Unpolarized Parton Distribution Functions Research Articles

Flavor asymmetry of light sea quarks in proton: a light-front spectator model

We formulate a light-front spectator model for the proton that incorporates the presence of light sea quarks. In this particular model, the sea quarks are seen as active partons, whereas the remaining components of the proton are treated as spectators. The proposed model relies on the formulation of the light-front wave function constructed by the soft wall AdS/QCD. The model wave functions are parameterized by fitting the unpolarized parton distribution functions of light sea quarks from the CTEQ18 global analysis. We then employ the light-front wave functions to obtain the sea quarks generalized parton distribution functions, transverse momentum dependent parton distributions, and their asymmetries, which are accessible in the upcoming Electron-Ion-Colliders. We investigate sea quarks’ spin and orbital angular momentum contributions to the proton spin.

Constraining the Sea Quark Distributions Through W Cross-Section Ratios Measured in pp Collisions at STAR

Although the precision to which we know the unpolarized parton distribution functions (PDFs) of the nucleon has improved over the years, there remain kinematic regions where more data are needed to constrain PDFs, such as the ratio of the sea quark distributions near the valence region. Furthermore, different measurements appear to suggest different high-x behaviors of this ratio. The W cross-section ratio (W+/W −) in pp collisions is sensitive to the unpolarized sea quark distributions at large Q 2, set by the W mass, and can be used to help constrain the ratio. The STAR experiment at RHIC is well equipped to measure the leptonic decays of W bosons produced in pp collisions at center of mass energies of 500 and 510 GeV. These proceedings present recent W cross-section ratio results measured by STAR, including preliminary results from data collected in 2017, which double the statistics when combined with the published results based on data samples recorded in 2011-2013.

EKO: evolution kernel operators

We present a new QCD evolution library for unpolarized parton distribution functions: EKO. The program solves DGLAP equations up to next-to-next-to-leading order. The unique feature of EKO is the computation of solution operators, which are independent of the boundary condition, can be stored and quickly applied to evolve several initial PDFs. The EKO approach combines the power of N-space solutions with the flexibility of a x-space delivery, that allows for an easy interface with existing codes. The code is fully open source and written in Python, with a modular structure in order to facilitate usage, readability and possible extensions. We provide a set of benchmarks with similar available tools, finding good agreement.

Continuum limit of parton distribution functions from the pseudodistribution approach on the lattice

Precise quantification of the structure of nucleons is one of the crucial aims of hadronic physics for the coming years. The expected progress related to ongoing and planned experiments should be accompanied by calculations of partonic distributions from lattice QCD. While key insights from the lattice are expected to come for distributions that are difficult to access experimentally, it is important that lattice QCD can reproduce the well-known unpolarized parton distribution functions (PDFs) with full control over systematic uncertainties. One of the novel methods for accessing the partonic $x$-dependence is the pseudo-distribution approach, which employs matrix elements of a spatially-extended nonlocal Wilson-line operator of length $z$. In this paper, we address the issue of discretization effects, related to the necessarily nonzero value of the lattice spacing $a$, which start at first order in $a$ as a result of the nonlocal operator. We use twisted mass fermions simulated at three values of the lattice spacing, at a pion mass of 370 MeV, and extract the continuum limit of isovector unpolarized PDFs. We also test, for the first time in the pseudo-distribution approach, the effects of the recently derived two-loop matching. Finally, we address the issue of the reliability of the extraction with respect to the maximal value of $z$.

Measurements of $W$ and $Z/γ^*$ cross sections and their ratios in $pp$ collisions at STAR

While the unpolarized parton distribution functions of the valence quarks (dd and uu) are well determined from DIS experiments, the sea quark counterparts, \bar{d}d‾ and \bar{u}u‾, are much less constrained, in particular, near the valence region. Measurements of W^+/W^-W+/W− production ratio in pppp collider experiments, such as the STAR experiment at RHIC, can probe the \bar{d}/\bar{u}d‾/u‾ ratio at a large Q^2Q2 set by the WW mass. These proceedings will discuss recent results of WW and ZZ cross-section measurements using the STAR pppp collision data at a center-of-mass energy of \sqrt{s} = 500/510\;\mathrm{GeV}s=500/510GeV collected in 2011, 2012, 2013 and 2017.

