W. James Stirling
Parton distribution functions (pdfs) are an important ingredient for LHC phenomenology. Recent progress in determining pdfs from global analyses is reviewed, and some of the most important outstanding issues are highlighted. Particular attention is paid to the precision with which predictions for LHC `standard-candle' cross sections can be made, and also to new information that LHC can provide on pdfs.
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I give an overview of the recent progress on the matching of fixed-order calculations and parton showers. The focus is on the matching with NNLO QCD corrections as well as with NLO EW ones.
I outline some of the most recent developments on the global fit to parton distributions performed by the MRST collaboration.
We briefly discuss recent research on the spin-averaged parton densities of the proton, focusing on some aspects relevant to hard processes at the LHC. Specifically, after recalling the basic framework and the need for higher-order calculations, we address the evolution equations governing the scale dependence of the parton distributions and their solution, schemes for initial conditions and the inclusion of heavy quarks, recent progress on fits to data, and future high-precision constraints from LHC measurements.
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon. Some predictions from a next-to-leading order QCD analysis are compared to recent experimental results. We also consider their extension to include their transverse momentum dependence.
The present status of the (JR) dynamical parton distribution functions is reported. Different theoretical improvements, including the determination of the strange sea input distribution, the treatment of correlated errors and the inclusion of alternative data sets, are discussed. Highlights in the ongoing developments as well as (very) preliminary results in the determination of the strong coupling constant are presented.
The determination of the parton distribution functions (PDFs) is crucial for a complete understanding of the protons and neutrons that make most of the visible matter in the universe. Years of dedicated studies have yielded a quite precise knowledge of the behavior of partons moving collinearly within a proton. However Deep Inelastic Scattering (DIS) experiments off nuclei have shown a non-trivial difference with respect to DIS in protons, hinting that the partons in a nuclear medium do not behave the same way as in a free proton. In this work we will discuss the latest results in nuclear part…
We give a status report on the determination of a set of parton distributions based on neural networks. In particular, we summarize the determination of the nonsinglet quark distribution up to NNLO, we compare it with results obtained using other approaches, and we discuss its use for a determination of $α_s$.
Recent progress in transverse momentum dependent (TMD) Parton Densities and corresponding parton showers
本研究采用Parton-Branching方法分析软胶子对TMD部分子密度的影响，明确常被忽略的z→1区间对应非微扰Sudakov形状因子，解释了Drell-Yan过程内禀kt宽度与质心系能量无关的特性。
We review the current state of the art in the determination of the parton substructure of the nucleon, as expressed in terms of parton distribution functions (PDFs), and probed in high-energy lepton-hadron and hadron-hadron collisions, and we assess their implications for current precision collider phenomenology, in particular at the Large Hadron Collider (LHC). We review the theoretical foundations of PDF determination: the way cross sections are expressed in terms of PDFs using perturbative QCD factorization and evolution, the methodology used to extract PDFs from experimental data, and the …
We describe techniques that simplify the calculation of one-loop QCD amplitudes with many external legs, which are needed for next-to-leading-order (NLO) corrections to multi-jet processes. The constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes are particularly useful. Certain sequences of one-loop helicity amplitudes may be obtained for an arbitrary number of external gluons using these techniques. We also report on progress in completing the set of one-loop helicity amplitudes required for NLO three-jet prod…
We report on the development of a new model for the underlying event in hadron-hadron collisions. The model includes parton showers for all interactions, as well as non-trivial flavour, momentum, and colour correlations between interaction initiators and beam remnant partons.
We review selected recent theoretical activity in perturbative QCD. We focus on progress in the description of parton densities, including latest developments in neural network parton densities, on the description of high multiplicity final states at the LHC at leading and next-to-leading order, on progress in next-to-next-to-leading order, and on novel developments in jets physics.
We review the latest progress in lattice QCD calculations of the partonic structure of hadrons. This structure is, in particular, described in terms of $x$-dependent distributions, the simplest of which are the standard parton distribution functions (PDFs). The lattice calculations rely on matrix elements probing spatial correlations between partons in a boosted hadron, that can be matched to light-cone correlations defining the relevant distributions. We discuss the recent theoretical and practical refinements of this strategy, as well as new exploratory directions. The latter include general…
Recent progress on the parton distribution functions of the photon, both real and virtual, is briefly reviewed and experimental possibilities at HERA are discussed.
