We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions in addition to the leading twist-2 ones by investigating all the possible decomposition of a quark correlation function in the Lorentz-invariant way. The Hermiticity and parity invariance are imposed in the decomposition; however, the time-reversal invariance is not used due to an active role of gauge links in the TMDs. Therefore, there exist time-reversal-odd functions in addition to the time-reversal even ones in the TMDs. We list all the functions up to twist-4 level because there were missing terms associated with the lightcone vector $n$ in previous works on the twist-2 part and there was no correlation-function study in the twist-3 and 4 parts for spin-1 hadrons. We show that 40 TMDs exist in the tensor-polarized spin-1 hadron in twists 2, 3, and 4. Some expressions of twist-2 structure functions are modified from previous derivations due to the new terms with $n$, and we find 30 new structure functions in twists 3 and 4 in this work. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtain new sum rules for the time-reversal-odd structure functions, $ \int d^2 k_T h_{LT}= \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0$. In addition, we indicate that new transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs are rare observables to find explicit color degrees of freedom in terms of color flow, which cannot be usually measured because the color is confined in hadrons.
Sum rules for structure functions and their twist-2 relations have important roles in constraining their magnitudes and $x$ dependencies and in studying higher-twist effects. The Wandzura-Wilczek (WW) relation and the Burkhardt-Cottingham (BC) sum rule are such examples for the polarized structure functions $g_1$ and $g_2$. Recently, new twist-3 and twist-4 parton distribution functions were proposed for spin-1 hadrons, so that it became possible to investigate spin-1 structure functions including higher-twist ones. We show in this work that an analogous twist-2 relation and a sum rule exist f…
Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist 3 and twist 4 in addition to the twist-2 ones, so that full investigations became possible for structure functions of spin-1 hadrons in the same level with those of the spin-1/2 nucleons. Furthermore, twist-3 tensor-polarized multiparton distribution functions were also recently found for spin-1 hadrons. In this work, we show relations among the collinear pa…
While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured …
We study the effect of parton angular momentum on the twist-four correction to the left-right asymmetry in the electron-deuteron parity-violating deep inelastic scattering (PVDIS). We show that this higher-twist correction is transparent to the dynamics of parton angular momentum needed to account for the Sivers and Boer-Mulders functions and spin-independent parton distribution functions. A sufficiently precise measurement of the PVDIS asymmetry may, thus, provide additional information about the parton dynamics responsible for nucleon spin.
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.
Precise measurements of polarized electro-production and Drell-Yan in the deep inelastic limit will soon provide first information on the higher twist parton distributions $g_T(x)$ and $h_L(x)$. Sum rules for higher-twist structure functions are only valid provided the corresponding Compton amplitudes satisfy un-subtracted dispersion relations. Subtracted dispersion relations have to be used when the (real part of the) forward scattering amplitudes does not fall off rapidly enough for $ν\rightarrow \infty$ (fixed $Q^2$). Formally, such subtractions lead to $δ$-functions at the origin in the pa…
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. On the basis of renormalization-group improved parton description and quantum-kinetic theory, it uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme that is governed by the dynamics itself. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densitie…
The path-integral formulation of the hadronic tensor W_{μν} of deep inelastic scattering is reviewed. It is shown that there are 3 gauge invariant and topologically distinct contributions. The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion. We shall discuss numerical issues associated with lattice calculation of th…
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme, as well as the development of hadron cascades after hadronization. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons…
Different methods to extract the polarized parton densities from the world polarized DIS data are considered. The higher twist corrections $h^N(x)/Q^2$ to the spin dependent proton and neutron $g_1$ structure functions are found to be non-negligible and important in the QCD analysis of the present experimental data. Their role in determining the polarized parton densities in the framework of the different approaches is discussed.
We discuss the inclusive high-pT charged-particle production in proton-proton collisions at the LHC. The experimental data are compared to the NLO perturbative QCD calculations employing various sets of parton-to-hadron fragmentation functions. Most of the theoretical predictions are found to disastrously overpredict the measured cross sections, even if the scale variations and PDF errors are accounted for. The problem appears to arise from the presently too hard gluon-to-hadron fragmentation functions.
$SU(N_c)$ colour-singlet restriction, along with flavour and spin symmetry, on thermal partonic ensemble is shown to recombine the partons with internal colour structure into colour-singlet multi-quark clusters which can be identified with various hadronic modes at a given temperature. This provides a possible basis for recombination model for hadronization of quark-gluon plasma. This also leads to a natural explanation for the ratio of (anti)protons to pions and the quark number scaling of the elliptic flow coefficient in relativistic heavy-ion collisions.
