Deep Inelastic Scattering Research Articles

Bjorken x weighted energy-energy correlators from the target fragmentation region to the current fragmentation region

We present the complete spectrum for the Bjorken x weighted energy-energy correlation in the deep inelastic scattering (DIS) process, from the target fragmentation region to the current fragmentation region, in the Breit frame. The corresponding collinear and transverse momentum-dependent logarithms are resummed to all orders with the accuracy of NLL and N3LL, respectively. The results in the full region are matched with an O(αs2) fixed-order calculation. The final numerical predictions are presented for both Electron-Ion Collider and Continuous Electron Beam Accelerator Facility kinematics. Published by the American Physical Society 2024

Spin-flip gluon generalized transverse-momentum-dependent parton distribution F1,2 at small x

Until recently the spin-flip processes in the deep inelastic scatterings are thought to be suppressed in the high energy. We found a positive intercept for the spin-flip generalized transverse momentum-dependent parton distribution (GTMDs) Re(F1,2) as Re(F1,2)∼(1x)α¯s(4 ln2−8/3)(cos3ϕkΔ+cosϕkΔ). This is done by analytically solving the integro-differential evolution equation for Re(F1,2), recently proposed by Hatta and Zhou, in the dilute regime. Interestingly, the surviving solution corresponds to conformal spin n=2 and carries an explicit cos3ϕkΔ+cosϕkΔ azimuthal dependence. As the imaginary part of F1,2, is related to the spin-dependent odderon or gluon Siver function and scales as Im(F1,2)∼x0, the positive intercept for Re(F1,2) implies that it is expected to dominate over the gluon Siver function in the small-x limit and may directly impact the modeling of unpolarized GTMDs and associated spin-flip processes. Published by the American Physical Society 2024

Semi-inclusive production of spin- 3/2 hadrons in deep inelastic scattering

We investigate the production of spin-3/2 hadrons in semi-inclusive deep inelastic lepton-nucleon scatterings. The complete differential cross section is derived through the kinematic analysis and expressed in terms of 288 structure functions, corresponding to all polarization configurations and azimuthal modulations. For an unpolarized lepton beam, half of the 192 structure functions have nonzero leading order contributions in the parton model, among which 42 are from rank-3 tensor polarized fragmentation functions of the hadron. For a polarized lepton beam, one third of the 96 structure functions contribute at the leading order and 14 of them are from rank-3 tensor polarized fragmentation functions. In addition to the formalism, we perform a model estimation of the spin transfer to a ShLLL polarized hadron and sizable asymmetry is expected. Therefore, these newly defined observables for the production of a spin-3/2 hadron in a deep inelastic scattering process can be explored in future experiments to understand nucleon spin structures and spin-dependent fragmentation functions. Published by the American Physical Society 2024

SIDIS at small x at next-to-leading order: Gluon contribution

We calculate the contribution of gluons to single inclusive hadron production at next-to-leading order (NLO) accuracy in deep inelastic scattering (DIS) at small x using the color glass condensate formalism. It is shown that the only divergence present is the standard collinear divergence, which is absorbed into scale evolution of quark-hadron fragmentation function. Our calculations are performed at finite Nc and we provide general finite Nc expressions for the structure of Wilson lines appearing in inclusive dihadron and single hadron production cross sections. We also comment on how one can obtain rapidity distribution of hadron multiplicities from our results. Published by the American Physical Society 2024

The LHC as a Neutrino-Ion Collider

Proton-proton collisions at the LHC generate a high-intensity collimated beam of neutrinos in the forward (beam) direction, characterised by energies of up to several TeV. The recent observation of LHC neutrinos by FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and SND@LHC signifies that this previously overlooked particle beam is now available for scientific investigation. Here we quantify the impact that neutrino deep-inelastic scattering (DIS) measurements at the LHC would have on the parton distributions (PDFs) of protons and heavy nuclei. We generate projections for DIS structure functions for FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and SND@LHC at Run III, as well as for the FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}2, AdvSND, and FLArE experiments to be hosted at the proposed Forward Physics Facility (FPF) operating concurrently with the High-Luminosity LHC (HL-LHC). We determine that up to one million electron-neutrino and muon-neutrino DIS interactions within detector acceptance can be expected by the end of the HL-LHC, covering a kinematic region in x and Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2$$\\end{document} overlapping with that of the Electron-Ion Collider. Including these DIS projections in global (n)PDF analyses, specifically PDF4LHC21, NNPDF4.0, and EPPS21, reveals a significant reduction in PDF uncertainties, in particular for strangeness and the up and down valence PDFs. We show that LHC neutrino data enable improved theoretical predictions for core processes at the HL-LHC, such as Higgs and weak gauge boson production. Our analysis demonstrates that exploiting the LHC neutrino beam effectively provides CERN with a “Neutrino-Ion Collider” without requiring modifications in its accelerator infrastructure.

