Fourier transform of the generalized parton distributions (GPDs) at zero skewness with respect to the transverse momentum transfer gives the distribution of partons in the impact parameter space. We investigate the GPDs as well as the impact parameter dependent parton distributions (ipdpdfs) by expressing them in terms of overlaps of light front wave functions (LFWFs) and present a comparative study using three different model LFWFs.
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.
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.
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.
We apply the phenomenological Reggeon Field Theory framework to investigate the relative importance of perturbative and nonperturbative multiparton correlations for the treatment of double parton scattering (DPS) in proton-proton collisions. We obtain a significant correction to the so-called effective cross section for DPS due to nonperturbative parton splitting. When combined with the corresponding perturbative contribution, this results in a rather weak energy and transverse momentum dependence of the effective cross section, in agreement with experimental observations at the Tevatron and t…
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.
We study generalized parton distributions in the impact parameter representation, including the case of nonzero skewness xi. Using Lorentz invariance, and expressing parton distributions in terms of impact parameter dependent wave functions, we investigate in which way they simultaneously describe longitudinal and transverse structure of a fast moving hadron. We compare this information with the one in elastic form factors, in ordinary and in k_T dependent parton distributions.
Generalized parton distributions (GPDs) with purely transverse momentum transfer can be interpreted as Fourier transforms of the distribution of partons in impact parameter space. The helicity-flip GPD $E(x,0,-\Dps)$ is related to the distortion of parton distribution functions in impact parameter space if the target is not a helicity eigenstate, but has some transverse polarization. This transverse distortion can be used to develop an intuitive explanation for various transverse single spin asymmetries.
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.
The Fourier transform of generalized parton distribution functions at xi=0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to the impact parameter distribution of unpolarized quarks for an unpolarized nucleon, H-tilde is related to the distribution of longitudinally polarized quarks in a lon…
We investigate the effect of large-x resummation on parton distributions by performing a fit of Deep Inelastic Scattering data from the NuTeV, BCDMS and NMC collaborations, using NLO and NLL soft-resummed coefficient functions. Our results show that soft resummation has a visible impact on quark densities at large x. Resummed parton fits would therefore be needed whenever high precision is required for cross sections evaluated near partonic threshold.
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We take an effective two-body spin-1/2 state, namely an electron dressed with a photon in QED. We express the impact parameter dependent parton distributions in terms of overlaps of light-cone wave functions. We obtain the scale dependence of both fermion and gauge boson distributions and show the distortion of the pdfs in the transverse space for transverse polarization of the state at one loop level.
Recently, it has been pointed out that there exists a connection between the generalized parton distribution $E(x,0,t)$ and the Sivers asymmetry. For transversely polarized nucleon targets, generalized parton distributions are asymmetric in impact parameter space. This impact parameter space asymmetry, together with the final state interaction of the active quark, gives rise to the Sivers asymmetry in momentum space. We demonstrate this phenomenon explicitly in the scalar diquark model. This result also illustrates the physics that underlies the correlation between the anomalous magnetic momen…
Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark is transversely polarized. In combination with the final state interactions, this transverse deformation provides a natural mechanism for naive-T odd transverse single-spin asymmetries in semi-inclusive DIS. The deformation can also be related to the transverse force acting on the active quark in polarized DIS at higher twist.
We consider impact parameter dependence of the polarized and unpolarized parton densities. Unitarity does not allow factorization of these structure functions over the Bjorken x and the impact parameter b variables. On the basis of the particular geometrical model approach we conclude that spin of constituent quark may have a significant orbital angular momentum component which can manifest itself through the peripherality of the spin dependent structure functions.
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We express them in terms of overlaps of light-cone wave functions for a self consistent two-body spin-1/2 state, namely an electron dressed with a photon in QED. The pdfs are distorted in the transverse space for transverse polarization of the state at one loop level.
New data sets have recently become available for neutrino and antineutrino deep inelastic scattering on nuclear targets and for inclusive dimuon production in pp pd interactions. These data sets are sensitive to different combinations of parton distribution functions in the large-x region and, therefore, provide different constraints when incorporated into global parton distribution function fits. We compare and contrast the effects of these new data on parton distribution fits, with special emphasis on the effects at large x. The effects of the use of nuclear targets in the neutrino and antin…
We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. The light-front wave function (LFWF) of this system gives a template for the quark spin-one diquark structure of the valence LFWF of the proton. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.