An overview of theoretical and experimental progress in double parton scattering (DPS) is presented. The theoretical topics cover factorization in DPS, models for double parton distributions and DPS in charm production and nuclear collisions. On the experimental side, CMS results for dijet and double J/ψ production, in light of DPS, as well as first results for the 4-jet channel are presented. ALICE reports on a study of open charm and J/ψ multiplicity dependence.
We present recent progress on the study of the deep inelastic structure of nuclei that improves our current understanding of the mechanisms of nuclear modifications of parton distribution functions.
Substantial progress has been made recently in the formalisms which form the basis of event generators. I discuss some of the ideas involved, emphasizing the role of higher-order QCD corrections and their interplay with parton showers
Structure functions are a measure of the partonic structure of hadrons, which is important for any process which involves colliding hadrons. They are a key ingredient for deriving partons distributions in nucleons. In recent years dramatic progress has been made in the understanding of the nucleon structure and the precision of its partonic content, due to vast theoretical progress, and the availability of new high precision measurements. This review gives an overview on present structure function and related data, and on the most recent techniques used to extract parton distribution functions…
We present the determination of Transverse Momentum Dependent (TMD) parton distributions from Monte Carlo parton showers. We investigate the effective TMD distributions obtained from the PYTHIA8 and HERWIG6 parton showers and compare them to the TMD distributions determined within the Parton Branching method.
I review recent progress in the determination of the parton structure of the nucleon, in particular from deep-inelastic structure functions. I explain how the needs of current and future precision phenomenology, specifically at the LHC, have turned the determination of parton distributions into a quantitative problem. I describe the results and difficulties of current approaches and ideas to go beyond them.
Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction $x$ of the hadron with $x >1$ or $x<-1$. The studied twist-4 parton distributions of collinear factoization are power-divergent for $\vert x\vert >1$. The corresponding transverse momentum dependent parton distributions have also no parton interpretation. They are finite. The implications of our results are discussed.
I review progress on selected issues connected with generalized parton distributions. Topics range from the description of hard exclusive reactions to the spatial distribution of quarks in the nucleon and the contribution of their orbital angular momentum to the nucleon spin.
We discuss the current developments by the European Twisted Mass Collaboration in extracting parton distribution functions from the quasi-PDF approach. We concentrate on the non-perturbative renormalization prescription recently developed by us, using the RI$'$ scheme. We show results for the renormalization functions of matrix elements needed for the computation of quasi-PDFs, including the conversion to the $\overline{\rm MS}$ scheme, and for renormalized matrix elements. We discuss the systematic effects present in the $Z$-factors and the possible ways of addressing them in the future.
It is shown that off-forward parton distributions for $ζ=0$, i.e. where the initial and final state differ only in their transverse momenta, can be interpreted as a simultaneous measurement of the longitudinal momentum and transverse position (impact parameter) of partons in the infinite momentum frame.
In this contribution we briefly report on the progress and open problems in parton distribution functions (PDFs), with emphasis on their implications for LHC phenomenology. Then we study the impact of the recent ATLAS and CMS W lepton asymmetry data on the NNPDF2.1 parton distributions. We show that these data provide the first constrains on PDFs from LHC measurements.
We show that Mellin moments of generalized parton distributions, given as even polynomials in the skewness parameter, are obtained from the Taylor expansion of light front wave functions. Furthermore, we derive non-standard versions of the inverse Radon transform to obtain the double distribution from the parton number conserved light front wave function overlap. These transformations are utilized to extend a generalized parton distribution from the outer region to the central one. We exemplify the formalism for a light front wave function that arises from an AdS/QCD duality conjecture.
A short review of form factors, parton distribution functions and generalized parton distributions is given. A possible application of generalized parton distributions in the weak sector is discussed.
I discuss the physical interpretation of GPDs in the limit $ξ=0$, where the $t$ dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also provides a physical interpretation for Ji's angular momentum sum rule.