Searching for axial neutral current non-standard interactions of neutrinos by DUNE-like experiments

The increasingly precise neutrino experiments raise the hope for searching for new physics through studying the impact of Neutral Current (NC) Non-Standard Interactions (NSI) of neutrinos with matter fields. Neutrino oscillation experiments along with the Elastic Coherent ν Nucleus Scattering (CEνNS) experiments already set strong bounds on all the flavor elements of the “vector” NC NSI. However, “axial” NC NSI can hide from these experiments. We show how a DUNE-like experiment can probe these couplings by studying NC Deep Inelastic Scattering (DIS) events. We find that strong bounds can be set on the axial NC NSI of neutrinos with the u, d, and s quarks. We show that using both the near and far detectors, a DUNE-like experiment can significantly improve the present bounds on all the flavor elements.

Probing transverse momentum dependent structures with azimuthal dependence of energy correlators

We study the azimuthal angle dependence of the energy-energy correlators \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\mathcal{E}\\left({\\widehat{n}}_{1}\\right)\\mathcal{E}\\left({\\widehat{n}}_{2}\\right)\\rangle $$\\end{document} in the back-to-back region for e+e− annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{S}}_{i}$$\\end{document} in the back-to-back limit \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\mathcal{E}}_{{\\mathbb{S}}_{1}}\\left({\\widehat{n}}_{1}\\right){\\mathcal{E}}_{{\\mathbb{S}}_{2}}\\left({\\widehat{n}}_{2}\\right)\\rangle $$\\end{document}. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

Direct quarkonium-plus-gluon production in DIS in the color glass condensate

We compute the differential cross-section for direct quarkonium production accompanied by a gluon in high-energy deep inelastic scattering (DIS) at small-x. We employ the Non-Relativistic QCD factorization framework, focusing on the S-wave contribution to the formation of the quarkonium, and including both color singlet and octet contributions. Our short distance coefficients for the production of the heavy quark pair are obtained within the Color Glass Condensate effective field theory. Our results pave the way towards the next-to-leading order computation of direct quarkonium in DIS, as well as the study of azimuthal correlations of direct quarkonium and jet.

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.

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions.

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Complete next-to-leading order calculation of single inclusive π0 production in forward proton-nucleus collisions

We present the first fully consistent calculation of inclusive π0 production at forward rapidities at next-to-leading order (NLO) accuracy in proton-lead collisions at s=8.16 TeV within the color glass condensate approach. The center-of-mass energy dependence is determined by the Balitsky-Kovchegov equation with the initial condition constrained at NLO accuracy by the proton structure function measurements. We find that the LHCb data further constrain this nonperturbative input, and that both the NLO corrections to the evolution equation and to the impact factor have significant effects on the nuclear modification factor RpPb. The complete NLO calculation is shown to be in qualitative agreement with the LHCb data, and the predictions are found to be sensitive to the details of the applied deep inelastic scattering (DIS) fit. These results demonstrate the need to perform global analyses of DIS and LHC data in order to probe gluon saturation phenomena at precision level at very small momentum fraction x. Published by the American Physical Society 2024

A POWHEG generator for deep inelastic scattering

We present a new event generator for the simulation of both neutral- and charged-current deep inelastic scattering (DIS) at next-to-leading order in QCD matched to parton showers using the POWHEG method. Our implementation builds on the existing POWHEG BOX framework originally designed for hadron-hadron collisions, supplemented by considerable extensions to account for the genuinely different kinematics inherent to lepton-hadron collisions. In particular, we present new momentum mappings that conserve the special kinematics found in DIS, which we use to modify the POWHEG BOX implementation of the Frixione-Kunszt-Signer subtraction mechanism. We compare our predictions to fixed-order and resummed predictions, as well as to data from the HERA ep collider. Finally we study a few representative distributions for the upcoming Electron Ion Collider.

Next-to-leading-logarithmic PanScales showers for deep inelastic scattering and vector boson fusion

We introduce the first family of parton showers that achieve next-to-leading logarithmic (NLL) accuracy for processes involving a t-channel exchange of a colour-singlet, and embed them in the PanScales framework. These showers are applicable to processes such as deep inelastic scattering (DIS), vector boson fusion (VBF), and vector boson scattering (VBS). We extensively test and verify the NLL accuracy of the new showers at both fixed order and all orders across a wide range of observables. We also introduce a generalisation of the Cambridge-Aachen jet algorithm and formulate new DIS observables that exhibit a simple resummation structure. The NLL showers are compared to a standard transverse-momentum ordered dipole shower, serving as a proxy for the current state-of-the-art leading-logarithmic showers available in public codes. Depending on the observable, we find discrepancies at NLL of the order of 15%. We also present some exploratory phenomenological results for Higgs production in VBF. This work enables, for the first time, to resum simultaneously global and non-global observables for the VBF process at NLL accuracy.

