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.

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.

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.

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.

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.

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

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 $\sqrt{2}\text{ }\text{ }\mathrm{GeV}$.

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.

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.

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.

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

Abstract: When a mobile hole is moving in an anti-ferromagnet it distorts the surrounding Neel order and forms a magnetic polaron. Such interplay between hole motion and anti-ferromagnetism is believed to be at the heart of high-Tc superconductivity in cuprates. We study a single hole described by the t-Jz model with Ising interactions between the spins in 2D. This situation can be experimentally realized in quantum gas microscopes. When the hole hopping is much larger than couplings between the spins, we find strong evidence that magnetic polarons can be understood as bound states of two partons, a spinon and a holon carrying spin and charge quantum numbers respectively. We introduce a microscopic parton description which is benchmarked by comparison with results from advanced numerical simulations. Using this parton theory, we predict a series of excited states that are invisible in the spectral function and correspond to rotational excitations of the spinon-holon pair. This is reminiscent of mesonic resonances observed in high-energy physics, which can be understood as rotating quark antiquark pairs. We also apply the strong coupling parton theory to study far-from equilibrium dynamics of magnetic polarons observable in current experiments with ultracold atoms. Our work supports earlier ideas that partons in a confining phase of matter represent a useful paradigm in condensed-matter physics and in the context of high-Tc superconductivity. While direct observations of spinons and holons in real space are impossible in traditional solid-state experiments, quantum gas microscopes provide a new experimental toolbox. We show that, using this platform, direct observations of partons in and out-of equilibrium are possible. Extensions of our approach to the t-J model are also discussed. Our predictions in this case are relevant to current experiments with quantum gas microscopes for ultracold atoms.

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...

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 excellent agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation

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.

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.

Abstract: Parton showers have become a standard component in the description of high-energy collisions. Nowadays most final-state ones are of the dipole character, wherein a pair of partons branches into three, with energy and momentum preserved inside this subsystem. For initial-state showers a dipole picture is also possible and commonly used, but the older global-recoil strategy remains a valid alternative, wherein larger groups of partons share the energy–momentum preservation task. In this article we introduce and implement a dipole picture also for initial-state radiation in Pythia, and compare with the existing global-recoil one, and with data. For the case of Deeply Inelastic Scattering we can directly compare with matrix element expressions and show that the dipole picture gives a very good description over the whole phase space, at least for the first branching.

Abstract: We present a lattice-QCD calculation of the unpolarized isovector parton distribution function (PDF) using ensembles at the physical pion mass with large proton boost momenta $P_z \in \{2.2,2.6,3.0\}$~GeV within the framework of large-momentum effective theory (LaMET). In contrast to our previous physical-pion PDF result, we increase the statistics significantly, double the boost momentum, increase the investment in excited-state contamination systematics, and switch to $\gamma_t$ operator to avoid mixing with scalar matrix elements. We use four source-sink separations in our analysis to control the systematics associated with excited-state contamination. The one-loop LaMET matching corresponding to the new operator is calculated and applied to our lattice data. We detail the systematics that affect PDF calculations, providing guidelines to improve the precision of future lattice PDF calculations. We find our final parton distribution to be in reasonable agreement with the PDF provided by the latest phenomenological analysis.

Abstract: A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in Nc power corrections are expressed in terms of leading power TMDs by QCD equations of motion.

Abstract: We show that the presence of an infrared cutoff Q0 in the parton shower (PS) evolution for massive quarks implies that the generator quark mass corresponds to a Q0-dependent short-distance mass scheme and is therefore not the pole mass. Our analysis considers an angular ordered parton shower based on the coherent branching formalism for quasi-collinear stable heavy quarks and splitting functions at next-to-leading logarithmic (NLL) order, and it is based on the analysis of the peak of hemisphere jet mass distributions. We show that NLL shower evolution is sufficient to describe the peak jet mass at full next-to-leading order (NLO). We determine the relation of this short-distance mass to the pole mass at NLO. We also show that the shower cut Q0 affects soft radiation in a universal way for massless and quasi-collinear massive quark production. The basis of our analysis is (i) an analytic solution of the PS evolution based on the coherent branching formalism, (ii) an implementation of the infrared cut Q0 of the angular ordered shower into factorized analytic calculations in the framework of Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of the jet mass distribution on the shower cut. Numerical comparisons to simulations with the Herwig 7 event generator confirm our findings. Our analysis provides an important step towards a full understanding concerning the interpretation of top quark mass measurements based on direct reconstruction.

Abstract: Studies of fully-reconstructed jets in heavy-ion collisions aim at extracting thermodynamical and transport properties of hot and dense QCD matter. Recently, a plethora of new jet substructure observables have been theoretically and experimentally developed that provide novel precise insights on the modifications of the parton radiation pattern induced by a QCD medium. This report, summarizing the main lines of discussion at the 5th Heavy Ion Jet Workshop and CERN TH institute "Novel tools and observables for jet physics in heavy-ion collisions" in 2017, presents a first attempt at outlining a strategy for isolating and identifying the relevant physical processes that are responsible for the observed medium-induced jet modifications. These studies combine theory insights, based on the Lund parton splitting map, with sophisticated jet reconstruction techniques, including grooming and background subtraction algorithms.

Abstract: Within the context of a hybrid strong/weak coupling model of jet quenching, we study the consequences of the fact that the plasma produced in a heavy ion collision cannot resolve the substructure of a collimated parton shower propagating through it with arbitrarily fine spatial resolution. We introduce a screening length parameter, Lres, proportional to the inverse of the local temperature in the plasma, estimating a range for the value of the proportionality constant via comparing weakly coupled QCD calculations and holographic calculations appropriate in strongly coupled plasma. We then modify the hybrid model so that when a parton in a jet shower splits, its two offspring are initially treated as unresolved, and are only treated as two separate partons losing energy independently after they are separated by a distance Lres. This modification delays the quenching of partons with intermediate energy, resulting in the survival of more hadrons in the final state with pT in the several GeV range. We analyze the consequences of different choices for the value of the resolution length, Lres, and demonstrate that introducing a nonzero Lres results in modifications to the jet shapes and jet fragmentations functions, as it makes it more probable for particles carrying a small fraction of the jet energy at larger angles from the jet axis to survive their passage through the quark-gluon plasma. These effects are, however, small in magnitude, something that we confirm via checking for effects on missing-pT observables.

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.

Abstract: Vector-boson scattering processes are of great importance for the current run-II and future runs of the Large Hadron Collider. The presence of triple and quartic gauge couplings in the process gives access to the gauge sector of the Standard Model (SM) and possible new-physics contributions there. To test any new-physics hypothesis, sound knowledge of the SM contributions is necessary, with a precision which at least matches the experimental uncertainties of existing and forthcoming measurements. In this article we present a detailed study of the vector-boson scattering process with two positively-charged leptons and missing transverse momentum in the final state. In particular, we first carry out a systematic comparison of the various approximations that are usually performed for this kind of process against the complete calculation, at LO and NLO QCD accuracy. Such a study is performed both in the usual fiducial region used by experimental collaborations and in a more inclusive phase space, where the differences among the various approximations lead to more sizeable effects. Afterwards, we turn to predictions matched to parton showers, at LO and NLO: we show that on the one hand, the inclusion of NLO QCD corrections leads to more stable predictions, but on the other hand the details of the matching and of the parton-shower programs cause differences which are considerably larger than those observed at fixed order, even in the experimental fiducial region. We conclude with recommendations for experimental studies of vector-boson scattering processes.