The need for accurate and precise polarised parton distribution functions (PDFs) is becoming increasingly crucial in view of the Electron-Ion Collider experimental program foreseen in the coming years. Two global PDF determinations at next-to-next-to-leading order accuracy have been recently presented, MAPPDFpol1.0 and BDSSV24. I review the former and I provide a comparative discussion of other PDF sets accurate to next-to-leading order. I show that differences between these PDF sets, due to the choice of experimental and methodological input, exceed differences due to perturbative accuracy.
We present preliminary results on the determination of spin-dependent, or polarised, Parton Distribution Functions (PDFs) from all relevant inclusive polarised DIS data. The analysis is performed within the NNPDF approach, which provides a faithful and statistically sound representation of PDFs and their uncertainties. We describe how the NNPDF methodology has been extended to the polarised case, and compare our results with other recent polarised parton sets. We show that polarised PDF uncertainties can be sizeably underestimated in standard determinations, most notably for the gluon.
We analyze spin dependent parton distributions consistent with the most recent measurements of the spin dependent deep inelastic scattering structure functions and obtained in the framework of the spin dilution model. Predictions for the doubly polarised proton-proton Drell-Yan asymmetry, for the high $p_{T}$ photon production mechanism and $J/Ψ$ excitation are calculated using these distributions and are shown to be particularly adequate to unveil the polarisation of partons in the proton.
We present the results of a QCD fit to global data on deep-inelastic polarised lepton-hadron scattering. We find that it is possible to fit the data with strongly broken SU(2) flavour for the polarised sea densities. This can easily be tested in $W$ production at polarised RHIC. The data fails to pin down polarised singlet sea quark and gluon densities. We explore the uncertainties in detail and show that improvement in statistics, achievable at polarised HERA for measurement of A_1 at moderately low values of x, have large payoffs in terms of the improvement in measurement of gluon and sea qu…
The $Q^2$ evolution of polarised parton distributions at small $x$ is studied. Various analytic approximations are critically discussed. We compare the full evolution with that obtained from the leading-pole approximation to the splitting functions, and show that the validity of this approximation depends critically on the $x \to 0$ behaviour of the starting distributions. A new analytic solution which is valid at small $x$ is obtained, and its domain of applicability is discussed.
We study the phenomenon of parton-hadron duality in both polarised and unpolarised electron proton scattering using the HERMES and the Jefferson Lab data, respectively. In both cases we extend a systematic perturbative QCD based analysis to the integrals of the structure functions in the resonance region. After subtracting target mass corrections and large x resummation effects, we extract the remaining power corrections up to order 1/Q^2. We find a sizeable suppression of these terms with respect to analyses using deep inelastic scattering data. The suppression appears consistently in both po…
Using the infrared-renormalon approach, we obtain the constraints on the next-to-leading order non-singlet polarised parton densities. The advocated feature follows from the consideration of the effect revealed in the process of the next-to-leading order fits to the data for the assymetry of polarised lepton-nucleon scattering which result in the approximate nullification of the $1/Q^2$-correction to A_1^N(x,Q^2).
