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Showing papers on "Parton published in 2018"


Journal ArticleDOI
TL;DR: The physics of heavy ion collisions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting quarks at lower energy scales as discussed by the authors.
Abstract: Heavy ion collisions quickly form a droplet of quark–gluon plasma (QGP) with a remarkably small viscosity. We give an accessible introduction to how to study this smallest and hottest droplet of liquid made on Earth and why it is so interesting. The physics of heavy ion collisions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales. These gluons quickly thermalize and form QGP, while the energetic partons traverse this plasma and end in a shower of particles called jets. Analyzing the final particles in various ways allows us to study the properties of QGP and the complex dynamics of multiscale processes in QCD that govern its formation and evolution, providing what is perhaps the simplest form of complex quantum matter that we know of. Much remains to be understood, and throughout the review big open questions are encountered.

384 citations


Journal ArticleDOI
TL;DR: The physics of heavy ion collisions quickly form a droplet of quark-gluon plasma (QGP) with a remarkably small viscosity as discussed by the authors, which is perhaps the simplest form of complex quantum matter that we know of.
Abstract: Heavy ion collisions quickly form a droplet of quark-gluon plasma (QGP) with a remarkably small viscosity We give an accessible introduction to how to study this smallest and hottest droplet of liquid made on earth and why it is so interesting The physics of heavy ions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales These gluons quickly thermalize and form QGP, while the energetic partons traverse this plasma and end in a shower of particles called jets Analyzing the final particles in a variety of different ways allows us to study the properties of QGP and the complex dynamics of multi-scale processes in QCD which govern its formation and evolution, providing what is perhaps the simplest form of complex quantum matter that we know of Much remains to be understood, and throughout the review big open questions will be encountered

301 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD calculations of good "lattice cross sections", which are basically single-hadron matrix elements that are computable and perturbative QCD factorizable into the PDFs.
Abstract: Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and the quarks and gluons within it. We propose to extract PDFs from QCD global analysis of “data” generated by lattice QCD calculations of good “lattice cross sections,” which are basically single-hadron matrix elements that are lattice QCD calculable and perturbative QCD factorizable into the PDFs. To demonstrate the existence of good “lattice cross sections,” we take quasiquark distribution introduced by Ji [Phys. Rev. Lett. 110, 262002 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.262002] as a case study to show that it could be factorized into the PDFs to all orders in perturbation theory if it can be multiplicatively renormalized. We calculate the factorized coefficients at the next-to-leading order in αs.

187 citations


Journal ArticleDOI
TL;DR: In this article, the authors present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments.

170 citations


Journal ArticleDOI
TL;DR: In this article, the authors reflect on what the experimental measurements have taught us so far, the limitations of the techniques used for studying jets, how the techniques can be improved, and how to move forward with the wealth of experimental data such that a complete description of energy loss in the QGP can be achieved.
Abstract: A hot, dense medium called a quark gluon plasma (QGP) is created in ultrarelativistic heavy ion collisions. Early in the collision, hard parton scatterings generate high momentum partons that traverse the medium, which then fragment into sprays of particles called jets. Understanding how these partons interact with the QGP and fragment into final state particles provides critical insight into quantum chromodynamics. Experimental measurements from high momentum hadrons, two particle correlations, and full jet reconstruction at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) continue to improve our understanding of energy loss in the QGP. Run 2 at the LHC recently began and there is a jet detector at RHIC under development. Now is the perfect time to reflect on what the experimental measurements have taught us so far, the limitations of the techniques used for studying jets, how the techniques can be improved, and how to move forward with the wealth of experimental data such that a complete description of energy loss in the QGP can be achieved. Measurements of jets to date clearly indicate that hard partons lose energy. Detailed comparisons of the nuclear modification factor between data and model calculations led to quantitative constraints on the opacity of the medium to hard probes. However, while there is substantial evidence for softening and broadening jets through medium interactions, the difficulties comparing measurements to theoretical calculations limit further quantitative constraints on energy loss mechanisms. Since jets are algorithmic descriptions of the initial parton, the same jet definitions must be used, including the treatment of the underlying heavy ion background, when making data and theory comparisons. An agreement is called for between theorists and experimentalists on the appropriate treatment of the background, Monte Carlo generators that enable experimental algorithms to be applied to theoretical calculations, and a clear understanding of which observables are most sensitive to the properties of the medium, even in the presence of background. This will enable us to determine the best strategy for the field to improve quantitative constraints on properties of the medium in the face of these challenges.

