Deep Inelastic Scattering Data Research Articles

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.

Global QCD analysis and dark photons

We perform a global QCD analysis of high energy scattering data within the JAM Monte Carlo framework, including a coupling to a dark photon that augments the Standard Model (SM) electroweak coupling via kinetic mixing with the hypercharge B boson. We first set limits on the dark photon mass and mixing parameter assuming that the SM is the true theory of Nature, taking into account also the effect on g – 2 of the muon. If instead we entertain the possibility that the dark photon may play a role in deep-inelastic scattering (DIS), we find that the best fit is preferred over the SM at 6.5σ, even after accounting for missing higher order uncertainties. The improvement in χ2 with the dark photon is stable against all the tests we have applied, with the improvements in the theoretical predictions spread across a wide range of x and Q2. The largest improvement corresponds to the fixed target and HERA DIS data, while the best fit yields a value of g – 2 which significantly reduces the disagreement with the latest experimental determination.

Impact of W and Z Production Data and Compatibility of Neutrino DIS Data in Nuclear Parton Distribution Functions

Vector boson production and neutrino deep-inelastic scattering (DIS) data are crucial for constraining the strange quark parton distribution function (PDF) and more generally for flavor decomposition in PDF extractions. We extend the nCTEQ15 nuclear PDFs (nPDFs) by adding the recent W and Z production data from the LHC in a global nPDF fit. The new nPDF set, referred to as nCTEQ15WZ, is used as a starting point for a follow-up study in which we assess the compatibility of neutrino DIS data with charged lepton DIS data. Specifically, we re-analyze neutrino DIS data from NuTeV, Chorus, and CDHSW, as well as dimuon data from CCFR and NuTeV. To scrutinize the level of compatibility, different kinematic regions of the neutrino data are investigated. Fits to the neutrino data alone and a preliminary global fit are performed and compared to nCTEQ15WZ.

Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme

In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the impact of target mass corrections and higher twist effects which are expected to be important in the region of large $x$ and intermediate-to-low $Q^2$. Our analysis is based on a publicly available open-source tool {\tt APFEL}, which has been modified to be applicable for our analysis of nuclear PDFs. Heavy quark contributions to nuclear DIS are considered within the framework of the {\tt FONLL} general-mass variable-flavor-number scheme. The most recent {\tt CT18} PDFs are used as baseline proton PDFs. The uncertainties of nuclear PDFs are determined using the standard Hessian approach. The results of our global QCD analysis are compared with existing nuclear PDF sets and with the fitted cross-sections, for which our set of nuclear PDFs provides a very good description.

Extending nuclear PDF analyses into the high- x , low- Q2 region

We use the nCTEQ analysis framework to investigate nuclear Parton Distribution Functions (nPDFs) in the region of large x and intermediate-to-low $Q$, with special attention to recent JLab Deep Inelastic Scattering data on nuclear targets. This data lies in a region which is often excluded by $W$ and $Q$ cuts in global nPDF analyses. As we relax these cuts, we enter a new kinematic region, which requires new phenomenology. In particular, we study the impact of i) target mass corrections, ii) higher twist corrections, iii) deuteron corrections, and iv) the shape of the nuclear PDF parametrization at large-$x$ close to one. Using the above tools, we produce a new nPDF set (named nCTEQ15HIX) which yields a good description of the new JLab data in this challenging kinematic region, and displays reduced uncertainties at large $x$, in particular for up and down quark flavors.

Reweighting the Sivers function with jet data from STAR

The reweighting procedure that using Bayesian statistics incorporates the information contained in a new data set, without the need of re-fitting, is applied to the quark Sivers function extracted from Semi-Inclusive Deep Inelastic Scattering (SIDIS) data. We exploit the recently published single spin asymmetry data for the inclusive jet production in polarized pp collisions from the STAR Collaboration at RHIC, which cover a much wider x region compared to SIDIS measurements. The reweighting method is extended to the case of asymmetric errors and the results show a remarkable improvement of the knowledge of the quark Sivers function.