Simultaneous Extraction of Unpolarized PDFs and Nuclear Effects

We present a new global QCD analysis of unpolarized parton distribution functions (PDFs) and nuclear effects including for the first time data from the SeaQuest and Marathon experiments in addition to high-energy weak-boson-production data from the Tevatron and Large Hadron Collider. Simultaneously extracting the PDFs and nuclear effects, we examine the impact of the SeaQuest and Marathon data on the light-quark sea asymmetry and the EMC ratios of deuterium, helium, and tritium.

Isovector EMC Effect from Global QCD Analysis with MARATHON Data

We report the results of a MonteCarlo global QCD analysis of unpolarized parton distribution functions (PDFs), including for the first time constraints from ratios of ^{3}He to ^{3}H structure functions recently obtained by the MARATHON experiment at Jefferson Lab. Our simultaneous analysis of nucleon PDFs and nuclear effects in A=2 and A=3 nuclei reveals the first indication for an isovector nuclear EMC effect in light nuclei. We find that while the MARATHON data yield relatively weak constraints on the F_{2}^{n}/F_{2}^{p} neutron to proton structure function ratio and on the d/u PDF ratio, they suggest an enhanced nuclear effect on the d-quark PDF in the bound proton, questioning the assumptions commonly made in nuclear PDF analyses.

The continuum and leading twist limits of parton distribution functions in lattice QCD

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.

Transverse momentum-dependent parton distributions of pion in the light-front holographic model

Using the light-front holographic model, we study the transverse momentum-dependent parton distributions (TMDs) for the case of pion. At leading twist, the unpolarized parton distribution function [Formula: see text] and the Boer–Mulders function [Formula: see text] are obtained for pion. We calculate both the functions using the light-front holographic model with spin improved wave function and compare the predicted results with available results of other models. In order to provide inputs in predicting future experimental data, an LO evolution is performed from model scale to experimental scale for the case of unpolarized parton distribution function [Formula: see text].

Flavor nonsinglet parton distribution functions from lattice QCD at physical quark masses via the pseudodistribution approach

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor non-singlet ($u-d$) unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-$x$ dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distribution $q_v$ and the combination with antiquarks $q_v+2\bar{q}$, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever \emph{ab initio} determinations of PDFs fully consistent with global fits in the whole $x$-range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g.\ singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

Future Tests of Parton Distributions

We discuss a test of the generalization power of the methodology used in the determination of parton distribution functions (PDFs). The "future test" checks whether the uncertainty on PDFs, in regions in which they are not constrained by current data, are compatible with future data. The test is performed by using the current optimized methodology for PDF determination, but with a limited dataset, as available in the past, and by checking whether results are compatible within uncertainty with the result found using a current more extensive dataset. We use the future test to assess the generalization power of the NNPDF4.0 unpolarized PDF and the NNPDFpol1.1 polarized PDF methodology. Specifically, we investigate whether the former would predict the rise of the unpolarized proton structure function $F_2$ at small $x$ using only pre HERA data, and whether the latter would predict the so-called "proton spin crisis" using only pre-EMC data.

Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point.

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudodistributions. Beyond the reconstruction of the Bjorken-x dependence, we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudodistribution. We compare our findings with the pertinent phenomenological determinations.

Parton distribution functions of Δ+ on the lattice

We perform a first calculation for the unpolarized parton distribution function of the $\Delta^+$ baryon using lattice QCD simulations within the framework of Large Momentum Effective Theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions are utilized with a pion mass of 270 MeV and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentum $P_3$ with values $\{0.42,0.83,1.25\}$ GeV, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function of $\Delta^+$ is obtained using a non-perturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute the $\overline{d}(x)-\overline{u}(x)$ asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.

Machine-learning prediction for quasiparton distribution function matrix elements

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-$x$ dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken-$x$) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small-$x$ reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(P_z a)^n$ will become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements (in finer lattice units), increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning (ML) algorithms can make correlator predictions to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon and $\eta_s$ unpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different fit quality and systematic errors. The predictions from smaller displacement $z$ to larger ones work better than those for momentum $p$ due to the higher correlation among the data.

