Proton Structure Function Research Articles

Evidence of quasi-partonic higher-twist effects in deep inelastic scattering at HERA at moderate $$Q^2$$ Q 2

The combined HERA data for the inclusive deep inelastic scattering (DIS) cross sections for the momentum transfer Q^2 > 1,mathrm {GeV}^2 are fitted within the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) framework at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy, complemented by a QCD-inspired parameterisation of twist 4 corrections. A modified form of the input parton density functions is also included, motivated by parton saturation mechanism at small Bjorken x and at a low scale. These modifications lead to a significant improvement of the data description in the region of low Q^2. For the whole data sample, the new benchmark NNLO DGLAP fit yields chi ^2/mathrm{d.o.f. } simeq 1.19 to be compared to 1.46 resulting from the standard NNLO DGLAP fit. We discuss the results in the context of the parton saturation picture and describe the impact of the higher-twist corrections on the derived parton density functions. The resulting description of the longitudinal proton structure function F_{mathrm {L}} is consistent with the HERA data. Our estimates of higher-twist contributions to the proton structure functions are comparable to the leading-twist contributions at low Q^2 simeq 2 GeV^2 and x simeq 10^{-5}. The x-dependence of the twist 4 corrections obtained from the best fit is consistent with the leading twist 4 quasi-partonic operators, corresponding to an exchange of four interacting gluons in the t-channel.

Improved determination ofd¯(x)−u¯(x)flavor asymmetry in the proton by data from the BONuS experiment at JLAB and using an approach by Brodsky, Hoyer, Peterson, and Sakai

The experimental data taken from both Drell-Yan and deep-inelastic scattering (DIS) experiments suggest a sign-change in $\bar d(x) - \bar u(x)$ flavor asymmetry in the proton at large values of momentum fraction $x$. In this work, we present a phenomenological study of $\bar d(x) - \bar u(x)$ flavor asymmetry. First, we extract the $\bar d(x)-\bar u(x)$ distribution using the more recent data from the BONuS experiment at Jefferson Lab on the ratio of neutron to proton structure functions, $F_2^n/F_2^p$, and show that it undergoes a sing-change and becomes negative at large values of momentum fraction $x$, as expected. The stability and reliability of our obtained results have been examined by including target mass corrections (TMCs) as well as higher twist (HT) terms which are particularly important at the large-$x$ region at low Q$^2$. Then, we calculate the $\bar d(x) - \bar u(x)$ distribution using the Brodsky, Hoyer, Peterson, and Sakai (BHPS) model and show that if one chooses a mass for the down quark smaller than the one for the up quark it leads to a better description for the Fermilab E866 data. In order to prove this claim, we determine the masses of down and up sea quarks by fitting to the available and up-to-date experimental data for the $\bar d(x)-\bar u(x)$ distribution. In this respect, unlike the previous performed theoretical studies, we have shown that this distribution has a sign-change at $x>0.3$ after evolution to the scale of available experimental data.

Neutrino cross-section in ultrahigh energy regime using double asymptotic limit of QCD

Studies on neutrino–nucleon (\({\nu }N\)) cross-sections have regained interest due to increasing importance of precision measurements, as they are needed as an ingredient in all neutrino experiments. In this work, we use the QCD-inspired double asymptotic limit fit of electron–proton structure function \(F_{2}^{ep}\) to low-\( x \) HERA data, to calculate \(\nu \) N cross-section for charged current (CC) and neutral current (NC) neutrino interactions in ultrahigh energy (UHE) neutrino energy (\(E_{\nu }\)) regime (\(10^{9}\, \mathrm {GeV} \le E_{\nu } \le 10^{12}\, \mathrm {GeV} \)). The form \(F_{2}^{ep} \sim x^{-\lambda (Q^{2})}\), used in our analysis, can be conjectured like a dynamic pomeron (DP)-type behaviour. We also find an analytic form of the total cross-sections, \(\sigma _{\mathrm {CC}}^{\nu N}\) and \(\sigma _{\mathrm {NC}}^{\nu N}\), which appear to be of Reggeon exchange type. We also do a comparative analysis of our results with those available in literature. Future measurements will support / confront our predictions.