160 citations


Journal ArticleDOI
TL;DR: The first global QCD analysis of parton distribution functions (PDFs) in the pion is performed, combining πA Drell-Yan data with leading neutron electroproduction from HERA within a Monte Carlo approach based on nested sampling.
Abstract: We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, combining πA Drell-Yan data with leading neutron electroproduction from HERA within a Monte Carlo approach based on nested sampling. Inclusion of the HERA data allows the pion PDFs to be determined down to much lower values of x, with relatively weak model dependence from uncertainties in the chiral splitting function. The combined analysis reveals that gluons carry a significantly higher pion momentum fraction, ∼30%, than that inferred from Drell-Yan data alone, with sea quarks carrying a somewhat smaller fraction, ∼15%, at the input scale. Within the same effective theory framework, the chiral splitting function and pion PDFs can be used to describe the d[over ¯]-u[over ¯] asymmetry in the proton.

144 citations


Journal ArticleDOI
TL;DR: In this article, a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation is presented.
Abstract: We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep-inelastic structure functions are computed consistently at $$\hbox {NLO+NLL}x$$ or $$\hbox {NNLO+NLL}x$$ , while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the recent NNPDF3.1 analysis. We demonstrate that the inclusion of small-x resummation leads to a quantitative improvement in the perturbative description of the HERA inclusive and charm-production reduced cross-sections in the small x region. The impact of the resummation in our fits is greater at NNLO than at NLO, because fixed-order calculations have a perturbative instability at small x due to large logarithms that can be cured by resummation. We explore the phenomenological implications of PDF sets with small-x resummation for the longitudinal structure function $$F_L$$ at HERA, for parton luminosities and LHC benchmark cross-sections, for ultra-high-energy neutrino–nucleus cross-sections, and for future high-energy lepton–proton colliders such as the LHeC.

144 citations


Journal ArticleDOI
TL;DR: This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an ab initio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.
Abstract: We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2 GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-x values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an ab initio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.

142 citations


Journal ArticleDOI
TL;DR: Using the heavy-quark effective theory formalism, a multiplicative renormalization of these operators at all orders in perturbation theory is shown, both in dimensional and lattice regularizations.
Abstract: In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

138 citations


Posted Content
TL;DR: In this paper, the future opportunities for high-density QCD studies with ion and proton beams at the LHC are presented, and four major scientific goals are identified: the characterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP) properties with unprecedented precision, the investigation of the microscopic parton dynamics underlying QGP properties, the development of a unified picture of particle production and QCD dynamics from small (pp) to large (nucleus--nucus) systems, the exploration of parton densities in nuclei in
Abstract: The future opportunities for high-density QCD studies with ion and proton beams at the LHC are presented. Four major scientific goals are identified: the characterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP) properties with unprecedented precision, the investigation of the microscopic parton dynamics underlying QGP properties, the development of a unified picture of particle production and QCD dynamics from small (pp) to large (nucleus--nucleus) systems, the exploration of parton densities in nuclei in a broad ($x$, $Q^2$) kinematic range and the search for the possible onset of parton saturation. In order to address these scientific goals, high-luminosity Pb-Pb and p-Pb programmes are considered as priorities for Runs 3 and 4, complemented by high-multiplicity studies in pp collisions and a short run with oxygen ions. High-luminosity runs with intermediate-mass nuclei, for example Ar or Kr, are considered as an appealing case for extending the heavy-ion programme at the LHC beyond Run 4. The potential of the High-Energy LHC to probe QCD matter with newly-available observables, at twice larger center-of-mass energies than the LHC, is investigated.

130 citations


Journal ArticleDOI
TL;DR: The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w(x) which incorporates Regge behavior at small x and inclusive counting rules at x→1, resulting in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits.
Abstract: The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w(x) which incorporates Regge behavior at small x and inclusive counting rules at x→1 A simple ansatz for w(x) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum

Journal ArticleDOI
TL;DR: In this article, the Linear Boltzmann Transport (LBT) model coupled to hydrodynamical background is extended to include transport of both light partons and heavy quarks through the quark-gluon plasma (QGP) in high-energy heavy-ion collisions.

