Nucleon Structure Functions Research Articles

Nonsinglet polarized nucleon structure function in infrared-safe QCD

The polarized nucleon structure function in the nonsinglet case is investigated here by a new insight rather than conventional perturbative QCD (pQCD). For this purpose we note that the solution of the evolution equations in moment space involves noninteger powers of the coupling constant. Therefore it is possible to employ a new approach which is called fractional analytical perturbation theory Consequently, it is possible to remove the Landau singularities of the renormalized coupling, i.e., at the scales $Q \sim \Lambda$, using this approach. This provides an opportunity to continue the desired calculations toward small values of energy scales even less than the $\Lambda$ scale. To modify the analytical perturbation theory, a newer approach is introduced, called 2$\delta$anQCD, in which the spectral function of the holomorphic coupling is parameterized in the low-energy region by two delta functions. This model gives us more reliable results for the considered QCD observables, even in the deep infrared region. We calculate the nonsinglet part of the polarized nucleon structure function, using the 2$\delta$anQCD model, and compare it with the result from the underlying pQCD where both are in a new defined scheme, called the Lambert scheme. For this purpose we employ the anQCD package in the \textit{Mathematica} environment to establish the analytic (holomorphic) coupling constant. The results at various energy scales are also compared with the available experimental data, and it turns out that there is a good consistency between them. The results show that the obtained nucleon structure function at small energy scales has smoother behavior when using the 2$\delta$anQCD model than the underlying pQCD. In fact the coupling constant in analytic QCD behaves moderately and it makes the result approach the available data in a better way.

Measurements of Nonsinglet Moments of the Nucleon Structure Functions and Comparison to Predictions from Lattice QCD for Q2=4 GeV2

We present extractions of the nucleon nonsinglet moments utilizing new precision data on the deuteron F_{2} structure function at large Bjorken-x determined via the Rosenbluth separation technique at Jefferson Lab Experimental Hall C. These new data are combined with a complementary set of data on the proton previously measured in Hall C at similar kinematics and world datasets on the proton and deuteron at lower x measured at SLAC and CERN. The new Jefferson Lab data provide coverage of the upper third of the x range, crucial for precision determination of the higher moments. In contrast to previous extractions, these moments have been corrected for nuclear effects in the deuteron using a new global fit to the deuteron and proton data. The obtained experimental moments represent an order of magnitude improvement in precision over previous extractions using high x data. Moreover, recent exciting developments in lattice QCD calculations provide a first ever comparison of these new experimental results with calculations of moments carried out at the physical pion mass, as well as a new approach that first calculates the quark distributions directly before determining moments.

Toward a First-Principles Calculation of Electroweak Box Diagrams.

We derive a Feynman-Hellmann theorem relating the second-order nucleon energy shift resulting from the introduction of periodic source terms of electromagnetic and isovector axial currents to the parity-odd nucleon structure function F_{3}^{N}. It is a crucial ingredient in the theoretical study of the γW and γZ box diagrams that are known to suffer from large hadronic uncertainties. We demonstrate that for a given Q^{2} one only needs to compute a small number of energy shifts in order to obtain the required inputs for the box diagrams. Future lattice calculations based on this approach may shed new light on various topics in precision physics including the refined determination of the Cabibbo-Kobayashi-Maskawa matrix elements and the weak mixing angle.

Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects

We have studied the nucleon structure functions $F_{iN}^{EM} (x,Q^2);~i=1,2$, by including contributions due to the higher order perturbative QCD effect up to NNLO and the non-perturbative effects due to the kinematical and dynamical higher twist (HT) effects. The numerical results for $F_{iN}^{EM}(x,Q^2)$ are obtained using Martin, Motylinski, Harland-Lang, Thorne (MMHT) 2014 NLO and NNLO nucleon parton distribution functions (PDFs). The dynamical HT correction has been included following the renormalon approach as well as the phenomenological approach and the kinematical HT effect is incorporated using the works of Schienbein et al. These nucleon structure functions have been used as an input to calculate the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$. In a nucleus, the nuclear corrections arise because of the Fermi motion, binding energy, nucleon correlations, mesonic contribution, shadowing and antishadowing effects. These nuclear corrections are taken into account in the numerical calculations to obtain the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$, for the various nuclear targets like $^{12}C$, $^{27}Al$, $^{56}Fe$, $^{64}Cu$, $^{118}Sn$, $^{197}Au$ and $^{208}Pb$ which are of experimental interest. The effect of isoscalarity correction for nonisoscalar nuclear targets has also been studied. The results for the $F_{iA}^{EM} (x,Q^2)$ are compared with nCTEQ nuclear PDFs parameterization as well as with the experimental results from JLab, SLAC and NMC in the kinematic region of $0.1 \le x \le 0.8$ for several nuclei.

Ψ(2S) production in p + A collisions

We have analyzed the data of ψ(2S) production in proton-nucleus (p + A) collisions, available from the NA50 Collaboration in the SPS energy domain. The investigated data sets include the absolute production cross-sections as well as ψ(2S)-to-Drell-Yan (DY) cross-section ratios. An adapted version of the two-component QVZ model has been employed to calculate ψ(2S) production cross-sections. For both ψ(2S) and DY production, nuclear modifications to the free nucleon structure functions are taken into account. For ψ(2S), the final state interaction of the produced pairs with the nuclear medium is also taken into account, in accordance with the previously analyzed data. A satisfactory description of the data in p + A collisions is obtained. Model calculations are extrapolated to predict the ψ(2S) suppression in proton-induced collisions at near-threshold energies.

Analysis of the neutron spin structure function g1n by using the Laplace transform technique

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

Baryons in the Nuclear Medium

Many QCD-based models predict changes in the structure of the bound nucleon in the nuclear medium. The changes of the nucleon wave function lead to changes in nucleon structure functions and electromagnetic form factors. While these in-medium form factors are not experimental observables, they provide a natural explanation of a variety of experimental results. I will review some of these findings and discuss upcoming experiments.

Dispersion Theory in Electromagnetic Interactions

We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information about hadron structure constants by connecting information from complementary scattering processes. We consider the real and virtual Compton scattering processes off the proton, and summarize recent advances in the DR analysis of experimental data to extract the proton polarizabilities, in comparison with alternative studies based on chiral effective field theories. We discuss a multipole analysis of real Compton scattering data, along with a DR fit of the energy-dependent dynamical polarizabilities. Furthermore, we review new sum rules for the double-virtual Compton scattering process off the proton, which allow for model-independent relations between polarizabilities in real and virtual Compton scattering, and moments of nucleon structure functions. Information on double-virtual Compton scattering is used to predict and constrain the polarizability corrections to muonic hydrogen spectroscopy.

Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions

We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent determination of the low-$Q^2$ subtraction function in the Compton amplitude, which enters the two-photon-exchange contribution to the Lamb shift of (muonic) hydrogen. An explicit calculation of the $\Delta(1232)$-resonance contribution to the muonic-hydrogen $2P-2S$ Lamb shift yields $-1 \pm 1$ $\mathsf\mu$eV, confirming the previously conjectured smallness of this effect.

Nuclear longitudinal structure function in eA processes at the LHeC

The nucleon and nuclear longitudinal structure functions are determined by the Kharzeev–Levin–Nardin (KLN) model of the low-[Formula: see text] gluon distribution. The behavior of the gluon distribution ratio [Formula: see text] and the ratio [Formula: see text] in [Formula: see text] processes are shown in this paper. The heavy longitudinal structure function ratios in [Formula: see text] processes at the LHeC region are discussed. Heavy contributions to the ratio of the total longitudinal structure function are considerable and should not be neglected especially at smaller [Formula: see text] of the LHeC project. In the KLN model, the new geometrical scaling for transition from the linear to nonlinear regions in accordance with the LHeC processes is used, whose results intensively depended on the heavy quark mass effect.