Impact of LHC vector boson production in heavy ion collisions on strange PDFs

The extraction of the strange quark parton distribution function (PDF) poses a long-standing puzzle. Measurements from neutrino-nucleus deep inelastic scattering (DIS) experiments suggest the strange quark is suppressed compared to the light sea quarks, while recent studies of W^pm /Z boson production at the LHC imply a larger strange component at small x values. As the parton flavor determination in the proton depends on nuclear corrections, e.g. from heavy-target DIS, LHC heavy ion measurements can provide a distinct perspective to help clarify this situation. In this investigation we extend the nCTEQ15 nPDFs to study the impact of the LHC proton-lead W^pm /Z production data on both the flavor differentiation and nuclear corrections. This complementary data set provides new insights on both the LHC W^pm /Z proton analyses and the neutrino-nucleus DIS data. We identify these new nPDFs as nCTEQ15WZ. Our calculations are performed using a new implementation of the nCTEQ code (nCTEQ++) based on C++ which enables us to easily interface to external programs such as HOPPET, APPLgrid and MCFM. Our results indicate that, as suggested by the proton data, the small x nuclear strange sea appears larger than previously expected, even when the normalization of the W^{pm }/Z data is accommodated in the fit. Extending the nCTEQ15 analysis to include LHC W^pm /Z data represents an important step as we advance toward the next generation of nPDFs.

Implementation of target mass corrections and higher-twist effects in the xFitter framework

Knowledge of parton distribution functions (PDFs) at large momentum fraction $ x $ is not only important to study the flavor and spin dynamics of quarks in the nucleon, but also to search for signals of new physics at collider experiments. It is well known now that the nonperturbative QCD effects generally play a more significant role at such kinematic regions. In this work, we present an open-source QCD analysis of PDFs considering target mass corrections (TMCs) and higher-twist (HT) effects which are necessary when the analysis includes also data points from deep inelastic scattering (DIS) with larger values of $ x $ and smaller values of photon virtuality $ Q^2 $. To this aim, we use the xFitter package, as a comprehensive and powerful tool for studying PDFs. We report and discuss our recent activities on the implementation of TMCs and HT effects in the xFitter framework in a user-friendly way, so that the user can switch on or off them, and also choose between different options. We check the validity of the modifications by performing sample analyses of PDFs considering TMCs and HT effects and using a wide range of DIS data.

Refined analysis on the parton distribution functions of the proton

We explore the application of a two-component model of proton structure functions in the analysis of deep-inelastic scattering (DIS) data at low Q2 and small x. This model incorporates both vector meson dominance and the correct photo-production limit. The CJ15 parameterization is applied to the QCD component, in order to take into account effects of order 1/Q2 effects, such as target mass corrections and higher twist (HT) contributions. The parameters of the leading twist parton distribution functions (PDFs) and HT coefficient functions are determined by fitting DIS data. The second moments of the PDFs are extracted and compared with other global fits and lattice determinations.

Phenomenology of leading nucleon production in ep collisions at HERA in the framework of fracture functions

In recent years, several experiments at the $e^-p$ collider HERA have collected high precision deep inelastic scattering (DIS) data on the spectrum of leading nucleon carrying a large fraction of the proton's energy. In this paper, we have analyzed recent experimental data on the production of forward proton and neutron in DIS at HERA in the framework of a perturbative QCD. We propose a technique based on the fractures functions framework, and extract the nucleon fracture functions (nucleon FFs) ${\cal M}_2^{(n/p)} (x, Q^2; x_L)$ from global QCD analysis of DIS data measured by ZEUS collaboration at HERA. We have shown that an approach based on the fracture functions formalism allows us phenomenologically parametrize the nucleon FFs. Considering both leading neutron as well as leading proton production data at HERA, we present the results for the separate parton distributions for all parton species, including valence quark densities, the anti-quark densities, the strange sea distribution, and the gluon distribution functions. We proposed several parameterizations for the nucleon FFs and open the possibility of these asymmetries. The obtained optimum set of nucleon FFs is accompanied by Hessian uncertainty sets which allow one to propagate uncertainties to other observables interest. The extracted results for the $t$-integrated leading neutron $F_2^{\rm LN(3)} (x, Q^2; x_L)$ and leading proton $F_2^{\rm LP(3)} (x, Q^2; x_L)$ structure functions are in good agreement with all data analyzed, for a wide range of fractional momentum variable $x$ as well as the longitudinal momentum fraction $x_L$.

