9 pages, 7 figures, 2 tables, invited talk given at Ringberg Workshop: New Trends in HERA Physics 2008, Ringberg Castle, Tegernsee, Germany, 5-10 October 2008
Recent measurements for F_2(x,Q^2) have been analyzed in terms of the `dynamical' and `standard' parton model approach at NLO and NNLO of perturbative QCD. Having fixed the relevant NLO and NNLO parton distributions, the implications and predictions for the longitudinal structure function F_L(x,Q^2) are presented. It is shown that the previously noted extreme perturbative NNLO/NLO instability of F_L(x,Q^2) is an artifact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 \geq O(2-3 GeV^2).
The basic concepts and predictions of the `dynamical' GRV parton distributions for hadrons and photons are discussed. Comparisons of these predictions with recent experimental results, especially from HERA, are presented.
The idea of ``dynamically'' generated parton distribution functions, based on regular initial conditions at low momentum scale, is reanalyzed with particular emphasize paid to its compatibility with the factorization mechanism. Basic consequences of this approach are discussed and compared to those of the conventional approach, employing singular initial distribution functions.
Precise determinations of the strong coupling constant in hadronic collisions demand sets of parton densities spanning a sufficiently wide range of values for the QCD scale parameter Lambda. For such applications, we supplement the recent GRV parametrization by five sets of dynamically generated parton distributions for Lambda-values corresponding to alpha_{S}(M_{Z}^{2}) between 0.104 and 0.122. Present DIS data, including recent small-x HERA results, do not appreciably discriminate between these sets.
Utilizing recent neutrino dimuon production measurement from NuTeV the assumptions on the determination of the strangeness content of the nucleon within the dynamical approach to parton distributions are investigated. The data are found to be in good agreement with the predictions derived from our (GJR08) dynamical parton distributions, which have been generated entirely radiatively starting from vanishing strange input distributions at an optimally chosen low resolution scale. Further, the data induce an asymmetry in the strange sea which is found to be small and positive in agreement with pr…
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.
A new generation of (unpolarized) dynamical parton distribution functions of the nucleon is determined. After introducing basic elements of perturbative QCD, the dynamical model is discussed and compared with the approach to parton distributions used by most other groups ("standard"). Parton distributions sets (with uncertainties) at different orders (LO, NLO, NNLO), using different factorization schemes (\overline{MS}, DIS) and different treatments of heavy quark masses (FFNS, VFNS) are extracted and compared. The astrophysical implications of the dynamical predictions are outlined before foc…
Dynamical parton densities, generated radiatively from valence-like inputs at some low resolution scale, are confronted with recent small-x data on deep inelastic and other hard scattering processes. It is shown that within theoretical uncertainties our previous (1994) dynamical/radiative parton distributions are compatible with most recent data and still applicable within the restricted accuracy margins of the presently available next-to-leading order calculations. Due to recent high precision measurements we also present an updated, more accurate, version of our (valence-like) dynamical inpu…
We suggest a duality between the standard (dynamical) and statistical distributions of partons in the nucleons. The temperature parameter entering into the statistical form for the quark distributions is estimated. It is found that this effective temperature is practically the same for the dependence on longitudinal and transverse momenta and, in turn, it is close to the freeze-out temperature in high energy heavy-ion collisions.
It is shown that the previously noted extreme perturbative NNLO/NLO instability of the longitudinal structure function F_L(x,Q^2) is a mere artefact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).
Utilizing recent DIS measurements (F_{2,L}) and data on dilepton and high-E_{T} jet production we determine the dynamical parton distributions of the nucleon generated radiatively from valence-like positive input distributions at optimally chosen low resolution scales. These are compared with `standard' distributions generated from positive input distributions at some fixed and higher resolution scale. It is shown that up to the next to leading order NLO(\bar{MS}, DIS) of perturbative QCD considered in this paper, the uncertainties of the dynamical distributions are, as expected, smaller than …
The dynamical parton distributions of the nucleon are generated radiatively from positive definite (valencelike) input distributions at an optimally chosen low resolution scale (Q_0^2 < 1 GeV^2). For the strange distribution in particular, it has been assumed that vanishing strange input distributions at this low scale is an appropriate choice. By confronting predictions derived from our (GJR08) NLO dynamical parton distributions with recent neutrino dimuon production measurement from NuTeV we show that this is indeed the case, and that little improvement is achieved by using a more general an…
It is shown that the previously noted extreme perturbative instability of the longitudinal structure function F_L(x,Q^2) in the small Bjorken-$x$ region, is a mere artefact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).