Grazing of leaf-associated Cercomonads (Protists: Rhizaria: Cercozoa) structures bacterial community composition and function.

Preferential food selection in protists is well documented, but we still lack basic understanding on how protist predation modifies the taxonomic and functional composition of bacterial communities. We conducted feeding trials using leaf-associated cercomonad Cercozoa by incubating them on a standardized, diverse bacterial community washed from plant leaves. We used a shotgun metagenomics approach to investigate the taxonomic and functional changes of the bacterial community after five days protist predation on bacteria. Predation-induced shifts in bacterial community composition could be linked to phenotypic protist traits. Protist reproduction rate, morphological plasticity and cell speed were most important in determining bacterial community composition. Analyses of co-occurrence patterns showed less complex correlations between bacterial taxa in the protist-grazed treatments with a higher proportion of positive correlations than in non-grazed controls, suggesting that predation reduced the influence of strong competitors. Protist predation influenced 14 metabolic core functions including membrane transport from which type VI secretion systems were in particular upregulated. In view of the functional importance of bacterial communities in the phyllosphere and rhizosphere of plants, a more detailed understanding of predator-prey interactions, changes in microbial composition and function, and subsequent repercussions on plant performance are clearly required.

Solution of QCD⊗QED coupled DGLAP equations at NLO

In this work, we present an analytical solution for QCD⊗QED coupled Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in perturbative QCD using double Laplace transform. This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function. We also obtain contribution of photon in proton at LO and NLO at high energy and successfully compare the proton structure function with HERA data [1] and APFEL results [2]. Some comparisons also have been done for the singlet and gluon distribution functions with the MSTW results [3]. In addition, the contribution of photon distribution function inside the proton has been compared with results of MRST [4] and with the contribution of sea quark distribution functions which obtained by MSTW [3] and CTEQ6M [5].

Momentum fractions carried by quarks and gluons in models of proton structure functions at small x

In this paper, we report an analysis of partial momentum fractions carried by quarks and gluons in six alternative phenomenological models of proton structure function valid in limited small [Formula: see text] regions: [Formula: see text], [Formula: see text] to 6; the limits being determined by phenomenological range of validity in each model. Since the physics of small [Formula: see text] is not completely understood at this point, we have considered both self-similarity-based as well as QCD-based models. The procedure by which one can determine the applicability ranges in [Formula: see text] and [Formula: see text] of the models is presented. We find that while the self-similarity-based models with linear rise in [Formula: see text] has limited phenomenological ranges of validity, an improved version with linear rise in [Formula: see text] has a wider phenomenological range. We then compare the partial momentum fractions in all the small [Formula: see text] models. Our analysis implies that the role of small [Formula: see text] sea quarks in calculating the second moments of parton distribution is minor one. We have also made a comprehensive comparison of all the phenomenological models considered to the available perturbative QCD, lattice QCD as well as Ads/QCD results.

Two-point similarity in turbulent planar jet flows

A similarity analysis was performed using the governing equations for the two-point velocity correlations and for the second order structures functions in the far field of a turbulent planar jet. The equilibrium of the large- and small-scale motions was ensured by requiring that the turbulent transfer terms are in equilibrium throughout the flow. The results show that the equations for the two-point velocity correlations at large separation distances admit similarity solutions where the dissipation rate is proportional to uo3/lo when the growth rate of the flow is constant and proportional to Uouo2/δ or uo3/lo(dδ/dx1)−12 when the growth rate decreases as the flow evolves. The turbulent normal stresses decay at x1−1 in all solutions suggesting that the change in dissipation rate is associated with a change in the development of the mean flow. The analysis for the structure functions show that these equations admit similarity solutions for the inertial range with a length scale proportional to the Taylor microscale λ. The scale for the third order structures function is proportional to ϵλ or uo3/Reλ in all cases, but the velocity scale for the second order structure functions is proportional to uoReλ−(1−ns)/(3−ns) where ns ≤ 1. The velocity scale is uo when ns is 1 but previous measurements in high Reynolds number planar jets (Pearson and Antonia, 2001, J. of Fluid Mech., 444, 343-382), indicate that ns ≲ 0.

Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

We analytically solved the QED[Formula: see text]QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED [Formula: see text] (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) [Formula: see text] (Ref. 4). We also compared the proton structure function, [Formula: see text], with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high [Formula: see text] and [Formula: see text].

Analytic derivation of the next-to-leading order proton structure function F2p(x,Q2) based on the Laplace transformation

An analytical solution based on the Laplace transformation technique for the DGLAP evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, $F_2^p(x, Q^2)$, in the Laplace $s$-space. We present the results for the separate parton distributions for all parton species, including valence quark densities, the anti-quark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions and the proton structure function with the results from {\tt GJR08} and {\tt KKT12} parametrization models as well as the $x$-space results using {\tt QCDnum} code. Our calculations show a very good agreement with the available theoretical models as well as the deep inelastic scattering (DIS) experimental data throughout the small and large values of $x$. The use of our analytical solution to extract the parton densities and the proton structure function is discussed in detail to justify the analysis method considering the accuracy and speed of calculations. Overall, the accuracy we obtain from the analytical solution using the inverse Laplace transform technique is found to be better than 1 part in 10$^{4}$ to 10$^{5}$. We also present a detailed QCD analysis of non-singlet structure functions using all available DIS data to perform global QCD fits. In this regard we employ the Jacobi polynomial approach to convert the results from Laplace $s$ space to Bjorken $x$ space. The extracted valence quark densities are also presented and compared to the {\tt JR14}, {\tt MMHT14}, {\tt NNPDF} and {\tt CJ15} PDFs sets. We evaluate the numerical effects of target mass corrections (TMCs) and higher twist (HT) terms on various structure functions, and compare fits to data with and without these corrections.

Comparative analysis of analytical solutions forF2P(x,t)in the DGLAP approach

Coupled DGLAP equations involving singlet quark and gluon distributions are explored by a Taylor expansion as two first order partial differential equations in two variables. The system of equations are then solved by the Lagrange's method and Method of Characteristics. We obtain the proton structure function by combining the corresponding non-singlet and singlet structure functions by both the methods. Analytical solutions for proton structure function thus obtained are compared with the data available and their compatibility is checked. Data favors the analytical solution by Lagrange's method.

Polarized parton densities and spin dependent structure function of the nucleon

We study the polarized parton distribution functions (PPDFs) from recent experimental data at the next-to-leading order (NLO) approximation in the fixed-flavor number scheme. In this analysis, we can compare our results with experimental data such as very recent COMPASS data. It would be very worth to study the PPDFs parametrization form when we want to use this new COMPASS data in QCD analysis on polarized proton structure and parton distribution functions.

An Improved Singularity Free Self-Similar Model of Proton Structure Function

In this paper we make re-analysis of a self-similarity based model of the proton structure function pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range of x: . We also suggest a plausible singularity free form of the model, which has a wider phenomenological range of validity in Q2 than the earlier ones.

How Bright is the Proton? A Precise Determination of the Photon Parton Distribution Function.

It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton (ep) scattering data, in effect viewing the ep→e+X process as an electron scattering off the photon field of the proton. To this end, we consider an imaginary, beyond the Standard Model process with a flavor changing photon-lepton vertex. We write its cross section in two ways: one in terms of proton structure functions, the other in terms of a photon distribution. Requiring their equivalence yields the photon distribution as an integral over proton structure functions. As a result of the good precision of ep data, we constrain the photon PDF at the level of 1%-2% over a wide range of momentum fractions.

Parton Distribution Functions and models of proton structure functions with self-similarity

Sometime back, a self-similarity based model of the proton structure function at small [Formula: see text] was proposed by Lastovicka. We make reanalysis of this model with most recent HERA data. No significance difference with the earlier analysis is found. Both the analyses have singularity within the kinematical range of [Formula: see text]: [Formula: see text]. We therefore study the model with the additional assumption that it should be singularity free, imposing positivity conditions on the model parameters. This results in a new model which is, however, phenomenologically valid only in a limited low [Formula: see text] range. We therefore make further generalization of the defining self-similar unintegrated Parton Density Function (uPDF) and show that the with proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a structure function with logarithmic growth in [Formula: see text] closer to QCD. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large [Formula: see text] in a parameter-free way. The possibility of incorporation of Transverse Momentum Dependent (TMD) PDF in this approach is explored as well.