We consider a general formalism to compute inclusive polarised and unpolarised cross sections within pQCD and the factorisation scheme, taking into account parton intrinsic motion in distribution and fragmentation functions, as well as in the elementary dynamics. Surprisingly, the intrinsic partonic motion, with all the correct azimuthal angular dependences, produces a strong suppression of the transverse single spin asymmetry arising from the Collins mechanism. As a consequence, and in contradiction with earlier claims, the Collins mechanism is unable to explain the large asymmetries found in…
We present for first time the computation at large $q_T$ (or small $b_T$) matching coefficients of Transverse Momentum Dependent Parton Distribution Function (TMDPDF) for linearly polarised to the integrated gluon distribution at next-to-next-to leading order (NNLO). The computation is performed using the modified $δ$-regulator for rapidity divergences and dimensional regularization. This TMDPDF matriz element presnts phenomenological interest in two kind of processes. The factorization of the Higgs production transverse momentum ($q_T$) distribution through gluon-gluon fusion and the quarkoni…
The present talk summarises the 1993 situation in understanding the spin structure of the nucleon via electron and muon polarised deep--inelastic scattering (PDIS). The central question I shall address here is if the data can be interpreted as evidence for polarisation in the ``strange'' nucleon ``sea'', and I conclude that they can not: incidentally, I also find that they can not be constructed as evidence for violation of perturbative QCD (PQCD), either. Talk presented at ``Quinto Convegno su Problemi di Fisica Nucleare Teorica'', Cortona (Arezzo, Italy), October 1993. To be published in the…
We have made next to leading order QCD fit to the deep inelastic spin asymmetries on nucleons and we determined polarised quark and gluon densities. The functional form for such distributions was inspired by the Martin, Roberts and Stirling fit for unpolarised case. In addition to usually used data points (averaged over $x$ and $Q^2$) we have also considered the sample containing points with similar $x$ and different $Q^2$. It seems that splitting of quark densities into valence and sea contribution is strongly model dependent and only their sum (i.e., $Δu$ and $Δd$) can be precisely determine…
We discuss how the experimental information from longitudinal single-spin asymmetries for $W^{\pm}$ boson production in polarised proton-proton collisions can be included in a polarised parton determination by Bayesian reweighting of a Monte Carlo set of polarised PDF replicas. We explicitly construct a prior ensemble of polarised parton distributions using available fits to inclusive and semi-inclusive DIS data and we discuss the potential impact of existing and future RHIC measurements on it.
In order to obtain polarised parton densities we have made next to leading order QCD fit using experimental data on deep inelastic structure functions on nucleons. This fit is compared with the updated fit to coresponding spin asymmetries. We get very similar results for all fits also for different data samples. It seems that only polarised parton densities for non-strange quarks $Δu$ and $Δd$ are relatively well determined from the present deep inelastic experiments. Inegrated gluon contribution at $Q^{2}=1 {\rm GeV^{2}}$ is, as in our previous fits, very small.
We have made next to leading order QCD fit to the deep inelastic spin asymmetries on nucleons and we have determined polarised quark and gluon densities. The functional form for such distributions was inspired by the unpolarised ones given by MRST (Martin, Roberts, Stirling and Thorne) fit. In addition to usually used data points (averaged over $Q^2$) we have also considered the sample containing points with the same $x$ and different $Q^2$. Our fits to both groups of data give very similar results. For the integrated quantities we get rather small gluon polarisation. For the non averaged data…
We report on the first calculation of the structure function g_1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised cases of F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order …
We have compared polarized parton densities determined in the NLO QCD fits to polarized structure functions and spin asymmetries. We consider models of such distributions based on MRST 99 and MRST 2001 fits to non-polarized data. Simple power law corrections corresponding to higher twists are taken into account and their importance is analyzed. The role of positivity conditions for parton densities and their influence on the values of $χ^{2}$ is discussed.
We present the results of a detailed study of the large transverse momentum Drell-Yan process, pp --> (Gamma^*, Z^*)X --> l^+l^- X at collider energies, with either one or both protons polarised, allowing the study of single- and double-spin asymmetries respectively. We show how these asymmetries obtained from angular distributions of the leptons in the Gamma^* (or Z^*) rest-frame, can be used to get information on the polarised parton distributions. Numerical results for the asymmetries and the cross-sections are presented, and the sensitivity of the asymmetries to the initial parton distribu…
We analyse polarised Drell-Yan process using the factorisation method and derive operator definitions for polarised parton distribution functions. We demonstrate that a factorisation analogous to that in the unpolarised Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarised Drell-Yan function and show that it is consistent with results obtained from polarised deep inelastic scattering.