We review recent progress towards a determination of a set of polarized parton distributions from a global set of deep-inelastic scattering data based on the NNPDF methodology, in analogy with the unpolarized case. This method is designed to provide a faithful and statistically sound representation of parton distributions and their uncertainties. We show how the FastKernel method provides a fast and accurate method for solving the polarized DGLAP equations. We discuss the polarized PDF parametrizations and the physical constraints which can be imposed. Preliminary results suggest that the unce…
Generalized parton distributions (GPDs) provide a link between form factors, parton distributions and other observables. I discuss the connection between GPDs and parton distributions as a function of the impact parameter. Since this connection involves GPDs in the limit of vanishing skewedness parameter $ξ$, i.e. when the off-forwardness is purely transverse, I also illustrate how to relate $ξ\neq 0$ data to $ξ=0$ data, which is important for experimental measurements of these observables.
Progress in top-quark pair production cross section calculations and impact on parton distribution functions of the proton
本研究分析LHC 13 TeV顶夸克对产生截面测量对质子PDF的影响，结合aN³LO QCD与NLO EW修正研究t̄t可观测量，验证大x胶子PDF效应并对比理论预测与实验数据。
Multi-parton distributions in a proton, the nonperturbative quantities needed to make predictions for multiple scattering rates, are poorly constrained from theory and data and must be modelled. All Monte Carlo event generators that simulate multiple parton interactions (e.g. Pythia) contain such a model of multi-parton PDFs. One important theoretical constraint for the case of double parton distributions is provided by the so-called number and momentum sum rules. In this paper we investigate to what extent the double parton distribution functions used in the Pythia event generator obey these …
The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $ξ$, i.e. when the off-forwardness is purely transverse. It is also illustrated how to relate $ξ\neq 0$ data to $ξ=0$ data, which is important for experimental measurements of these observables.
We present the construction of unintegrated double parton distribution functions which include dependence on transverse momenta of partons. We extend the formulation which was used to obtain the single unintegrated parton distributions from the standard, integrated parton distribution functions. Starting from the homogeneous part of the evolution equations for the integrated double parton distributions, we construct the unintegrated double parton distributions as the convolutions of the integrated double distributions and the splitting functions, multiplied by the Sudakov form factors. We show…
We outline the basic properties of a pertubative QCD factorization formalism that maintains exact over-all kinematics in both the initial and final states. Such a treatment requires the use of non-perturbative factors that depend on all components of parton four-momentum. These objects are referred to as parton correlation functions. We describe the complications faced in defining parton correlation functions and discuss recent progress. Emphasis is placed on the need for precise operator definitions in a complete derivation of factorization.
Generalized Parton Distributions describe, within QCD factorization, the non perturbative component in the amplitudes for deeply virtual exclusive processes. However, in order for a partonic interpretation to hold, semi-disconnected diagrams should not contribute. We show that this condition is not satisfied for non-forward kinematics at leading order, and that gluon mediated re-interactions are essential for a consistent description in terms of parton degrees of freedom.
Transverse-momentum-dependent parton distributions (TMDs) provide three-dimensional images of the partonic structure of the nucleon in momentum space. We made impressive progress in understanding TMDs, both from the theoretical and experimental point of view. This brief overview on TMDs is divided in two parts: in the first, an essential list of achievements is presented. In the second, a selection of open questions is discussed.
The large-momentum effective theory (LaMET) framework has been widely used to determine the Bjorken-$x$ dependence of parton distribution functions (PDFs) in lattice-QCD hadron-structure calculations. In this proceeding, I highlighted selected recent lattice-QCD results on parton distributions from MSULat group. We use clover valence fermions on ensembles generated by MILC Collaboration with lattice spacing $a \approx 0.06$, 0.09, and 0.12 fm, with $M_πL \approx 4$, and with pion masses including 135, 220 and 310 MeV and $N_f=2+1+1$ flavors of highly improved staggered dynamical quarks. Result…
Initial state evolution in parton shower event generators involves parton distribution functions. We examine the probability for the system to evolve from a higher scale to a lower scale without an initial state splitting. A simple argument suggests that this probability, when multiplied by the ratio of the parton distributions at the two scales, should be independent of the parton distribution functions. We call this the PDF property. We examine whether the PDF property actually holds using Pythia and Deductor. We also test a related property for the Deductor shower and discuss the physics be…
When the initial state evolution of a parton shower is organized according to the standard "backward evolution'' prescription, ratios of parton distribution functions appear in the splitting probabilities. The shower thus organized evolves from a hard scale to a soft cutoff scale. At the end of the shower, one expects that only the parton distributions at the soft scale should affect the results. The other effects of the parton distributions should have cancelled. This means that the kernels for parton evolution should be related to the shower splitting functions. If the initial state partons …
We present main elements of the construction of unintegrated double parton distribution functions which depend on transverse momenta of partons. We follow the method proposed by Kimber, Martin and Ryskin for a construction of unintegrated single parton distributions from the standard parton distribution functions.
