F L upto Next-to-Next-to-Leading Order and Its t-Evolution at Small-x

The aim of the present paper is to calculate longitudinal structure function FL from QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) at small-x. The calculation of FL is important for the phenomenological study of gluon distribution function inside the nucleon. Here we use Taylor Series Expansion method to solve the evolution equation for small-x and thus obtain t-evolution of FL structure function. The calculated results are compared with H1 and ZEUS data and results of Block and Donnachie-Landshoff (DL) models.

NON-SINGLET PART OF THE LONGITUDINAL STRUCTURE FUNCTION FL UP TO $O(\alpha_s^3)$

The unpolarized longitudinal nucleon structure function FL, measured in the deep inelastic lepton-nucleon scattering, is contained of three parts, singlet, non-singlet and gluon. The aim of this paper is to perform a QCD analysis of the longitudinal heavy and light structure functions FL(x, Q2) in the non-singlet part up to [Formula: see text]. We use the light and heavy flavor Wilson coefficients and distribution functions in Mellin space. Also we need to use the Padé approximation for αs analysis.

Recent results from HERA

After the end of data taking in 2007, the experiments H1 and ZEUS have entered into an intense phase of data analysis. Recent results of this effort on neutral (NC) and charged current (CC) cross sections at high Q2, the longitudinal structure function FL, inclusive diffraction, heavy flavour production and on searches for glueballs are presented. Also shown are results of a combined analysis on inclusive NC and CC cross sections performed by H1 and ZEUS using HERA-I data.

Nonlinear correction to the longitudinal structure function at small x

We computed the longitudinal proton structure function FL, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation approach at small x . For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As the very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated, we show that the strong rise that corresponds to the linear QCD evolution equations can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small x . We computed the predictions for all details of the nonlinear longitudinal structure function in the kinematic range where it has been measured by the H1 Collaboration and made comparisons with the computation by Moch, Vermaseren and Vogt at the second order with input data from the MRST QCD fit.

Threshold resummation of the structure functionFL

The behaviour of the quark coefficient function for the longitudinal structure function FL in deep-inelastic scattering is investigated for large values of the Bjorken variable x. We combine a highly plausible conjecture on the large-x limit of the physical evolution kernel for this quantity with our explicit three-loop results to derive the coefficients of the three leading large-x logarithms, αs nln2n−1−k(1 − x), k = 1, 2, 3, to all orders in the strong coupling constant αs. Corresponding results are derived for the non-CF part of the gluon coefficient function suppressed by a factor 1 − x, and for the analogous subleading (1 − x)lnk(1 − x) contributions in the quark case. Our results appear to indicate an obstacle for an exponentiation with a higher logarithmic accuracy.

Proton structure and QCD dynamics at low x

A brief overview is given on most recent, preliminary results obtained by the HERA experiments H1 and ZEUS on the measurement of the neutral current e±p scattering cross section. The paper focuses on the first combinations and QCD analyses of joint H1 and ZEUS data, on an H1 measurement in the transition region from hadronic to partonic behavior and presents the first results obtained on the measurement of the longitudinal structure function FL at low Bjorken x using recent data collected at reduced proton beam energies.

Measurement of the proton structure function [formula omitted] at low x

A first measurement is reported of the longitudinal proton structure function FL(x,Q2) at the ep collider HERA. It is based on inclusive deep inelastic e+p scattering cross section measurements with a positron beam energy of 27.5 GeV and proton beam energies of 920, 575 and 460 GeV. Employing the energy dependence of the cross section, FL is measured in a range of squared four-momentum transfers 12⩽Q2⩽90 GeV2 and low Bjorken x0.00024⩽x⩽0.0036. The FL values agree with higher order QCD calculations based on parton densities obtained using cross section data previously measured at HERA.

The longitudinal structure function at the third order

We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function FL, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD. Our exact results agree with determinations of low even-integer Mellin moments and of the leading small-x terms in the flavour-singlet sector. In this Letter we present compact and accurate parametrizations of the results and illustrate the numerical impact of the NNLO corrections.

Determination of the longitudinal structure function FL at HERA

Recent results from the HERA experiment H1 on the longitudinal structure function FL of the proton are presented. They include proton structure function analyses with particular emphasis on those kinematic regions which are sensitive to FL. All results can be consistently described within the framework of perturbative QCD.

How open charm production and scaling violations probe the rightmost hard BFKL pole exchange

In 1994 Zakharov and the present authors argued that in color dipole (CD) BFKL approach to DIS excitation of open charm at moderately large Q2 is dominated by hard BFKL exchange. In view of the rapid accumulation of the experimental data on small-x charm structure function of the proton F2cc from HERA, we subject the issue of dominance of the rightmost hard BFKL pole exchange to further scrutiny. Based on CD BFKL-Regge factorization we report parameter-free predictions for the charm structure function F2cc and show that the background to the dominant rightmost hard BFKL exchange from subleading hard BFKL and soft-pomeron exchanges is negligible small from real photo-production to DIS at Q2 lsim 50-100 GeV2. The agreement with the experiment is good and lends strong support for the intercept of the rightmost hard BFKL pole DeltaPom=alphaPom-1=0.4 as found in 1994 in the color dipole approach. We comment on the related determination of DeltaPom from the x-dependence of the longitudinal structure function FL(x,Q2) and of the scaling violation dF2/dlog Q2 taken at a suitable value of Q2. \

Comparison between variable flavor number schemes for charm quark electroproduction

A comparison is made between two variable flavor number schemes which describe charm quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Since the coefficient functions in the variable flavornumber schemes have to be finite in the limit m → 0 we have defined a prescription for those processes where the virtual photon is attached to a light quark. Furthermore one has to construct a parton density set with four active flavors (u,d,s,c) out of a set which only contains three light flavors (u,d,s). In order � 2 the two sets are discontinuous at µ = mc which follows from mass factorization of the heavy quark coefficient functions. The charm component ofthe structure function F2,c is insensitive to the different variable flavor number schemes. In particular in the threshold region they both agree with the description in fixed order perturbation theory presented in a three flavor scheme. However one version does not lead to a correct description of the threshold behavior of the longitudinal structure function FL,c. This happens when one requires a non-vanishing zeroth order longitudinal coefficient function.