NLO production of W± and Z0 vector bosons via hadron collisions in the frameworks of Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distribution functions

In a series of papers, we have investigated the compatibility of the $Kimber$-$Martin$-$Ryskin$ ($KMR$) and $Martin$-$Ryskin$-$Watt$ ($MRW$) $unintegrated$ parton distribution functions ($UPDF$) as well as the description of the experimental data on the proton structure functions. The present work is a sequel to that survey, via calculation of the transverse momentum distribution of the electro-weak gauge vector bosons in the $k_t$-factorization scheme, by the means of the $KMR$, the $LO\;MRW$ and the $NLO\;MRW$ $UPDF$, in the next-to leading order ($NLO$). To this end, we have calculated and aggregated the invariant amplitudes of the corresponding $involved$ diagrams in the $NLO$, and counted the individual contributions in different frameworks. The preparation process for the $UPDF$ utilizes the $PDF$ of $Martin$ et al, $MSTW2008-LO$, $MSTW2008-NLO$, $MMHT2014-LO$ and $MMHT2014-NLO$ as the inputs. Afterwards, the results have been analyzed against each other, as well as the existing experimental data. Our calculation show excellent agreement with the experiment data. It is however interesting to point-out that, the calculation using the $KMR$ framework illustrates a stronger agreement with the experimental data, despite the fact that the $LO\;MRW$ and the $NLO\;MRW$ formalisms employ a better theoretical description of the $DGLAP$ evolution equation. This is of course due to the use of the different implementation of the angular ordering constraint in the $KMR$ approach, in which automatically includes the re-summation of $ln({1/x})$, $BFKL$ logarithms, in the $LO$-$DGLAP$ evolution equation.

Molecular Electrochemistry: Recent Trends and Upcoming Challenges

AbstractCurrent efforts to address contemporary energy challenges give a boost to the development of molecular electrochemistry. It involves the design of new catalysts for the activation of small molecules and the understanding of the implemented mechanisms. Their rapidly increasing number has led to the design of a new benchmarking tool, namely the catalytic Tafel plot. Illustrative examples are given, demonstrating how complex multi‐electron–multi‐step mechanisms can be resolved. It is also shown that mastering substituent effects may lead to the design of ultra‐efficient catalysts by installing the right groups inside the catalyst molecule. On these bases, the next prospect is to heterogenize such remarkable molecular catalysts. Several new problems are then likely to arise, among which the deciphering of how catalytic mesoporous structures function. One may also attempt to marry the nanoparticle world with the realm of molecular catalysis and, for example, start by raising the question of the possible change of product selectivity upon nanoscaling.