We show how the operator product expansion evaluated in the approximation of ignoring gluons leads to the covariant formulation of the quark parton model. We discuss the connection with other formulations and show how the free quark model prediction, $g_2=0$, changes smoothly into the Wandzura-Wilczek (WW) relation for quark masses small relative to the nucleon mass. Previous contradictory parton model predictions are shown to follow from an inconsistent treatment of the mass shell conditions. The description is extended to include quark mass corrections.
The importance of polarised gluons fragmenting into $Λ$ in the polarised $e^+ e^-$ annihilation is discussed using the Altarelli-Parisi evolution equations satisfied by the quark and gluon fragmentation functions. In this context, the polarised fragmentaion function $\hat g_1^Λ(x,Q^2)$ appearing in the cross section is discussed within the parton model. We relate this fragmentation function to the quark, anti-quark and gluon fragmentation functions and also find the QCD corrections to order $α_s$.
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by feeding alternative sets of evolution kernels into the program. A versatile convolution engine provides tools to compute parton luminosities, cross-sections in hadron-hadron scattering, and deep inelasti…
The $Q^2$ evolution of polarised parton fragmentation functions is discussed using Altarelli-Parisi evolution equations. The first moments of both polarised quark and gluon fragmentation functions are shown to behave in a similar fashion at very high energies. This analysis is applicable to any hard processes involving production of polarised hadrons. The polarised $Λ$ hyperon production in $e^+~e^-$ annihilation where this can be realised is considered. We present a complete $α_s(Q^2)$ corrections to the asymmetries discussed in the paper of Burkardt and Jaffe which demonstrates the extractio…
We briefly review some of the developments in the study of parton distributions which have occurred since DIS2000, including discussion of uncertainties, shadowing, unintegrated and generalized distributions.
We present the new preliminary MRST parton distributions at NLO and NNLO. The analysis includes some new data and there is an improvement in the theoretical treatment at NNLO. Essentially complete NNLO partons are presented for the first time, together with uncertainties.
We report on a calculation of the full one-loop weak corrections through the order $α_{\mathrm{S}}^2α_{\mathrm{W}}$ to parton-parton scattering in all possible channels at the Relativistic Heavy Ion Collider (RHIC) running with polarised $pp$ beams (RHIC-Spin). This study extends the analysis previously carried out for the case of $2\to2$ subprocesses with two external gluons, by including all possible four-quark modes with and without an external gluon. The additional contributions due to the new four-quarks processes are extremely large, of order 50 to 100% (of either sign), not only in the …
A review of the present knowledge on polarized parton distributions is given. The effects of perturbative evolution on these distributions are discussed qualitatively and a comparison of various recent parametrizations is made.
This is a personal summary of the meeting "Saturation, the Color Glass Condensate and Glasma: What Have we Learned from RHIC?" that took place at BNL in May 2010. The purpose of the meeting was to discuss the status of high density QCD and parton saturation, and to review the progress that RHIC has allowed in the field.
The handbag contribution to Compton scattering at moderately large momentum transfer factorises into parton-photon subprocess amplitudes and new form factors representing 1/x-moments of skewed parton distributions. A detailed phenomenological study for polarised and unpolarised real and virtual Compton scattering is presented
The current status of global QCD analysis of parton distribution functions of the nucleon is reviewed. Recent progress made in determining various features of the parton structure of the nucleon, as well as outstanding open questions are discussed. These include: the small-$x$ and large-$x$ behavior of the partons, particularly the gluon; the differentiation of $u$ and $d$ quarks; the strangeness sea ($s+\bar{s}$), the strangeness asymmetry ($s-\bar{s}$); and the heavy quark distributions $c$ and $b$. Important issues about assessing the uncertainties of parton distributions and their physical…
We present the parton distribution functions (PDFs) for un- polarised, longitudinally polarized and transversely polarized quarks in a proton using the light-front quark diquark model. We also present the scale evolution of PDFs and calculate axial charge and tecsor charge for $u$ and $d$ quarks at a scale of experimental findings.
