Deep Inelastic Scattering Structure Functions Research Articles

Disorder: Deep inelastic scattering at high orders

We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing \mathcal{O}(\alpha_{\mathrm{s}}^2)𝒪(αs2) dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to \mathcal{O}(\alpha_{\mathrm{s}}^3)𝒪(αs3).

Codebase release r1.0 for disorder

We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing \mathcal{O}(\alpha_{\mathrm{s}}^2)𝒪(αs2) dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to \mathcal{O}(\alpha_{\mathrm{s}}^3)𝒪(αs3).

Yangian symmetry applied to quantum chromodynamics

We review applications of Yangian symmetry to high-energy Quantum chromodynamics (QCD) phenomenology. Some basic facts about high-energy QCD are recalled, in particular the spinor-helicity form of scattering amplitudes, the scale evolution equations of deep-inelastic scattering structure functions and the high-energy asymptotics of scattering. As the working tool the Yangian symmetric correlators are introduced and constructed in the framework of the Yangian algebra of [Formula: see text] type. We present the application to the tree scattering amplitudes and their iterative relation, to the parton splitting amplitudes and the kernels of the scale evolution equations of structure functions and to the equations describing the high-energy asymptotics of scattering.

The full set of polarized deep inelastic scattering structure functions at NNLO accuracy

We present the second order contributions to the coefficient functions for the parity violating polarized structure functions g_L and g_4, thus completing the {mathcal {O}}(alpha _S^2) knowledge on DIS structure functions. We obtain the missing {mathcal {O}}(alpha _S^2) pieces from the known parity conserving unpolarized coefficient functions. We also present a phenomenological analysis for the phase space region the future Electron-Ion Collider is set to explore.

Differential heavy quark distributions and correlations in longitudinally polarized deep-inelastic scattering

We present a first calculation of the heavy flavor contribution to the longitudinally polarized deep-inelastic scattering structure function $g_1^{Q}$, differential in the transverse momentum or the rapidity of the observed heavy quark $Q$ or antiquark $\overline Q$. All results are obtained at next-to-leading order accuracy in QCD within the framework of a newly developed parton-level Monte Carlo generator that also allows one to study observables associated with the produced heavy quark pair such as its invariant mass distribution or its correlation in azimuthal angle. First phenomenological studies are carried out for various heavy quark distributions in a kinematic regime relevant for a future Electron-Ion Collider with a particular emphasis on the expected size of the corresponding double-spin asymmetries and their sensitivity to the still poorly constrained helicity gluon distribution. Theoretical uncertainties associated with the choice of the factorization scale are discussed for selected observables.

Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)

We present a method to extract, in the leading and next-to-leading order approximations, the longitudinal deep-inelastic scattering structure function FL(x,Q2) from the experimental data by relying on a Froissart-bounded parametrization of the transversal structure function F2(x,Q2) and, partially, on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. Particular attention is paid on kinematics of low and ultra low values of the Bjorken variable x. Analytical expressions for FL(x,Q2) in terms of the effective parameters of the parametrization of F2(x,Q2) are presented explicitly. We argue that the obtained structure functions FL(x,Q2) within both, the leading and next-to-leading order approximations, manifestly obey the Froissart boundary conditions. Numerical calculations and comparison with available data from ZEUS and H1-Collaborations at HERA demonstrate that the suggested method provides reliable structure functions FL(x,Q2) at low x in a wide range of the momentum transfer (1 GeV2 < Q2 < 3000 GeV2) and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos.

High-energy neutrino-nucleus interactions

High-energy neutrino-nucleus interactions are discussed by considering neutrino-oscillation experiments and ultra-high-energy cosmic neutrino interactions. The largest systematic error for the current neutrino oscillation measurements comes from the neutrino-nucleus interaction part, and its accurate understanding is essential for high-precision neutrino physics, namely for studying CP violation in the lepton sector. Depending on neutrino beam energies, quasi-elastic, resonance, Regge, or/and deep inelastic scattering (DIS) processes contribute to the neutrino cross section. It is desirable to have a code to calculate the neutrino-nucleus cross section in any kinematical range by combining various theoretical descriptions. On the other hand, the IceCube collaboration started obtaining cross section data up to the 1015 eV range, so that it became necessary to understand ultra-high-energy neutrino interactions beyond the artificial lepton-accelerator energy range. For future precise neutrino physics including the CP measurement, it is also necessary to understand accurate nuclear corrections. The current status is explained for nuclear corrections in DIS structure functions. The possibility is also discussed to find gravitational sources within nucleons and nuclei, namely matrix elements of quark-gluon energy-momentum tensor. They could be probed by neutrino interactions without replying on direct ultra-weak “gravitational interactions” with high-intensity neutrino beams, possibly at a future neutrino factory, by using techniques of hadron tomography.