Journal ArticleDOI
TL;DR: The lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum subtraction scheme (RI/MOM) renormalization on the lattice were presented in this paper.
Abstract: We present lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum-subtraction scheme (RI/MOM) renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-$x$ dependence of a momentum-dependent quasidistribution is calculated on the lattice and matched to the ordinary light cone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

Journal ArticleDOI
TL;DR: In this article, the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD was performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing.
Abstract: We present the first direct calculation of the renormalized transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Apart from physically light quarks, novel elements of the calculations are nonperturbative renormalization and extraction of a formula for the matching to light-cone parton distribution functions. Final results are presented in the $\overline{\mathrm{MS}}$ scheme at a scale of $\sqrt{2}\text{ }\text{ }\mathrm{GeV}$.

Journal ArticleDOI
TL;DR: In this paper, a master formula for renormalizing the nonlocal operator that depends on three parameters is presented, and the renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
Abstract: Parton quasidistribution functions provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters, we show the effect of renormalization on nucleon matrix elements with a pion mass of approximately 370 MeV and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Journal ArticleDOI
TL;DR: In this article, a GPU parallelized (3 + 1 )D hydrodynamics that has a source term from the energy-momentum deposition by propagating jet shower partons and provides real time update of the bulk medium evolution for subsequent jet transport is developed for co-current and event-by-event simulations of jet transport and jet-induced medium excitation.

Journal ArticleDOI
TL;DR: In this paper, a direct matching from the regularization independent momentum subtraction scheme (RI/MOM) to the collinear parton distribution was carried out for the quasi-PDF and PDF, determining the non-singlet quark matching coefficient at next to leading order in perturbation theory.
Abstract: The quasiparton distribution is a spatial correlation of quarks or gluons along the $z$ direction in a moving nucleon which enables direct lattice calculations of parton distribution functions. It can be defined with a nonperturbative renormalization in a regularization independent momentum subtraction scheme (RI/MOM), which can then be perturbatively related to the collinear parton distribution in the $\overline{\mathrm{MS}}$ scheme. Here we carry out a direct matching from the RI/MOM scheme for the quasi-PDF to the $\overline{\mathrm{MS}}$ PDF, determining the non-singlet quark matching coefficient at next-to-leading order in perturbation theory. We find that the RI/MOM matching coefficient is insensitive to the ultraviolet region of convolution integral, exhibits improved perturbative convergence when converting between the quasi-PDF and PDF, and is consistent with a quasi-PDF that vanishes in the unphysical region as the proton momentum ${P}^{z}\ensuremath{\rightarrow}\ensuremath{\infty}$, unlike other schemes. This direct approach therefore has the potential to improve the accuracy for converting quasidistribution lattice calculations to collinear distributions.

Journal ArticleDOI
TL;DR: In this paper, a complete set of independent leading-color two-loop five-parton amplitudes with external fermions in dimensional regularization is presented, which constitute a fundamental ingredient for the next-to-next-toleading order QCD corrections to three-jet production at hadron colliders.
Abstract: We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity method. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute leading-color two-loop four-parton amplitudes as a check of our implementation. Results are presented for all independent four- and five-parton processes including contributions with massless closed fermion loops.

Journal ArticleDOI
TL;DR: In this paper, the role of the soft-gluon resolution scale in the evolution of QCD evolution equations was analyzed using the unitarity picture in terms of resolvable and non-resolvable branchings.
Abstract: We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1% over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.

Journal ArticleDOI
TL;DR: In this paper, a hybrid transport model was developed to combine the strengths of both of these approaches: heavy quarks scatter with medium partons using matrix-elements calculated in perturbative QCD, while between these discrete hard scatterings they evolve using a Langevin equation with empirical transport coefficients to capture the nonperturbative soft part of the interaction.
Abstract: In relativistic heavy-ion collisions, the production of heavy quarks at large transverse momenta is strongly suppressed compared to proton-proton collisions. In addition, an unexpectedly large azimuthal anisotropy was observed for the emission of charmed hadrons in noncentral collisions. Both observations pose challenges to the theoretical understanding of the coupling between heavy quarks and the quark-gluon plasma produced in these collisions. Transport models for the evolution of heavy quarks in a QCD medium offer the opportunity to study these effects; two of the most successful approaches are based on the linearized Boltzmann transport equation and the Langevin equation. In this work, we develop a hybrid transport model that combines the strengths of both of these approaches: Heavy quarks scatter with medium partons using matrix-elements calculated in perturbative QCD, while between these discrete hard scatterings they evolve using a Langevin equation with empirical transport coefficients to capture the nonperturbative soft part of the interaction. With the hybrid transport model coupled to a state-of-the-art event-by-event bulk evolution model based on 2+1D relativistic viscous fluid dynamics, we study the azimuthal anisotropy and nuclear modification factor of heavy quarks in Pb+Pb collisions at $\sqrt{s}=5.02$ TeV. The parameters related to heavy-flavor transport are calibrated using a Bayesian analysis comparing them to available $D$-meson and $B$-meson data at the Large Hadron Collider. Using the calibrated model, we study the implications on heavy-flavor transport properties and predict observables.