Inclusive neutral and charged current cross sections and structure functions measured at HERA-I are briefly reviewed. The impact of these measurements on parton density functions is discussed. The emphasis is put on the high x region. A first result obtained using the HERA-II data is also shown followed by future prospects for HERA.
We study an influence of precise data on uncertainty of polarized parton distribution functions. This analysis includes the SLAC-E155 proton target data which are precise measurements. Polarized PDF uncertainties are estimated by using the Hessian matrix. We examine correlation effect between the antiquark and gluon uncertainties. It suggests that reducing the gluon uncertainty is needed to determine the polarized antiquark distribution clearly.
Diffractive parton distributions of the proton are determined from fits to diffractive data from HERA. In addition to the twist--2 contribution, the twist--4 contribution from longitudinally polarised virtual photons is considered, which is important in the region of small diffractive masses. A new prediction for the longitudinal diffractive structure function is presented which differs significantly from that obtained in the pure twist--2 analyses.
New experimental results on polarized structure functions, cross sections for $e^{\pm}p$ neutral and charge current reactions and $ν$ ($\barν$) charge current on isoscalar targets are compared with predictions using the statistical parton distributions, which were previously determined. New data on cross sections for Drell-Yan processes, single jet in $p\bar{p}$ collisions and inclusive $π^0$ production in $pp$ collisions are also compared with predictions from this theoretical approach. The good agreement which we find with all these tests against experiment, strenghtens our opinion on the re…
Electron Ion Collider is a future high energy facility for studies of the structure of the nucleon. Three-dimensional parton structure is one of the main goals of EIC. In momentum space Transverse Momentum Dependent Distributions (TMDs) are the key ingredients to map such a structure. At leading twist spin structure of spin-1/2 hadron can be described by 8 TMDs. Experimentally these functions can be studied in polarised SIDIS experiments. We discuss Sivers distribution function that describes distribution of unpolarised quarks in a transversely polarised nucleon and transversity that measures …
The theoretical framework for a next-to-leading order QCD analysis of the spin-dependent parton densities Delta f^{gamma}(x,Q^2) of the longitudinally polarized photon and of its structure function g_1^{gamma}(x,Q^2) is reviewed in some detail. Special emphasis is given to the specific features of different factorization schemes. Two conceivable scenarios for the polarized parton densities Delta f^{gamma}(x,Q^2) are introduced, which are suitable to study the sensitivity of future experiments to the so far unmeasured Delta f^{gamma}. The experimental prospects of determining Delta f^{gamma} at…
We summarize recent developments in understanding the concept of generalized parton distributions (GPDs), its relation to nucleon structure, and its application to high-Q2 electroproduction processes. Following a brief review of QCD factorization and transverse nucleon structure, we discuss (a) new theoretical methods for the analysis of deeply-virtual Compton scattering (t-channel-based GPD parametrizations, dispersion relations); (b) the phenomenology of hard exclusive meson production (experimental tests of dominance of small-size configurations, model-independent comparative studies); (c) …
We report on the extraction of dihadron fragmentation functions (DiFF) from the semiinclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite $π^+π^-$ pairs is related to the transverse polarization of fragmenting quarks through a significant polarized DiFF. A combined analysis of this asymmetry and the spin asymmetry in the SIDIS process $ep^{\uparrow}\to e'(π^+π^-)X$ has led to the first extraction of the u and d-flavor transversity parton distribution function in the framework of collinear…
A brief review on the status of unpolarized parton densities and the determination of the QCD scale $Λ_{\rm QCD}$ from deep-inelastic scattering data is presented.
We provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, an…
We review the experimental as well as the phenomenology status of Generalized Parton Distributions (GPDs), focusing on recent data on Deeply Virtual Compton Scattering and Deep Virtual Meson Production. We also describe the various strategies for extraction of GPDs from these data. Finally we conclude with a summary of we know about GPDs and the experimental outlook in the years to come.