Electroweak gauge boson parton distribution functions

Transverse and longitudinal electroweak gauge boson parton distribution functions (PDFs) are computed in terms of deep-inelastic scattering structure functions, following the recently developed method to determine the photon PDF. The calculation provides initial conditions at the electroweak scale for PDF evolution to higher energies. Numerical results for the W± and Z transverse, longitudinal and polarized PDFs, as well as the γZ transverse and polarized PDFs are presented.

Lattice calculation of hadronic tensor of the nucleon

We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.

Towards semi-inclusive deep inelastic scattering at next-to-next-to-leading order

In this paper, we compute the first set of ${\cal O}(\alpha_s^2)$ corrections to semi-inclusive deep inelastic scattering structure functions. We start by studying the impact of the contribution of the partonic subprocesses that open at this order for the longitudinal structure function. We perform the full calculation analytically, and obtain the expression of the factorized cross section at this order. Special care is given to the study of their flavour decomposition structure. We analyze the phenomenological effect of the corrections finding that, even though expected to be small a priori, it turns out to be sizable with respect to the previous order know, calling for a full NNLO calculation.

O(αs3)heavy flavor contributions to the charged current structure functionxF3(x,Q2)at large momentum transfer

Deep inelastic scattering (DIS) experiments can be used to determine the quark distributions of the nucleons. The authors calculate certain heavy quark contributions to the deep-inelastic scattering structure function at $3$-loop order in QCD. While such contributions are tiny, they may become relevant for the comparison with data from future DIS experiments.

The 3-loop pure singlet heavy flavor contributions to the structure function [formula omitted] and the anomalous dimension

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function F2(x,Q2) and the corresponding transition matrix element AQq(3),PS in the variable flavor number scheme are computed. In Mellin-N space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function F2(x,Q2) are presented.

Solution of DGLAP Evolution Equation for xF&lt;sub&gt;3&lt;/sub&gt; Structure Function in Leading and Next-to-Leading Order at Small-x

This report attempts to the phenomenological study of the charged-current neutrino deep-inelastic scattering (DIS) within the perturbative QCD framework. The study is based on the solution of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in leading and next-to-leading order at small-x for parity-violating DIS structure function

Deep inelastic scattering structure functions of holographic spin-1 hadrons with N f ≥ 1

Two-point current correlation functions of the large $N$ limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with $N_f > 1$. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of their moments are also derived. Aspects of the sub-leading contributions in the $1/N$ and $N_f/N$ expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.

Deep inelastic scattering from holographic spin-one hadrons

We study deep inelastic scattering structure functions from hadrons using different holographic dual models which describe the strongly coupled regime of gauge theories in the large $N$ limit. Particularly, we consider scalar and vector mesons obtained from holographic descriptions with fundamental degrees of freedom, corresponding to ${\cal {N}}=2$ supersymmetric and non-supersymmetric Yang-Mills theories. We explicitly obtain analytic expressions for the full set of eight structure functions, i.e., $F_1$, $F_2$, $g_1$, $g_2$, $b_1$, $b_2$, $b_3$, $b_4$, arising from the standard decomposition of the hadronic tensor of spin-one hadrons. We obtain the relations $2 F_1 = F_2$ and $2 b_1 = b_2$. In addition, we find $b_1 \sim {\cal {O}}(F_1)$ as suggested by Hoodbhoy, Jaffe and Manohar for vector mesons. Also, we find new relations among some of these structure functions.