We investigate the generalized parton distributions (GPDs) with non-zero $ξ$ and $Δ^\perp$ for a relativistic spin-1/2 composite system, namely for an electron dressed with a photon, in light-front framework by expressing them in terms of overlaps of light-cone wave functions. The wave function provides a template for the quark spin-one diquark structure of the valence light cone wave function of the proton. We verify the inequalities among the GPDs with different helicities and show the qualitative behaviour of the fermion and gauge boson GPDs in the impact parameter space.
In the present work we have studied the chiral odd Generalized Parton Distributions (GPDs) in the impact parameter space by assuming a flexible parametrization in a quark-diquark model. In order to obtain the explicit contributions from the up and down quarks, we have considered both the scalar (spin-0) and the axial-vector (spin-1) configurations for the diquark. We have also studied the spin densities for the up and down quarks in this model for monopole, dipole and quadrupole contributions for unpolarized and polarized quarks in unpolarized and polarized proton.
In this paper we discuss the impact of the Double Parton Scattering (DPS) mechanism for the production of $J/ψ$ pairs at the COMPASS energy. We find that the kinematics suppresses the DPS cross section by a factor of $\sim1/2$. The upper limit for the double $J/ψ$ production DPS cross section at the COMPASS energy is estimated. The Feynman-$x$ distributions of double $J/ψ$ production with the CERN $π^-$ beam are presented.
A model for the parton distributions of hadrons in impact parameter space has been constructed using soft gluon summation. This model incorporates the salient features of distributions obtained from the intrinsic transverse momentum behaviour of hadrons. Under the assumption that the intrinsic behaviour is dominated by soft gluon emission stimulated by the scattering process, the b-spectrum becomes softer and softer as the scattering energy increases. In minijet models for the inclusive cross-sections, this will counter the increase from $σ_{jet}$ .
Realistic modeling of medium-jet interactions in heavy ion collisions is becoming increasingly important to successfully predict jet structure and shape observables. In JEWEL, all partons belonging to the parton showers initiated by hard scattered partons undergo collisions with thermal partons from the medium, leading to both elastic and radiative energy loss. The recoiling medium partons carry away energy and momentum from the jet. Since the thermal component of these recoils' momenta is part of the soft background activity, comparison with data requires the implementation of a subtraction p…
The high precision and large kinematic coverage of the data from the HERA-I running period (1994-2000) have already allowed precise extractions of proton parton distribution functions. The HERA-II running program is now underway and is expected to provide a substantial increase in the luminosity collected at HERA. In this paper, a study is presented which investigates the potential impact of future HERA data on the proton PDF uncertainties, within the currently planned running scenario. Next-to-leading order QCD predictions for inclusive jet cross sections at the LHC centre-of-mass energy are …
The level of precision achieved by the experimental measurements at the LHC requires the inclusion of higher order electroweak effects to the processes of $ pp $ scattering. In particular the photon-induced process $ γγ\to \ell^+\ell^- $ make a significant contribution ($ \sim 10 \%$) to the dilepton invariant mass distribution. To evaluate the cross-section of this process one need to know the parton distribution function (PDF) of the photon in the proton $ γ(x,μ^2) $. The aim of the current study is to investigate the impact of QED corrections on PDFs and describe the implementation of QED-m…
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.
In this talk we discuss recent results on the impact of LHC jet data on global fits of parton distribution functions using theoretical predictions at NNLO in QCD supplemented by electroweak (EW) corrections.
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.
Electroweak corrections to hadron collider processes become relevant at the level of precision reached by present-day LHC experiments. We provide a preliminary discussion of the impact of electroweak corrections to parton distributions, concentrating on electrodynamics corrections to parton evolution equations, and showing a preliminary assessment of their impact. Furthermore, we determine the parton distribution function of the photon from deep inelastic scattering data using the NNPDF methodology.