We discuss the present situation with regard to polarised nucleon structure function measurements. In particular we examine the status of the Bjorken sum rule in the light of the recent data on the spin structure functions of (i) the deuteron obtained by the SMC group at CERN and (ii) the neutron by the E142 group at SLAC. In order to fully exploit all the available data it is necessary to study the complete Bjorken system of equations, which may be done in any of several equivalent ways. Combining the new data with that already obtained for the proton by the EMC group and earlier SLAC/YALE co…
The present status of the longitudinal polarized parton densities (PDFs) and the contribution of their first moments to the nucleon spin is discussed. Special attention is paid to the role of higher twist effects in determining the PDFs and to the polarized strange quark and gluon densities, which are still not well determined from the present data.
I discuss the current status of parton distributions. I outline the wide variety of different parton distributions available, and highlight which are either necessary or suitable for use at present.
Theoretical progress on the formulation and classification of the quark and gluon orbital angular momenta (OAM) is reviewed. Their relation to parton distributions and open questions and puzzles are discussed. We give a status report on the lattice calculation of the parton kinetic and canonical OAM and point out several strategies to calculate the quark and gluon canonical OAM on the lattice.
The COMPASS experiment at CERN is one of the leading experiments studying the nucleon spin structure. Until 2012 the Parton Distribution Functions and the Transverse Momentum Dependent Parton Distribution Functions (TMDs) were extensively studied at COMPASS using Semi-Inclusive Deep Inelastic Scattering measurements. In 2015, the Drell-Yan measurements with a negative pion beam interacting with a transversely polarized ammonia target have started and will be continued through 2018. The goal is to access the TMDs of both pions and protons without any prior knowledge about fragmentation function…
In the past decade the observation of cross section modification for leading hadrons, heavy flavor and two particle correlations in heavy ion collisions has provided important insights into the dynamics of parton propagation in dense strongly-interacting matter. The development of the theory of reconstructed jets and related experimental measurements have further shed light on the characteristics of in-medium parton showers. So far, experimental results from ultra-relativistic nuclear collisions at RHIC and LHC have been analyzed in the framework of parton energy loss, where the precision of t…
We relate ordinary and skewed parton distributions to soft overlap contributions to elastic form factors and large angle Compton scattering, using light-cone wave functions in a Fock state expansion of the nucleon. With a simple ansatz for the wave functions of the three lowest Fock states we achieve a good description of unpolarised and polarised parton distributions at large x, and of the data for the Dirac form factor and for Compton scattering, both of which can be saturated with soft contributions only. Large angle Compton scattering appears as a good case to investigate the relative impo…
A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the spin--structure of nucleons in the future.
A short review is given of the idea and of the present status of recently proposed evolution equations that respect the Gribov-Lipatov reciprocity between space-like and time-like parton dynamics in all orders.
We introduce the neural network approach to global fits of parton distrubution functions. First we review previous work on unbiased parametrizations of deep-inelastic structure functions with faithful estimation of their uncertainties, and then we summarize the current status of neural network parton distribution fits.
We review the current status of collinear and Transverse Momentum Dependent densities based on the Parton Branching method. We investigate the performance of the PB-TMD evolution as well as PB-TMD parton shower with different configurations of the hard process in the four- and five-flavour schemes.
In this review, we describe the status of transverse momentum dependence (TMD) in double parton scattering (DPS). The different regions of TMD DPS are discussed, and expressions given for the DPS cross section contributions that make use of as much perturbative information as possible. The regions are then combined with each other as well as with single parton scattering to obtain a complete expression for the cross section. Particular emphasis is put on the differences and similarities to transverse momentum dependence in single parton scattering. We further discuss the status of the factoris…
Reliable knowledge of parton distributions at large x is crucial for many searches for new physics signals in the next generation of collider experiments. Although these are generally well determined in the small and medium x range, it has been shown that their uncertainty grows rapidly for x>0.1. We examine the status of the gluon and quark distributions in light of new questions that have been raised in the past two years about "large-x" parton distributions, as well as recent measurements which have improved the parton uncertainties. Finally, we provide a status report of the data used in t…