The Bjorken sum rule with Monte Carlo and Neural Network techniques

Determinations of structure functions and parton distribution functions have been recently obtained using Monte Carlo methods and neural networks as universal, unbiased interpolants for the unknown functional dependence. In this work the same methods are applied to obtain a parametrization of polarized Deep Inelastic Scattering (DIS) structure functions. The Monte Carlo approach provides a bias-free determination of the probability measure in the space of structure functions, while retaining all the information on experimental errors and correlations. In particular the error on the data is propagated into an error on the structure functions that has a clear statistical meaning. We present the application of this method to the parametrization from polarized DIS data of the photon asymmetries A1p and A1d from which we determine the structure functions g1p(x,Q2) and g1d(x,Q2), and discuss the possibility to extract physical parameters from these parametrizations. This work can be used as a starting point for the determination of polarized parton distributions.

Soft-gluon resummation effects on parton distributions

We gauge the impact of soft-gluon resummation on quark distributions by performing a simple fit of Deep Inelastic Scattering structure function data using next-to-leading order (NLO) and next-to-leading-logarithmic (NLL)-resummed coefficient functions. We make use of NuTeV charged-current data, as well as New Muon Collaboration (NMC) and Bologna-CERN-Dubna-Munich-Saclay (BCDMS) neutral-current results, which probe large values of x. Our results suggest that the inclusion of resummation effects in global fits of parton distributions is both feasible and desirable, in order to achieve at large x the accuracy goals of the LHC physics program.

A transverse lattice QCD model for mesons

QCD is analysed with two light-front continuum dimensions and two transverse lattice dimensions. In the limit of large number of colours and strong transverse gauge coupling, the contributions of light-front and transverse directions factorise in the dynamics, and the theory can be analytically solved in a closed form. An integral equation is obtained, describing the properties of mesons, which generalises the 't Hooft equation by including spin degrees of freedom. The meson spectrum, light-front wavefunctions and form factors can be obtained by solving this equation numerically. These results would be a good starting point to model QCD observables which only weakly depend on transverse directions, e.g. deep inelastic scattering structure functions.

Deep inelastic scattering asx→1using soft-collinear effective theory

Soft-collinear effective theory (SCET) is used to sum Sudakov double-logarithms in the x ->1 endpoint region for the deep inelastic scattering structure function. The calculations are done in both the target rest frame and the Breit frame. The separation of scales in the effective theory implies that the anomalous dimension of the SCET current is linear in ln mu, and the anomalous dimension for the Nth moment of the structure function is linear in ln N, to all orders in perturbation theory. The SCET formulation is shown to be free of Landau pole singularities. Some important differences between the deep inelastic structure function and the shape function in B decay are discussed.

Neutron structure function and inclusive deep inelastic scattering from3Hand3Heat large Bjorkenx

A detailed study of inclusive deep inelastic scattering (DIS) from mirror $A=3$ nuclei at large values of the Bjorken variable x is presented. The main purpose is to estimate the theoretical uncertainties in the extraction of the neutron DIS structure function from such nuclear measurements. On the one hand, within models in which no modification of the bound nucleon structure functions is taken into account, we have investigated the possible uncertainties arising from (i) charge symmetry breaking terms in the nucleon-nucleon interaction, (ii) finite ${Q}^{2}$ effects neglected in the Bjorken limit, (iii) the role of different prescriptions for the nucleon spectral function normalization providing baryon number conservation, and (iv) the differences between the virtual-nucleon and light-cone formalisms. Although these effects have not yet been considered in existing analyses, our conclusion is that all these effects cancel at the level of $\ensuremath{\approx}1%$ for $x\ensuremath{\lesssim}0.75,$ in overall agreement with previous findings. On the other hand, we have considered several models in which the modification of the bound nucleon structure functions is accounted for to describe the EMC effect in DIS scattering from nuclei. It turns out that within these models the cancellation of nuclear effects is expected to occur only at a level of $\ensuremath{\approx}3%,$ leading to an accuracy of $\ensuremath{\approx}12%$ in the extraction of the neutron to proton structure function ratio at $x\ensuremath{\approx}0.7--0.8.$ Another consequence of considering a broad range of models of the EMC effect is that the previously suggested iteration procedure does not improve the accuracy of the extraction of the neutron to proton structure function ratio.