We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties lead to systematic biases. We develop a method which is unbiased, based on a self--consistent iterative procedure. We demonstrate the use of this method by applying it to the determination of parton distribution functions with the NNPDF methodology, which uses a Monte Carlo method for uncertainty estimation.
We propose a new approach for combining next-to-leading order (NLO) and parton shower (PS) calculations so as to obtain three core features: (a) applicability to general showers, as with the MCatNLO and POWHEG methods; (b) positive-weight events, as with the KrkNLO and POWHEG methods; and (c) all showering attributed to the parton shower code, as with the MCatNLO and KrkNLO methods. This is achieved by using multiplicative matching in phase space regions where the shower overestimates the matrix element and accumulative (additive) matching in regions where the shower underestimates the matrix …
Extracting parton distribution functions (PDFs) from lattice QCD calculation of quasi-PDFs has been actively pursued in recent years. We extend our proof of the multiplicative renormalizability of quasi-quark operators in Ref. [1] to quasi-gluon operators, and demonstrated that quasi-gluon operators could be multiplicatively renormalized to all orders in perturbation theory, without mixing with other operators. We find that using a gauge-invariant UV regulator is essential for achieving this proof. With the multiplicative renormalizability of both quasi-quark and quasi-gluon operators, and QCD…
We calculate the isosinglet unpolarized quark-- and antiquark distributions at a low normalization point in the large--$N_c$ limit. The nucleon is described as a self-consistent soliton solution of the effective chiral theory. The ultraviolet cutoff is implemented by a Pauli-Villars subtraction. The quark and antiquark distributions satisfy the momentum as well as the baryon number sum rule, corresponding to ``constituent'' quarks whose structure is not yet resolved at the low scale. Already at this level a sizable number of antiquarks is present.
At large N_c the nucleon can be viewed as a soliton of the effective chiral lagrangian. This picture of nucleons allows a consistent nonperturbative calculation of the leading-twist parton distributions at a low normalization point. We derive general formulae for the polarized and unpolarized distributions (singlet and non-singlet) in the chiral quark-soliton model. The consistency of our approach is demonstrated by checking the baryon number, isospin and total momentum sum rules, as well as the Bjorken sum rule. We present numerical estimates of the quark and antiquark distributions and find …
We review recent progress in calculating the twist--2 parton distribution functions at a low normalization point in the large--$N_c$ limit, where the nucleon can be described as a soliton of the effective chiral lagrangian. This field-theoretic approach preserves all general requirements on the distribution functions (positivity, normalization etc.). In particular, it allows to calculate the polarized and unpolarized antiquark distributions at the low normalization point.
The compatibility of neutrino-nucleus deep inelastic scattering data within the universal, factorizable nuclear parton distribution functions has been studied independently by several groups in the past few years. The conclusions are contradictory, ranging from a violation of the universality up to a good agreement, most of the controversy originating from the use of the neutrino-nucleus data from the NuTeV Collaboration. Here, we pay attention to non-negligible differences in the absolute normalization between different neutrino data sets. We find that such variations are large enough to prev…
Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula fo…
Numerical Study of MRW-Type Unintegrated Double Parton Distribution Functions from Non-Factorized DPDFs
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所粒子与加速器学院）；Department of Physics, University of Tehran（德黑兰大学物理系）；Department of Physics, Dogus University（多乌斯大学物理系）
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities is infinite. Several particular cases are considered explicitly.
Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasi parton distributions. Like a light-cone parton distribution, a quasi parton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of non-local operators in general is not well understood. However, in the case of quasi quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizabl…
We derive new positivity bounds on spin-dependent parton distributions in multicolored QCD. They are stronger than Soffer inequality. We check that the new inequalities are stable under one-loop DGLAP evolution to higher normalization points.
Positivity bounds for twist-two parton distributions in multicolored QCD are stronger than their analogs at finite $N_c$. They include the enhanced large $N_{c}$ version of Soffer inequality. These bounds are compatible with the DGLAP evolution to higher normalization points.