Journal ArticleDOI
Albert M. Sirunyan, Armen Tumasyan, Wolfgang Adam1, Federico Ambrogi1  +2275 moreInstitutions (158)
TL;DR: In particular, the transverse momentum distribution of the top quarks is more steeply falling than predicted as mentioned in this paper, and the multiplicities of jets associated with the t (t) over bar production are measured.
Abstract: Differential and double-differential cross sections for the production of top quark pairs in proton-proton collisions at root s = 13 TeV are measured as a function of kinematic variables of the top quarks and the top quark- antiquark (t (t) over bar) system. In addition, kinematic variables and multiplicities of jets associated with the t (t) over bar production are measured. This analysis is based on data collected by the CMS experiment at the LHC in 2016 corresponding to an integrated luminosity of 35.8 fb(-1). The measurements are performed in the lepton + jets decay channels with a single muon or electron and jets in the final state. The differential cross sections are presented at the particle level, within a phase space close to the experimental acceptance, and at the parton level in the full phase space. The results are compared to several standard model predictions that use different methods and approximations. The kinematic variables of the top quarks and the t (t) over bar system are reasonably described in general, though none predict all the measured distributions. In particular, the transverse momentum distribution of the top quarks is more steeply falling than predicted. The kinematic distributions and multiplicities of jets are adequately modeled by certain combinations of next-to-leading-order calculations and parton shower models.

Journal ArticleDOI
TL;DR: It is shown that, due to the scatterings off the plasma, the in-medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside the medium can violate angular ordering.
Abstract: We study the fragmentation of a jet propagating in a dense quark-gluon plasma Using a leading, double-logarithmic approximation in perturbative QCD, we compute for the first time the effects of the medium on multiple vacuumlike emissions We show that, due to the scatterings off the plasma, the in-medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside the medium can violate angular ordering We compute the jet fragmentation function and find results in qualitative agreement with LHC measurements

Journal ArticleDOI
TL;DR: In this paper, a one-loop study of the small-z 3 2 -dependence of the Ioffe-time distribution (ITD) M ( ν, z 3 2 ), the basic function that may be converted into parton pseudo-and quasi-distributions, was performed.

Journal ArticleDOI
TL;DR: In this paper, a parton state is proposed as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level, and the wave function for this state is shown to be particle-hole symmetric to a high degree.
Abstract: In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL} \Phi_{1}^3[\Phi_{2}^{*}]^{2}\sim\Psi^{2}_{2/3}/\Phi_{1}$ and in the spherical geometry it occurs at the same flux as the anti-Pfaffian state. This state has a good overlap with the anti-Pfaffian state and with the ground state obtained by exact diagonalization, using the second Landau level Coulomb interaction pseudopotentials for an ordinary semiconductor such as GaAs. By calculating the entanglement spectrum we show that this state lies in the same phase as the anti-Pfaffian state. A major advantage of this parton state is that its wave function can be evaluated for large systems, which makes it amenable to variational calculations. In the appendix of this work we have numerically assessed the validity of another candidate state at filling factor $ u=5/2$, namely the particle-hole-symmetric Pfaffian (PH-Pfaffian) state. We find that the proposed candidate wave function for the PH-Pfaffian state is particle-hole symmetric to a high degree but it does not appear to arise as the ground state of any simple Hamiltonian with two-body interactions.