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.

Analysis of the Diffractive Deep Inelastic Scattering Data with Running Coupling and Gluon Number Fluctuations**Supported by the National Natural Science Foundation of China under Grant Nos 11305040, 11505036 and 11447203, the Education Department of Guizhou Province Talent Fund under Grant No [2015]5508, and the Science and Technology Department of Guizhou Province Fund under Grant Nos [2015]2114 and [2014]7053.

We study the effects of running coupling and gluon number fluctuations in the latest diffractive deep inelastic scattering data. It is found that the description of the data is improved once the running coupling and gluon number fluctuations are included with χ2 /d.o.f. = 0.867, χ2 /d.o.f. = 0.923 and χ2/d.o.f. = 0.878 for three different groups of experimental data. The values of diffusive coefficient subtracted from the fit are smaller than the ones obtained by considering only the gluon number fluctuations in our previous studies. The smaller values of the diffusive coefficient are in agreement with the theoretical predictions, where the gluon number fluctuations are suppressed by the running coupling which leads to smaller values of the diffusive coefficient.

Experimental results on TMDs

QCD factorisation for semi-inclusive deep inelastic scattering (DIS) at low transverse momentum in the current-fragmentation region has been established recently, providing a rigorous basis to study the transverse-momentum-dependent (TMD) distribution and fragmentation functions of partons from semi-inclusive DIS data using different spin-dependent and spin-independent observables. The main focus of the experiments were the measurements of various single- and double-spin asymmetries in hadron electro-production ( $ e p^{\uparrow} \rightarrow ehX$ with unpolarised, longitudinally and transversely polarised targets. The joint use of a longitudinally polarised beam and longitudinally and transversely polarised targets allowed to measure double-spin asymmetries related to leading-twist distribution functions describing the transverse-momentum distribution of longitudinally and transversely polarised quarks in a longitudinally and transversely polarised nucleons (helicity and worm-gear TMDs). The single-spin asymmetries measured with transversely polarised targets, provided access to specific leading-twist parton distribution functions: the transversity, the Sivers function and the so-called “pretzelosity” function. In this review we present the current status and some future measurements of TMDs worldwide.

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.

Collins functions for pions from SIDIS and newe+e−data: A first glance at their transverse momentum dependence

New data from Belle and BaBar Collaborations on azimuthal asymmetries, measured in e+e- annihilations into pion pairs at Q^2=112 GeV^2, allow to take the first, direct glance at the transverse momentum dependence of the Collins functions, in addition to their z dependence. These data, together with available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins asymmetry, are simultaneously analysed in the framework of the generalised parton model assuming two alternative Q^2 evolution schemes and exploiting two different parameterisations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e+e- annihilations into pion pairs at the lower Q^2 of 13 GeV^2, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse momentum dependent evolution effects.

Phenomenology from SIDIS ande+e−multiplicities: multiplicities and phenomenology - part I

This study is part of a project to investigate the transverse momentum dependence in parton dis- tribution and fragmentation functions, analyzing (semi-)inclusive high-energy processes within a proper QCD framework. We calculate the transverse-momentum-dependent (TMD) multiplicities for e + e − annihilation into two hadrons (considering different combinations of pions and kaons) aiming to investigate the impact of in- trinsic and radiative partonic transverse momentum and their mixing with flavor. Different descriptions of the non-perturbative evolution kernel (see, e.g., Refs. (1-5)) are available on the market and there are 200 sets of flavor configurations for the unpolarized TMD fragmentation functions (FFs) resulting from a Monte Carlo fit of Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data at Hermes (see Ref. (6)). We build our predictions of e + e − multiplicities relying on this rich phenomenology. The comparison of these calculations with future experimental data (from Belle and BaBar collaborations) will shed light on non-perturbative aspects of hadron structure, opening important insights into the physics of spin, flavor and momentum structure of hadrons.