We evaluate the kinematic distributions in phase space of 4-parton final-state subprocesses produced by double parton scattering, and we contrast these with the final-state distributions that originate from conventional single parton scattering. Our goal is to establish the distinct topologies of events that arise from these two sources and to provide a methodology for experimental determination of the relative magnitude of the double parton and single parton contributions at Large Hadron Collider energies. We examine two cases in detail, the $b \bar{b} \rm{jet jet}$ and the 4 jet final states…
By extending the statistical distributions to the transverse degree of freedhom, we account for a multiplicative factor in the Fermi-Dirac functions of the light quarks, we were led to introduce in a previous work to comply with experiment. We can also get light antiquark distributions, similar to those we proposed earlier
Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations. However, unlike the parton distribution functions, the quasi-parton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. In this paper, we identify all sources of ultraviolet divergences for the quasi-parton distribution functions in coordinate-space, a…
Perturbative expansions for short-distance quantities in QCD are factorially divergent and this deficiency can be turned into a useful tool to investigate nonperturbative corrections. In this work, we use this approach to study the structure of power corrections to parton quasi-distributions and pseudo-distributions which appear in lattice calculations of parton distribution functions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-distributions on the Bjorken $x$ variable. We also show that these corrections can be strongly affected …
Generalized Parton Distributions of the pion are evaluated in chiral quark models with the help of double distributions. As a result the polynomiality conditions are automatically satisfied. In addition, positivity constraints, proper normalization and support, sum rules, and soft pion theorems are fulfilled. We obtain explicit expressions holding at the low-energy quark-model scale, which exhibit no factorization in the t-dependence. The crucial QCD evolution of the quark-model distributions is carried out up to experimental or lattice scales. The obtained results for the Parton Distribution …
We construct a model for inelastic neutrino- and electron-nucleon scattering cross sections using effective leading order parton distribution functions with a new scaling variable $ξ_w$. Non-perturbative effects are well described using the $ξ_w$ scaling variable, in combination with multiplicative $K$ factors at low $Q^2$.Our model describes all inelastic charged lepton-nucleon scattering (including resonance) data (HERA/NMC/BCDMS/SLAC/JLab) ranging from very high $Q^2$ to very low $Q^2$ and down to the photo-production region. The model describes existing inelastic neutrino-nucleon scatterin…
The unpolarized spin-flip isoscalar generalized parton distribution function (E^u+E^d)(x,xi,t) is studied in the large-Nc limit at a low normalization point in the framework of the chiral quark-soliton model. This is the first study of generalized parton distribution functions in this model, which appear only at the subleading order in the large-Nc limit. Particular emphasis is put therefore on the demonstration of the theoretical consistency of the approach. The forward limit of (E^u+E^d)(x,xi,t) of which only the first moment -- the anomalous isoscalar magnetic moment of the nucleon -- is kn…
The transversity Generalized Parton Distributions (tGPDs) and related transversity form factors of the pion are evaluated in chiral quark models, both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent quark mass. The obtained tGPDs satisfy all a priori formal requirements, such as the proper support, normalization, and polynomiality. We evaluate generalized transversity form factors accessible from the recent lattice QCD calculations. These form factors, after the necessary QCD evolution, agree very well with the lattice data, confirming the fact that the spontaneously b…
We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules and soft pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale…
We present a new global QCD analysis of parton distribution functions, allowing for possible intrinsic charm (IC) contributions in the nucleon inspired by light-front models. The analysis makes use of the full range of available high-energy scattering data for Q^2 > 1 GeV^2 and W^2 > 3.5 GeV^2, including fixed-target proton and deuteron cross sections at lower energies that were excluded in previous global analyses. The expanded data set places more stringent constraints on the momentum carried by IC, with <x>_IC at most 0.5% (corresponding to an IC normalization of ~ 1%) at the 4-sigma level …
We reexamine the dominant contribution of parton distribution function (PDF) uncertainties to the W mass measurement, and determine their contribution is +-39(30) MeV when running the Large Hadron Collider at 7(13) TeV. We find that spurious correlations in older PDF sets led to over-optimistic assumptions regarding normalization to Z observables. In order to understand the origin of the large uncertainties we break down the contribution of the PDF errors into effects at the hard matrix element level, in showering, and in sensitivity to finite detector resolutions. Using CT10, CT10W, and charm…