ELUQuant: event-level uncertainty quantification in deep inelastic scattering

We introduce a physics-informed Bayesian neural network with flow-approximated posteriors using multiplicative normalizing flows for detailed uncertainty quantification (UQ) at the physics event-level. Our method is capable of identifying both heteroskedastic aleatoric and epistemic uncertainties, providing granular physical insights. Applied to deep inelastic scattering (DIS) events, our model effectively extracts the kinematic variables x, Q 2, and y, matching the performance of recent deep learning regression techniques but with the critical enhancement of event-level UQ. This detailed description of the underlying uncertainty proves invaluable for decision-making, especially in tasks like event filtering. It also allows for the reduction of true inaccuracies without directly accessing the ground truth. A thorough DIS simulation using the H1 detector at HERA indicates possible applications for the future electron–ion collider. Additionally, this paves the way for related tasks such as data quality monitoring and anomaly detection. Remarkably, our approach effectively processes large samples at high rates.

The physics of the EIC

In this presentation I will give brief overview of the main physics topics which will be explored at the new Deep Inelastic Scattering facility, the Electron Ion Collider (EIC), planned for the construction at Brookhaven National Laboratory in the United States.

Perspectives of Semi-Inclusive Deep-Inelastic Scattering

This contribution highlights some topics addressed by current and future experiments in Semi-Inclusive Deep-Inelastic Scattering. We concentrate on the programs at 12 and 22 GeV at Jefferson Lab using the CLAS detector, and at the future Electron-Ion Collider.

Global extraction of proton and pion Transverse Momentum Distributions

We present the most recent global analysis of unpolarized proton Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs) and Fragmentation Functions (TMD FFs) derived from a diverse set of experimental datasets, including Semi-Inclusive Deep-Inelastic Scattering, Drell-Yan, and Z-boson production. Additionally, we present an extraction of the unpolarized pion TMD PDFs from all available data of unpolarized pion induced Drell–Yan processes. Both fits are performed at next-to-next-to-next-to-leading logarithmic (N3LL) accuracy.

Probing the Onset of Maximal Entanglement inside the Proton in Diffractive Deep Inelastic Scattering.

It has been proposed that at small Bjorken x, or equivalently at high energy, hadrons represent maximally entangled states of quarks and gluons. This conjecture is in accord with experimental data from the electron-proton collider HERA at the smallest accessible x. In this Letter, we propose to study the onset of the maximal entanglement inside the proton using diffractive deep inelastic scattering. It is shown that the data collected by the H1 Collaboration at HERA allow one to probe the transition to the maximal entanglement regime. By relating the entanglement entropy to the entropy of final-state hadrons, we find a good agreement with the H1 data using both the exact entropy formula as well as its asymptotic expansion which indicates the presence of a nearly maximally entangled state. Finally, future opportunities at the Electron Ion Collider are discussed.

Extraction of the strong coupling with HERA and EIC inclusive data

Sensitivity to the strong coupling αS(MZ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _S(M^2_Z)$$\\end{document} is investigated using existing Deep Inelastic Scattering data from HERA in combination with projected future measurements from the Electron Ion Collider (EIC) in a next-to-next-to-leading order QCD analysis. A potentially world-leading level of precision is achievable when combining simulated inclusive neutral current EIC data with inclusive charged and neutral current measurements from HERA, with or without the addition of HERA inclusive jet and dijet data. The result can be obtained with substantially less than one year of projected EIC data at the lower end of the EIC centre-of-mass energy range. Some questions remain over the magnitude of uncertainties due to missing higher orders in the theoretical framework.

Proton structure functions at low x: The fractal distributions

This paper presents a method for extracting the parton distribution functions (PDFs) at small momentum fractions [Formula: see text] and at the next-to-leading order (NLO) accuracy in perturbative quantum chromodynamics. It turns out that the PDFs can be described by the “Fractal” or self-similar distributions at low [Formula: see text] below [Formula: see text]. To this end, a simple parametrization for the unintegrated PDFs based on the “Fractal” approach is considered. These functions have self-similar behavior at low [Formula: see text] and [Formula: see text] for sea quarks and have self-similar behavior at low [Formula: see text] for gluon distribution. By integration from these transverse momentum distributions (TMDs), the initial input densities are obtained and the model’s free parameters are then calculated using the experimental data released by the HERA experiment. The small-[Formula: see text] experimental datasets on electron–proton ([Formula: see text]) and positron–proton ([Formula: see text]) for natural current (NC) interactions in deep inelastic scattering (DIS) processes at HERA for the range of [Formula: see text] (GeV2) and [Formula: see text] are included in this analysis. The uncertainty estimations in this analysis are carried out using the standard “Hessian” method. Considering the overall value of [Formula: see text] and theory-to-data comparisons, the results indicate good agreements between the experimental datasets and the theoretical predictions. A detailed comparison is also presented between the model’s predictions for the relevant small-[Formula: see text] observable and recent parametrizations for the PDFs.