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD

We present a new technique for extracting decay and transition rates into final states with any number of hadrons. The approach is only sensitive to total rates, in which all out-states with a given set of QCD quantum numbers are included. For processes involving photons or leptons, differential rates with respect to the non-hadronic kinematics may also be extracted. Our method involves constructing a finite-volume Euclidean four-point function, whose corresponding spectral function measures the decay and transition rates in the infinite-volume limit. This requires solving the inverse problem of extracting the spectral function from the correlator and also necessitates a smoothing procedure so that a well-defined infinite-volume limit exists. Both of these steps are accomplished by the Backus-Gilbert method and, as we show with a numerical example, reasonable precision can be expected in cases with multiple open decay channels. Potential applications include nucleon structure functions and the onset of the deep inelastic scattering regime, as well as semi-leptonic $D$ and $B$ decay rates.

SHiP: a new facility with a dedicated detector for studying tau-neutrino properties and nucleon structure functions

SHiP is a new general purpose fixed target facility, whose Technical Proposal has been recently reviewed by the CERN SPS Committee, who recommended that the experiment proceeds further to a Comprehensive Design phase. In its initial phase, the 400 GeV proton beam extracted from the SPS will be dumped on a heavy target with the aim of integrating 2 × 1020 pot in 5 years. A dedicated detector downstream of the target will allow to probe a variety of models with light long-lived exotic particles and masses below a few GeV/c2. Another dedicated detector will allow the study of neutrino cross-sections and angular distributions, which was the focus of the poster. ντ deep inelastic scattering cross sections will be measured with a statistics 1000 times larger than currently available, with the extraction of the F4 and F5 structure functions, never measured so far and allow for new tests of lepton non-universality with sensitivity to BSM physics. Moreover, ντ’s will be distinguished from ’s, thus providing the first observation of the . With νµ scattering it will be possible to reduce by about 50% the current uncertainty on the strange content of the nucleon in the range of the x variable between 0.05 and 0.3, complementary to LHC measurements. The detector will be based on several techniques developed for the OPERA experiment at LNGS.

Nucleon Structure Functions from Operator Product Expansion on the Lattice

Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

Nucleon structure functions in noncommutative space-time

In the context of noncommutative space-time we investigate the nucleon structure functions which play an important role in identifying the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of the noncommutative tensor theta _{mu nu }. To check our results we plot the nucleon structure function (NSF), F_2(x), and compare it with experimental data and the results from the GRV, GJR and CT10 parametrization models. We show that with the new vertex that arises the noncommutativity correction will lead to a better consistency between theoretical results and experimental data for the NSF. This consistency will be better for small values of the Bjorken variable x. To indicate and confirm the validity of our calculations we also act conversely. We obtain a lower bound for the numerical values of Lambda _{mathrm{NC}} scale which correspond to recent reports.

Nucleon structure functions and longitudinal spin asymmetries in the chiral quark constituent model

We have analysed the phenomenological dependence of the spin independent ($F_1^{p,n}$ and $F_2^{p,n}$) and the spin dependent ($g_1^{p,n}$) structure functions of the nucleon on the the Bjorken scaling variable $x$ using the unpolarized distribution functions of the quarks $q(x)$ and the polarized distribution functions of the quarks $\Delta q(x)$ respectively. The chiral constituent quark model ($\chi$CQM), which is known to provide a satisfactory explanation of the proton spin crisis and related issues in the nonperturbative regime, has been used to compute explicitly the valence and sea quark flavor distribution functions of $p$ and $n$. In light of the improved precision of the world data, the $p$ and $n$ longitudinal spin asymmetries ($A_1^p(x)$ and $A_1^n(x)$) have been calculated. The implication of the presence of the sea quarks has been discussed for ratio of polarized to unpolarized quark distribution functions for up and down quarks in the $p$ and $n$ $\frac{\Delta u^p(x)}{u^p(x)}$, $\frac{\Delta d^p(x)}{d^p(x)}$, $\frac{\Delta u^n(x)}{u^n(x)}$, and $\frac{\Delta d^n(x)}{d^n(x)}$. The ratio of the $n$ and $p$ structure functions $R^{np}(x)=\frac{F_2^n(x)}{F_2^p(x)}$ has also been presented. The results have been compared with the recent available experimental observations. The results on the spin sum rule have also been included and compared with data and other recent approaches.