We investigate the relations between transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs) in a light-front quark-diquark model motivated by soft wall AdS/QCD. Many relations are found to have similar structure in different models. It is found that a relation between the Sivers function and the GPD $E_q$ can be obtained in this model in terms of a lensing function. The quark orbital angular momentum is calculated and the results are compared with the results in other similar models. Implications of the results are discussed. Relations among diffe…
The program to study the Generalized Parton Distributions in deeply virtual exclusive processes with CLAS at Jefferson Lab is discussed.
Parton recombination corrections to the standard spin-dependent Altarelli-Parisi evolution equation are considered in a nonlinear evolution equation. The properties of this recombination equation and its relation with the spin-averaged form are discussed.
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.
The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $ζ$, i.e. when the off-forwardness is purely transverse. For the $2^{nd}$ moment it is also illustrated how to relate $ζ\neq 0$ data to $ζ=0$ data, which is important for experimental measurements of these observables.
Several positivity bounds are derived for generalized parton distributions (GPDs) with helicity flip.
We consider double parton distributions in the general case in which the virtualities of the interacting partons are different. We elaborate the corresponding evolution equations and their extension to next-to-leading logarithmic accuracy.
We present a calculation of the generalized parton distributions of the photon using overlaps of photon light-front wave functions.
Applications of perturbative QCD to hard exclusive electroproduction processes in the Bjorken limit at small invariant momentum transfer t bring in a new type of parton distributions which have hybrid properties, resembling both the parton distribution functions and the distribution amplitudes. Their t-dependence is analogous to that of hadronic form factors. We discuss general properties of these new parton distributions, their relation to usual parton densities and the evolution equations which they satisfy.
Two-parton correlations in the pion are investigated in terms of double parton distribution functions. A Poincaré covariant Light-Front framework has been adopted. As non perturbative input, the pion wave function obtained within the so-called soft-wall AdS/QCD model has been used. Results show how novel dynamical information on the structure of the pion, not accessible through one-body parton distribution, are encoded in double parton distribution functions.
The non-perturbative parton distributions in hadrons are derived from simple physical arguments resulting in an analytical expression for the valence parton distributions. The sea partons arise mainly from pions in hadronic fluctuations. The model gives new insights and a good description of structure function data.
We present a study of the results obtained combining LO partonic matrix elements with different orders of partons distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have faults so a modified optimal LO set is suggested.
We propose a parametrization for the generalized parton distributions (GPDs) which is based on representation of parton distributions as an infinite series of t-channel exchanges. The entire generalized parton distribution is given as an infinite sum over contributions of generalized light-cone distribution amplitudes in the t-channel. We also discuss the relations of the lowest Mellin moments of GPDs to basic mechanical characteristics of the nucleon as a compound system.
The overlap representation of skewed parton distributions is discussed and applications to wide-angle Compton scattering and electroproduction of mesons are presented. The amplitudes for these processes factorise into parton-level subprocess amplitudes and form factors representing 1/x-moments of skewed parton distributions.
The basic properties of generalized parton distributions (GPDs) and some recent applications of GPDs are discussed
An integral representation for generalized parton distributions of spin-0 hadrons is suggested, which satisfies both polynomiality and positivity constraints.
In this brief Snowmass White Paper for the Theory Frontier, we argue that there have been important recent developments in the algorithms used to generate a simulated parton shower and that further progress can be achieved in the coming decade. A much more detailed exposition can be found in a corresponding White Paper of the Energy Frontier.
Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.
In this article, we review recent lattice calculations on the $x$-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of…
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