The consequences of a flavor broken SU(3)_f dynamical parton model are studied in the context of the elastic scattering of supersymmetric dark matter off nucleons. It is shown that the predictions of this model differ considerably from those of the commonly applied `standard' parton model. Some notable properties of the dynamical parton model are finally presented and discussed.
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.
Determination of proton parton distribution functions is present under the dynamical parton model assumption by applying DGLAP equations with GLR-MQ-ZRS corrections. We provide two data sets, referred as IMParton16, which are from two different nonperturbative inputs. One is the naive input of three valence quarks and the other is the input of three valence quarks with flavor-asymmetric sea components. Basically, both data sets are compatible with the experimental measurements at high scale ($Q^2>2$ GeV$^2$). Furthermore, our analysis shows that the input with flavor-asymmetric sea components …
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.
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.
Dynamical gluon effects in proton transversity and off-forward parton distributions from a light-front Hamiltonian approach
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Iowa State University（爱荷华州立大学）
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.
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 determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2<1 GeV^2) by employing the "fixed flavor number factorization scheme" (FFNS). These are compared with "standard" NNLO distributions, generated at some fixed and higher resolution scale (Q_0^2>1 GeV^2). The NNLO corrections imply in both approaches an improved value of χ^2, typically χ^2_{NNLO} \sim 0.9χ^2_{NLO}. The dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both …
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 derive new Lorentz Invariance and Equation of Motion Relations between twist-three Generalized Parton Distributions (GPDs) and moments in the parton transverse momentum, $k_T$, of twist-two Generalized Transverse Momentum-Dependent Distributions (GTMDs), as a function of the parton longitudinal momentum fraction $x$. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connec…
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.
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…
Based on parametric reasoning, we provide a simple dynamical picture of how a perturbative parton cascade, in interaction with a QCD medium, fills phase space as a function of time.
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.
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.
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 determine the time evolution of the colour screening mass in high energy nuclear collisions, as provided by the parton cascade model. Using our result, we discuss the onset of deconfinement and the onset of quarkonium suppression in a general, not necessarily equilibrated environment of strongly interacting constituents.
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.
An integral representation for generalized parton distributions of spin-0 hadrons is suggested, which satisfies both polynomiality and positivity constraints.
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%.
For an unpolarized target, the generalized parton distribution $H_q(x,0,t)$ is related to the distribution of partons in impact parameter space. The transverse distortion of this distribution for a transversely polarized target is described by $E_q(x,0,t)$.
Positivity constraints are derived for the generalized parton distributions (GPDs) of spin-1/2 hadrons. The analysis covers the full set of eight twist-2 GPDs. Several new inequalities are obtained which constrain GPDs by various combinations of usual (forward) unpolarized and polarized parton distributions including the transversity distribution.
We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely-polarizedproton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally-polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter is shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.
Recent CDF measurements of the inclusive cross section for a double parton scattering attach a great importance to any theoretical calculations of two-particle distribution functions. Using a parton interpretation of the leading logarithm diagrams of perturbative QCD theory, generalized Lipatov-Altarelli-Parisi-Dokshitzer equations for the two-parton distributions are re-obtained. The solutions of these equations are not at all the product of two single-parton distributions what is usually applied to the current analysis as ansatz.
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.
We review Shuvaev's transformations, that relate off-forward parton distributions (OFPDs) to so-called effective forward parton distributions (EFPDs). The latter evolve like conventional forward partons. We express nonforward amplitudes, depending on OFPDs, directly in terms of EFPDs and construct a model for the EFPDs, which allows to consistently express them in terms of the conventional forward parton distributions and nucleon form factors. Our model is self-consistent for arbitrary x, xi, mu, and t.
We present the polarized parton distribution functions from a QCD analysis of the worldwide polarized deep inelastic scattering data, based on the dynamical parton distribution model. All the sea quarks and gluons are dynamically generated from QCD radiations, with the nonperturbative input contains only the polarized valence quark distributions. This approach leads to a simple parametrization, which has only four free parameters. In the analysis, we apply the DGLAP equations with parton-parton recombination corrections. The parameterized nonperturbative input at an extremely low $Q_0^2$ repro…