We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the four-particle nucleon WFs involving three valence quarks and a gluon with total orbital momentum zero, and estimate their normalization (WF at the origin) using QCD sum rules. We demonstrate that these WFs provide one with a reasonable description of both polarized and unpolarized gluon parton densities at large values of Bjorken variable x > 0.5. Twist-three parton di…
Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and 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 quasi-quark distribution introduced by Ji [1] as a case study to show that it could be factorized into the PDFs to all ord…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology: NNPDF2.0. Experimental data include deep-inelastic scattering with the combined HERA-I dataset, fixed target Drell-Yan production, collider weak boson production and inclusive jet production. Next-to-leading order QCD is used throughout without resorting to K-factors. We present and utilize an improved fast algorithm for the solution of evolution equations and the computation of general hadronic processes. We introduce improved techniques for the training…
We present an antenna-shower formalism that includes helicity dependence for massless partons. The formalism applies to both traditional (global) showers and to sector-based variants. We combine the shower with VINCIA's multiplicative approach to matrix-element matching, generalized to operate on each helicity configuration separately. The result is a substantial gain in computational speed for high parton multiplicities. We present an implementation of both sector and global showers, with min and max variations, and helicity-dependent tree-level matching applied for vector bosons or Higgs dec…
We investigate the parton-distribution functions (PDFs) for the positively charged pion and kaon at a low-renormalization scale ~ 1 GeV. To this end, we employ the gauge-invariant effective chiral action from the nonlocal chiral-quark model, resulting in that the vector currents are conserved. All the model parameters are determined phenomenologically with the normalization condition for PDF and the empirical values for the pseudoscalar-meson weak-decay constants. We consider the momentum dependence of the effective quark mass properly within the model calculations. It turns out that the leadi…
We study the proposal by Kharzeev-Levin to determine entanglement entropy in Deep Inelastic Scattering (DIS) from parton distribution functions (PDFs) and to relate the former to the entropy of final state hadrons. We find several uncertainties in the current comparison to data, in particular the overall normalization, the relation between charged versus total hadron multiplicity in the comparison to experimental results as well as different methods to determine the number of partons in Deep Inelastic Scattering. We further provide a comparison to data based on leading order HERA PDF as well a…
We report a parton distribution function (PDF) analysis of a complete set of hadron scattering data, in which a color-octet fermion (such as a gluino of supersymmetry) is incorporated as an extra parton constituent along with the usual standard model constituents. The data set includes the most up-to-date results from deep-inelastic scattering and from jet production in hadron collisions. Another feature is the inclusion in the fit of data from determinations of the strong coupling alpha_s(Q) at large and small values of the hard scale Q. Our motivation is to determine the extent to which the …
We present an improved leading-order global DGLAP analysis of nuclear parton distribution functions (nPDFs), supplementing the traditionally used data from deep inelastic lepton-nucleus scattering and Drell-Yan dilepton production in proton-nucleus collisions, with inclusive high-$p_T$ hadron production data measured at RHIC in d+Au collisions. With the help of an extended definition of the $χ^2$ function, we now can more efficiently exploit the constraints the different data sets offer, for gluon shadowing in particular, and account for the overall data normalization uncertainties during the …
The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1 fm. These short-distance interactions influence the intrinsic transverse momentum distributions of partons and their correlations at a low normalization point. We study this phenomenon in an effective description of low-energy dynamics based on chiral constituent quark degrees of freedom, which refers to the large-N_c limit of QCD. The nucleon is obtained as a system of constituent quarks and antiquarks moving in a self-consistent classic…
Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses
At a low resolution scale with $Q^2=μ^2$ corresponding to the nucleon bound state; deep inelastic unpolarized structure functions $F_1(x,μ^2)$ and $F_2(x,μ^2)$ are derived with correct support using the symmetric part of the hadronic tensor under some simplifying assumptions in the Bjorken limit. For doing this; the nucleon in its ground state has been represented by a suitably constructed momentum wave packet of its valence quarks in their appropriate SU(6) spin flavor configuration with the momentum probability amplitude taken phenomenologically in reference to the independent quark model of…