On the momentum dependence of the flavor structure of the nucleon sea

Difference between the u¯ and d¯ sea quark distributions in the proton was first observed in the violation of the Gottfried sum rule in deep-inelastic scattering (DIS) experiments. The parton momentum fraction x dependence of this difference has been measured over the region 0.02<x<0.35 from Drell–Yan and semi-inclusive DIS experiments. The Drell–Yan data suggested a possible sign-change for d¯(x)−u¯(x) near x∼0.3, which has not yet been explained by existing theoretical models. We present an independent evidence for the d¯(x)−u¯(x) sign-change at x∼0.3 from an analysis of the DIS data. We further discuss the x-dependence of d¯−u¯ in the context of meson cloud model and the lattice QCD formulation.

Connection of the virtualγ*pcross section ofepdeep inelastic scattering to realγpscattering, and the implications forνNandeptotal cross sections

We show that it is possible to fit all of the HERA DIS (deep inelastic scattering) data on $F_2^{\gamma p}$ at small values of Bjorken $x$, including the data at {\em very low} $Q^2$, using a new model for $F_2^{\gamma p}$ which both includes an asymptotic (high energy) part that satisfies a saturated Froissart bound behavior, with a vector-dominance like mass factor in the parameterization, and extends smoothly to $Q^2=0$. We require that the corresponding part of the virtual $\gamma^* p$ cross section match the known asymptotic part of the real $\gamma p$ cross section at $Q^2=0$, a cross section which is determined by strong interactions and asymptotically satisfies a saturated Froissart bound of the form $\alpha +\beta\ln s+\gamma\ln^2s$. Using this model for the asymptotic part of $F_2^{\gamma p}$ plus a known valence contribution, we fit the asymptotic high energy part of the HERA data with $x\le 0.1$ and $W\ge 25$ GeV; the fit is excellent. We find that the mass parameter in the fit lies in the region of the light vector mesons, somewhat above the $\rho$ meson mass, and is compatible with vector dominance. We use this fit to obtain accurate results for the high energy $ep$ and isoscalar $\nu N$ total cross sections. Both cross sections obey an analytic expression of the type $a +b \ln E +c \ln^2 E +d \ln^3 E$ at large energies $E$ of the incident particle, reflecting the fact that the underlying strong interaction parts of the $\gamma^*p$, $Z^*N$ and $W^*N$ cross sections satisfy the saturated Froissart bound. Since approximately 50% of the $\nu N$ center of mass (cms) energy is found in $W$---the cms energy of the strongly interacting intermediate vector boson-nucleon system---a study of ultra-high-energy neutrino-nucleon cross sections would allow us, for the first time, to explore {\em strong interactions at incredibly high energies}.

The Drell-Yan measurement at COMPASS-II

The Drell-Yan process can be used to access Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs), such as the Sivers and the Boer-Mulders functions, as well as the transversity function providing complementary information to what is known from Semi Inclusive Deep Inelastic Scattering (SIDIS) data. The COMPASS experiment offers the possibility to study single polarized Drell-Yan processes (π− + p↑ → μμ + X), making use of its large acceptance spectrometer and its unique transversely polarised proton target. Moreover a fundamental test of the factorization theorem in the non-perturbative QCD can be performed, by verifying the sign change of the T-odd Boer-Mulders and Sivers functions depending if they are accessed via SIDIS or Drell-Yan process. As the start of the Drell-Yan program at COMPASS is approaching, foreseen in late 2014, the spectrometer has been updated to fulfill the needs of this measurement

Agreement of Neutrino Deep Inelastic Scattering Data with Global Fits of Parton Distributions

The compatibility of neutrino-nucleus deep inelastic scattering data within the universal, factorizable nuclear parton distribution functions has been studied independently by several groups in the past few years. The conclusions are contradictory, ranging from a violation of the universality up to a good agreement, most of the controversy originating from the use of the neutrino-nucleus data from the NuTeV Collaboration. Here, we pay attention to non-negligible differences in the absolute normalization between different neutrino data sets. We find that such variations are large enough to prevent a tensionless fit to all data simultaneously and could therefore misleadingly point towards nonuniversal nuclear effects. We propose a concrete method to deal with the absolute normalization and show that an agreement between independent neutrino data sets is established.