Abstract 2520: IRS-1/LC3 nuclear structures and glioblastoma drug resistance

Abstract Drug resistance and frequent tumor relapses are the major obstacles in glioblastoma therapy, and recurrent tumors are practically incurable. We previously reported that insulin receptor substrate 1 (IRS-1), which is a typical signaling molecule for insulin and insulin-like growth factor 1 receptors, can translocate to nucleus, and that nuclear IRS-1 (nIRS-1) was found in different tumor cells, including glioblastomas. To unravel its function, we employed glioblastoma cell culture, animal models, and clinical samples. Using confocal imaging, molecular cloning, subcellular fractionation, mass spectrometry, gene expression analysis, and different approaches to verify protein-protein interactions, we demonstrate for the first time that nIRS-1 can form complex nuclear structures in a restricted number of cancer cells in glioblastoma biopsies and in intracranial glioblastoma xenografts. We also demonstrated the formation of highly organized ring-like structures in several cell lines, following ectopic expression of IRS-1 cloned in frame with nuclear localization signal (NLS-IRS-1). In these nuclear structures IRS-1 localizes at the periphery, and the core of the structure harbors a key autophagy protein, LC3; however, other autophagy proteins or biological membranes were not detected. In living cells expressing NLS-IRS-1-GFP fusion protein, IRS-1/LC3 structures are highly dynamic. They rapidly exchange IRS-1 molecules with nucleoplasm and interact with other nuclear complexes including BMI1-positive Polycomb bodies, PML bodies and Cajal bodies. Importantly, clones and mixed populations of cells expressing the NLS-IRS-1 and capable of forming the IRS-1/LC3 ring-like structures undergo extensive remodeling of gene expression, which suggests a transition to stem-like phenotype and associated resistance to several different anticancer drugs, including temozolomide. This is the first demonstration of IRS-1/LC3 nuclear complexes, which are highly dynamic and may play a role in epigenetic remodeling of glioblastoma cells towards stemness. Further studies are required to determine detailed molecular composition and to explain how these new nuclear structures function. Citation Format: Adam Lassak, Dorota Wyczechowska, Anna Wilk, Adriana Zapata, Mathew Dean, Luis DelValle, Jann N. Sarkaria, Augusto Ochoas, Francesca Peruzzi, Krzysztof Reiss. IRS-1/LC3 nuclear structures and glioblastoma drug resistance. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2520.

Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach

We present a first QCD analysis of next-to-next-leading-order (NNLO) contributions of the spin-dependent parton distribution functions (PPDFs) in the nucleon and their uncertainties using the Jacobi polynomial approach. Having the NNLO contributions of the quark-quark and gluon-quark splitting functions in perturbative QCD (Nucl. Phys. B 889 (2014) 351-400), one can obtain the evolution of longitudinally polarized parton densities of hadrons up to NNLO accuracy of QCD. A very large sets of recent and up-to-date experimental data of spin structure functions of the proton $g_1^p$, neutron $g_1^n$, and deuteron $g_1^d$ have been used in this analysis. The predictions for the NNLO calculations of the polarized parton distribution functions as well as the proton, neutron and deuteron polarized structure functions are compared with the corresponding results of the NLO approximation. We form a mutually consistent set of polarized PDFs due to the inclusion of the most available experimental data including the recently high-precision measurements from {\tt COMPASS16} experiments (Phys. Lett. B 753 (2016) 18-28). We have performed a careful estimation of the uncertainties using the most common and practical method, the Hessian method, for the polarized PDFs originating from the experimental errors. The proton, neutron and deuteron structure functions and also their first moments, $\Gamma^{\rm p, n, d}$, are in good agreement with the experimental data at small and large momentum fraction of $x$. We will discuss how our knowledge of spin-dependence structure functions can improve at small and large value of $x$ by the recent {\tt COMPASS16} measurements at CERN, the {\tt PHENIX} and {\tt STAR} measurements at RHIC, and at the future proposed colliders such as Electron-Ion collider (EIC).

High-xstructure function of the virtually free neutron

The pole extrapolation method is applied to the semi-inclusive inelastic electron scattering off the deuteron with tagged spectator protons to extract the high-x structure function of the neutron. This approach is based on the extrapolation of the measured cross sections at different momenta of the spectator proton to the non-physical pole of the bound neutron in the deuteron. The advantage of the method is in the possibility of suppression of the nuclear effects in a maximally model-independent way. The neutron structure functions obtained in this way demonstrate a surprising x dependence at $x\ge 0.6$ and $1.6 \leq Q^2 \leq 3.38$ GeV$^2$, indicating a possible rise of the neutron to proton structure function ratio. If the observed rise is valid in the true deep inelastic region then it may indicate new dynamics in the generation of high-x quarks in the nucleon. One such mechanism we discuss is the possible dominance of short-range isosinglet quark-quark correlations that can enhance the d-quark distribution in the proton.

Two-photon exchange correction to muon–proton elastic scattering at low momentum transfer

We evaluate the two-photon exchange (TPE) correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we account for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in our evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we provide an explicit evaluation based on a Regge fit of high-energy proton structure function data. It is found that, for the kinematics of the forthcoming muon-proton elastic scattering data of the MUSE experiment, the elastic TPE contribution dominates, and the size of the inelastic TPE contributions is within the anticipated error of the forthcoming data.