Journal ArticleDOI
TL;DR: In this article, the authors used algebraic Ansaetze for the Poincare-covariant Bethe-Salpeter wave functions of the pion and kaon to calculate their light-front wave functions (LFWFs), parton distribution amplitudes (PDAs), quasi-PDAs, and quasi-PDFs (qPDFs).
Abstract: Algebraic Ansaetze for the Poincare-covariant Bethe-Salpeter wave functions of the pion and kaon are used to calculate their light-front wave functions (LFWFs), parton distribution amplitudes (PDAs), quasi-PDAs (qPDAs), valence parton distribution functions (PDFs), and quasi-PDFs (qPDFs). The LFWFs are broad, concave functions; and the scale of flavour-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the $s$-and $u$-quark sectors. qPDAs computed with longitudinal momentum $P_z =1.75\,$GeV provide a semiquantitatively accurate representation of the objective PDA; but even with $P_z=3\,$GeV, they cannot provide information about this amplitude's endpoint behaviour. On the valence-quark domain, similar outcomes characterise qPDFs. In this connection, however, the ratio of kaon-to-pion $u$-quark qPDFs is found to provide a good approximation to the true PDF ratio on $0.3\lesssim x \lesssim 0.8$, suggesting that with existing resources computations of ratios of quasi-parton-distributions can yield results that support empirical comparison.

Journal ArticleDOI
TL;DR: In this paper, the relation of moments of parton distribution functions to matrix elements of non-local operators computed in lattice quantum chromodynamics was examined and it was shown that these moments are in agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation.
Abstract: We examine the relation of moments of parton distribution functions to matrix elements of non-local operators computed in lattice quantum chromodynamics. We argue that after the continuum limit is taken, these non-local matrix elements give access to moments that are finite and can be matched to those defined in the $$ \overline{MS} $$ scheme. We demonstrate this fact with a numerical computation of moments through non-local matrix elements in the quenched approximation and we find that these moments are in agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation.

Journal ArticleDOI
TL;DR: Analytic calculations of the hadron spectrum have now being realized using light-front holography and superconformal quantum mechanics, a novel approach providing a well-founded semiclassical approximation to QCD.
Abstract: We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules -- such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons -- are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of...

Journal ArticleDOI
Albert M. Sirunyan1, Armen Tumasyan1, Wolfgang Adam, Federico Ambrogi  +2232 moreInstitutions (142)
TL;DR: The momentum ratio of the two leading partons, resolved as subjets, provides information about the parton shower evolution and indicates a more unbalanced momentum ratio in central PbPb and pp collisions.
Abstract: Data from heavy ion collisions suggest that the evolution of a parton shower is modified by interactions with the color charges in the dense partonic medium created in these collisions, but it is not known where in the shower evolution the modifications occur. The momentum ratio of the two leading partons, resolved as subjets, provides information about the parton shower evolution. This substructure observable, known as the splitting function, reflects the process of a parton splitting into two other partons and has been measured for jets with transverse momentum between 140 and 500 GeV, in pp and PbPb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair. In central PbPb collisions, the splitting function indicates a more unbalanced momentum ratio, compared to peripheral PbPb and pp collisions.. The measurements are compared to various predictions from event generators and analytical calculations.

Journal ArticleDOI
TL;DR: Partons as discussed by the authors is a C++ framework dedicated to the phenomenology of Generalized Parton Distributions (GPD) which can describe the three-dimensional structure of hadrons in terms of quarks and gluons and can be accessed in deeply exclusive lepto- or photo-production of mesons or photons.
Abstract: We describe the architecture and functionalities of a C++ software framework, coined PARTONS, dedicated to the phenomenology of Generalized Parton Distributions. These distributions describe the three-dimensional structure of hadrons in terms of quarks and gluons, and can be accessed in deeply exclusive lepto- or photo-production of mesons or photons. PARTONS provides a necessary bridge between models of Generalized Parton Distributions and experimental data collected in various exclusive production channels. We outline the specification of the PARTONS framework in terms of practical needs, physical content and numerical capacity. This framework will be useful for physicists – theorists or experimentalists – not only to develop new models, but also to interpret existing measurements and even design new experiments.

Journal ArticleDOI
TL;DR: The first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass were obtained using the large-momentum effective field theory (LaMET) framework in this paper.
Abstract: We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-$x$ dependence of finite-momentum PDFs, called ``quasi-PDFs,'' can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized nonperturbatively in the RI/MOM-scheme. However, the recent renormalized quasi-PDFs suffer from unphysical oscillations that alter the shape of the true distribution as a function of Bjorken-$x$. In this paper, we propose two possible solutions to overcome this problem and demonstrate the efficacy of the methods on the $2+1+1$-flavor lattice data at physical pion mass with lattice spacing 0.09 fm and volume $(5.76\text{ }\text{ }\mathrm{fm}{)}^{3}$.