In this work, the impact of recent measurements of heavy-flavour production in $pp$ collisions on parton distribution functions (PDFs) and their uncertainties is studied. In this regard, the absolute and normalised cross sections of beauty hadron production measured by LHCb at center-of-mass energy of 7 TeV and 13 TeV are separately included in the next-to-leading order (NLO) global QCD analysis together with the measurements of the inclusive and heavy-flavour production cross sections at HERA. It is illustrated that the heavy-flavour data of the LHCb experiment impose additional constraints o…
I study the impact of recent measurements performed at the Relativistic Heavy Ion Collider on the determination of helicity-dependent parton distribution functions of the proton. Specifically, I consider: preliminary data on longitudinally single-spin asymmetries for $W$-boson production recorded by the STAR experiment during the 2013 run at a center-of-mass energy $\sqrt{s}=510$ GeV; data on longitudinally double-spin asymmetries for di-jet production recorded by the STAR experiment during the 2009 run at $\sqrt{s}=200$ GeV; and data on longitudinally double-spin asymmetries for neutral pion …
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.
In this work, we present a new investigation about the impact of intrinsic charm (IC) on the physical observables, in particular, on the heavy structure function $F_2^c$. Since IC distribution is dominant at large Bjorken variable $x$, normally, it is expected that it can be explored only at large $x$. But, by studying the correlation of the charm density in the proton with $F_2^c$, we are going to show that the IC component can also be effective at low $x$. To investigate further, we perform three QCD global analyses of parton distribution functions (PDFs), by including the EMC $F_2^c$ data t…
Recent measurements of top quark pair production cross section, which is performed at the LHC and the Tevatron collider, are studied using Hessian profiling technique to obtain their impact on the parton distribution functions (PDFs). The top quark production data covers different center-of-mass energies $\sqrt{s}$= 1.96, 5.02, 7, 8 and 13 TeV in either $pp$ or $p\bar{p}$ collisions. It is explained how the Hessian profiling method may be used to assess the impact of these new data on PDFs and consequently on their predictions. In this research, the impact of recent measurements of top quark p…
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 …
Elastic nucleon form factors constrain the spatial distribution of quarks in the impact parameter plane. A recent analysis found that the average impact parameter of quarks strongly depends on their longitudinal momentum, and obtained an estimate of the orbital angular momentum carried by valence quarks in the proton.
In these proceedings we present three possible interpretations of the ordering variable implemented in the Herwig7 angular-ordered parton shower. Each interpretation determines a different recoil-scheme prescription and we show how it can impact the logarithmic accuracy of the algorithm. We also present comparisons with LEP data.
Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when target and/or quark are transversely polarized. In combination with the final state interactions, this transverse deformation provides a natural mechanism for naive-T odd transverse single-spin asymmetries in semi-inclusive DIS. The deformation of PDFs in impact parameter space can also be related to the transverse force acting on the active quark in polarized DIS at higher twist.
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…
Heavy quark parton distribution functions (PDFs) play an important role in several Standard Model and New Physics processes. Most analyses rely on the assumption that the charm and bottom PDFs are generated perturbatively by gluon splitting and do not involve any non-perturbative degrees of freedom. On the other hand, non- perturbative, intrinsic heavy quark parton distributions have been predicted in the literature. We demonstrate that to a very good approximation the scale-evolution of the intrinsic heavy quark content of the nucleon is governed by non-singlet evolution equations. This allow…
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.
We study the potential of the LHCb 13 TeV single $W^{\pm}$ and $Z$ boson pseudo-data for constraining the parton distribution functions (PDFs) of the proton. As an example, we demonstrate the sensitivity of the LHCb 13 TeV data, collected with integrated luminosities of 5 fb$^{-1}$ and 300 fb$^{-1}$, to reducing the PDF uncertainty bands of the CT14HERA2 PDFs, using the error PDF updating package {\sc ePump}. The sensitivities of various experimental observables are compared. Generally, sizable reductions in PDF uncertainties can be observed in the 300 fb$^{-1}$ data sample, particularly in th…
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…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology including heavy quark mass effects: NNPDF2.1. In comparison to the previous NNPDF2.0 parton determination, the dataset is enlarged to include deep--inelastic charm structure function data. We implement the FONLL-A general-mass scheme in the FastKernel framework and assess its accuracy by comparison to the Les Houches heavy quark benchmarks. We discuss the impact on parton distributions of the treatment of the heavy quark masses, and we provide a determinat…
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.
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.