We determine the spatial (impact parameter) dependence of nuclear parton distribution functions (nPDFs) using the $A$-dependence of the spatially independent (averaged) global fits EPS09 and EKS98. We work under the assumption that the spatial dependence can be formulated as a power series of the nuclear thickness functions $T_A$. To reproduce the $A$-dependence over the entire $x$ range we need terms up to $[T_A]^4$. As an outcome, we release two sets, EPS09s (LO, NLO, error sets) and EKS98s, of spatially dependent nPDFs for public use. We also discuss the implementation of these into the exi…
We firstly examine hadroproduction of prompt J/psi's at the Fermilab Tevatron in a Monte Carlo Framework by means of the event generator PYTHIA 5.7 in which those colour-octet matrix elements processes relevant for charmonium production have been implemented accordingly. We find that colour-octet matrix elements presented in literature from p-pbar collider data are systematically overestimated due to overlooking of the effective primordial transverse momentum of partons (i.e. including higher-order QCD effects). We estimate the size of these effects using different parton distribution function…
We extract the leading Fock-state light front wave functions (LF-LFWFs) of both the light and heavy pseudoscalar mesons, e.g., the pion (at masses of 130 MeV, 310 MeV and 690 MeV), $η_c$ and $η_b$, from their covariant Bethe-Salpeter wave functions within the rainbow-ladder (RL) truncation. It is shown that the LF-LFWFs get narrower in $x$ (the longitudinal momentum fraction of meson carried by the quark) with the increasing current quark mass, and the leading twist parton distribution amplitudes (PDAs) inherit this feature. Meanwhile, we find in the pion the LF-LFWFs only contribute around 30…
We present an intuitive, light front reduction scheme for the Bethe-Salpeter equation that consists of iterations of the (light front) energy dependent covariant equation followed by an instantaneous approximation. This scheme is equivalent to and motivates the form of a standard reduction that reproduces light front, time ordered perturbation theory for bound states. We use this three-dimensional light front formalism to compute electromagnetic form factors between bound states to show how higher, light front Fock components arise from the covariant Bethe-Salpeter wave function. Moreover, we …
We extract diffractive parton densities from diffractive, deep inelastic (DIS) ep data from the ZEUS experiment. Then we use these fits to predict the diffractive production of jets and of W's and Z's in p\bar p collisions at the Tevatron. Although the DIS data require a hard quark density in the pomeron, we find fairly low rates for the Tevatron processes (a few percent of the inclusive cross section). This results from the combined effects of Q^{2} evolution and of a normalization of the parton densities to the data. The calculated rates for W production are generally consistent with the pre…
The isosinglet unpolarized and isovector polarized twist-2 quark distributions of the nucleon at low normalization point are calculated in the large-Nc limit. The nucleon is described as a soliton of the effective chiral theory. We derive the expressions for the distribution functions in the large-Nc limit starting from their definition as numbers of partons carrying momentum fraction x in the infinite momentum frame. We develop a numerical method for computation of the quark and antiquark distributions as sums over the quark single-particle levels in the pion field of the soliton. The contrib…
We present the first attempt to extract the "$x$" dependence of the parton distribution function (PDF) of the quark gluon plasma (QGP). In the absence of knowledge regarding the mass of a QGP constituent, we define the new variable $x_N$, the nucleonic momentum fraction, which represents the ratio of the momentum of the parton to that of a self-contained section of the plasma that has the mass of a nucleon. Calculations are compared to data for single hadron suppression in terms of the nuclear modification factor $R_{AA}$ and the azimuthal anisotropy parameter $v_{2}$, as a function of transve…
In the framework of Color Glass Condensate, the pseudo-rapidity distributions of charged hadrons in pp and pA collisions at the LHC are studied with the UGD function from the GBW model. With a $χ^{2}$ analysis of the CMS data in pp collisions at $\sqrt{s}=0.9,~2.36,~7$ TeV, the normalization factor is obtained and the theoretical results are in good agreement with the perimental data. Then, considering the influence of nucleon hard partons distribution on the number of participants in pA collisions by a Glauber Monte Carlo method, we give the predictive results for the multiplicity distributio…
Recent analyses suggest that in TeV scales that will be made accessible at the LHC copious amounts of color scalar parton bound states may be produced. Would this be the case, the scalars would leave long enough to interact and this could lead to new physics. These interaction could be direct, but also take place with a mediation of the dense parton medium through which they propagate. Since multiple processes would have to be included, the latter case is too convoluted to be treated with perturbative methods applied to the Standard Model. We explore a possibility of describing such interactio…