Investigating GPDs in the framework of the double distribution model

In this paper, we construct the generalized parton distribution (GPD) in terms of the kinematical variables [Formula: see text], [Formula: see text], [Formula: see text], using the double distribution model. By employing these functions, we could extract some quantities which makes it possible to gain a three-dimensional insight into the nucleon structure function at the parton level. The main objective of GPDs is to combine and generalize the concepts of ordinary parton distributions and form factors. They also provide an exclusive framework to describe the nucleons in terms of quarks and gluons. Here, we first calculate, in the Double Distribution model, the GPD based on the usual parton distributions arising from the GRV and CTEQ phenomenological models. Obtaining quarks and gluons angular momenta from the GPD, we would be able to calculate the scattering observables which are related to spin asymmetries of the produced quarkonium. These quantities are represented by [Formula: see text] and [Formula: see text]. We also calculate the Pauli and Dirac form factors in deeply virtual Compton scattering. Finally, in order to compare our results with the existing experimental data, we use the difference of the polarized cross-section for an initial longitudinal leptonic beam and unpolarized target particles [Formula: see text]. In all cases, our obtained results are in good agreement with the available experimental data.

Bilinear quark operator renormalization at generalized symmetric point

We compute Green's functions with a bilinear quark operator inserted at nonzero momentum for a generalized momentum configuration to two loops. These are required to assist lattice gauge theory measurements of the same quantity in matching to the high energy behavior. The flavor nonsinglet operators considered are the scalar, vector and tensor currents as well as the second moment of the twist-2 Wilson operator used in deep inelastic scattering for the measurement of nucleon structure functions.

Photon structure functions at small x in holographic QCD

We investigate the photon structure functions at small Bjorken variable x in the framework of the holographic QCD, assuming dominance of the Pomeron exchange. The quasi-real photon structure functions are expressed as convolution of the Brower–Polchinski–Strassler–Tan (BPST) Pomeron kernel and the known wave functions of the U(1) vector field in the five-dimensional AdS space, in which the involved parameters in the BPST kernel have been fixed in previous studies of the nucleon structure functions. The predicted photon structure functions, as confronted with data, provide a clean test of the BPST kernel. The agreement between theoretical predictions and data is demonstrated, which supports applications of holographic QCD to hadronic processes in the nonperturbative region. Our results are also consistent with those derived from the parton distribution functions of the photon proposed by Glück, Reya, and Schienbein, implying realization of the vector meson dominance in the present model setup.

27aSM-6 Nucleon isovector form factors and structure functions in 2+1-falvor domain-wall lattice QCD at physical mass

27aSM-6 Nucleon isovector form factors and structure functions in 2+1-falvor domain-wall lattice QCD at physical mass

Nuclear medium effects in structure functions of nucleon at moderate [formula omitted

Recent experiments performed on inclusive electron scattering from nuclear targets have measured the nucleon electromagnetic structure functions F1(x,Q2), F2(x,Q2) and FL(x,Q2) in 12C, 27Al, 56Fe and 64Cu nuclei. The measurements have been done in the energy region of 1 GeV2<W2<4 GeV2 and Q2 region of 0.5 GeV2<Q2<4.5 GeV2. We have calculated nuclear medium effects in these structure functions arising due to the Fermi motion, binding energy, nucleon correlations, mesonic contributions from pion and rho mesons and shadowing effects. The calculations are performed in a local density approximation using a relativistic nucleon spectral function which includes nucleon correlations. The numerical results are compared with the recent experimental data from JLab and also with some earlier experiments.