Gluon Quasi-Parton-Distribution Functions from Lattice QCD.

We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a=0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(α_{s}) matching and the mixing from the quark PDFs.

Role of transverse momentum dependence of unpolarized parton distribution and fragmentation functions in the analysis of azimuthal spin asymmetries

Information on the Sivers distribution and the Collins fragmentation functions and their transverse momentum dependence is mainly based on fitting single spin asymmetry data from semi-inclusive deep inelastic scattering (SIDIS). Independent information, respectively on the Sivers distribution and the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$ annihilation processes. In the SIDIS case, the transverse momentum of the final observed hadron, which is the quantity measured, is generated both by the average transverse momentum in the distribution and in the fragmentation functions. As a consequence, these are strongly correlated and a separate extraction is made difficult. In this paper we investigate, in a simple kinematical Gaussian configuration, this correlation, its role on the transverse single spin asymmetries in SIDIS and the consequences for predictions of the Sivers asymmetry in Drell-Yan processes and for the Collins asymmetry in $e^+e^-$ annihilation. We find that, in some cases, these effects can be relevant and must be carefully taken into account.

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].

Power corrections and renormalons in Transverse Momentum Distributions

We study the power corrections to Transverse Momentum Distributions (TMDs) by analyzing renormalon divergences of the perturbative series. The renormalon divergences arise independently in two constituents of TMDs: the rapidity evolution kernel and the small-b matching coefficient. The renormalon contributions (and consequently power corrections and non-perturbative corrections to the related cross sections) have a non-trivial dependence on the Bjorken variable and the transverse distance. We discuss the consistency requirements for power corrections for TMDs and suggest inputs for the TMD phenomenology in accordance with this study. Both unpolarized quark TMD parton distribution function and fragmentation function are considered.

Heavy Flavour Production as Probe of Gluon Sivers Function

Heavy flavour production like $J/\psi$ and $D$- meson production in scattering of electrons/unpolarized protons off polarized proton target offer promising probes to investigate gluon Sivers function. In this talk, I will summarize our recent work on trasverse single spin asymmetry in $J/\psi $ -production and $D$ - meson production in $p p^\uparrow$ scattering using a generalized parton model approach. We compare predictions obtained using different models of gluon Sivers function within this approach and then, taking into account the transverse momentum dependent evolution of the unpolarized parton distribution functions and gluon Sivers function, we study the effect of evolution on asymmetry.

Transverse single spin asymmetry inp+p↑→D+X

We present expected values of the Single Spin Asymmetry (SSA) in $D$-meson production in the process $p+p^\uparrow \rightarrow D^0 + X $ at RHIC energy $(\sqrt{s}=200\text{ GeV})$ using a generalized parton model approach. We use fits to the gluon Sivers function obtained recently by D'Alesio {\it et al.,} by fitting to the asymmetry data for the process $p+p^\uparrow \rightarrow \pi^0+ X$ measured by the PHENIX collaboration at RHIC. These fits give peak asymmetry predictions which lie in a broad range, $0.5\%\lesssim A_N\lesssim10\%$ for the kinematic regions considered. This is to be compared with the upper bound of 18\% expected for the maximal gluon Sivers function. We extend our analysis to two other centre of mass energies of proposed experiments - AFTER@LHC $(\sqrt{s}=115\text{ GeV})$ and a future RHIC run $(\sqrt{s}=500\text{ GeV})$. We further investigate (at $\sqrt{s}=200$ GeV) the effect of the transverse momentum dependent (TMD) evolution of the unpolarized parton distribution functions (pdf's) and of the gluon Sivers function on the asymmetry predictions. We perform this study using an evolution setup given by Anselmino {\it et al}. We find that the effect of evolution is an overall reduction of the asymmetry predictions. For example, for the saturated gluon Sivers function, upon taking into account TMD evolution, peak asymmetry predictions reduce by a factor 3 or more. This decrease is similar to that noticed earlier for Single Spin Asymmetries (SSA) in the electroproduction of $J/\psi$.