We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $ΔG_T(x)$, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functi…
We discuss hadron-tomography studies for the nucleon and exotic hadrons by high-energy hadron reactions. First, the constituent-counting rule is explained for determining internal quark configurations of exotic-hadron candidates by scaling properties of high-energy exclusive cross sections. Next, possibilities are discussed for investigating the generalized parton distributions (GPDs) of the nucleon and exotic hadrons at J-PARC. In particular, we study hadronic $2 \to 3$ process $p+p \to N+π+B$, exclusive Drell-Yan process, and exotic-hadron GPDs. For determining three-dimensional structure of…
Twist-3 partonic distributions contain important information that characterizes nucleon's structure. In this work, we show our lattice exploration of the twist-3 PDFs $g_T(x)$, and $h_L(x)$. We also present our preliminary results on the twist-3 GPD $\tilde{G}_2(x)$. We use the quasi-distribution approach to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that we developed in parallel. We also calculate the twist-2 counterparts of $g_T(x)$ and $h_L(x)$, i.e. $g_1(x)$, and $h_1(x)$, and test the Wandz…
We define in the framework of light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the $π^0$) up to twist 6. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 28 real GPDs, which are subject to constraints coming from the QCD equations of motion.
The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD approach is applied to nucleus-nucleus collisions from low SPS to LHC energies. The traces of partonic interactions are found in particular in the elliptic flow of hadrons and in their transverse mass spectra. We investigate also the equilibrium properties of strongly-interacting infinite parton-hadro…
Within the framework of the generalized factorization in pQCD, we investigate the multiple parton scattering and induced parton energy loss at twist-6 in deeply inelastic e-A scattering with the helicity amplitude approximation. It is shown that twist-6 processes will give rise to additional nuclear size dependence of the parton energy loss due to LPM interference effect while its contribution is power suppressed.
The genuine twist-3 quark-gluon contributions to the Generalized Parton Distributions (GPDs) are estimated in the model of the instanton vacuum. These twist-3 effects are found to be parametrically suppressed relative to the ``kinematical'' twist-3 ones due to the small packing fraction of the instanton vacuum. We derive exact sum rules for the twist-3 GPDs.
We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. …
The present status of the longitudinal polarized parton densities (PDFs) and the contribution of their first moments to the nucleon spin is discussed. Special attention is paid to the role of higher twist effects in determining the PDFs and to the polarized strange quark and gluon densities, which are still not well determined from the present data.
We estimate the energy loss distribution and investigate the quenching of hadron spectra in ultrarelativistic heavy-ion collisions due to the collisional energy loss of energetic partons from hard parton collisions in the initial stage.
We examine the effects of color screening on the transition of a parton plasma into a hadron gas at RHIC energies. It is found that as expected, color screening posed itself as a significant barrier for hadronization. Parton-hadron conversion would therefore be delayed and prolonged when compared to that occuring in a vacuum. Due to the on-going expansion, the resulting hadron densities are lowered. Parton equilibration is also shown to be seriously disrupted in the process.
The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is applied to Pb+Pb collisions from 20 to 160 A GeV in order to explore the space-time regions of 'partonic matter'. We find that even central collisions at the top-SPS energy of 158 A GeV show a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona. Furthermore, we observe that the partonic phase has a very low impact on rapidity distributions of hadrons but a …
We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N_f=2+1+1 ensembles having pion masses of 210 MeV and 354 MeV at two values of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 18 N_f=2+1+1 ensembles generated at three values of the lattice spacing, $a$. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of ${\cal O}(a^2)$-terms. The…
Recent experimental and theoretical results presented in the working group "Parton densities from DIS and hadron colliders to LHC" at the DIS2010 workshop are summarized in this contribution.
We investigate the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in very good agreement with deep inelastic scattering experimental data from HERA.
We report on the results of a recent work, where 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 (LCWFs). These WFs provide one with a reasonable description of both polarized and unpolarized parton densities at large values of the Bjorken variable. Twist-3 parton distributions are then constructed as convolution integrals of qqqg and usual three-quark WFs.
In a recent paper Yang and Bodek extracted the free neutron structure function at large x by extrapolating the density dependence of the nuclear EMC ratios to the deuteron. We clarify why this approach is ill-defined for light nuclei, and introduces a large theoretical bias into the extraction of F_2n at large x.
The Parton-Hadron-String Dynamics (PHSD) transport approach consistently simulates the full evolution of a relativistic heavy-ion collision from the initial hard scatterings string formation through the dynamical deconfinement phase transition to the quark gluon plasma (QGP), to the hadronization and to subsequent interactions in the hadronic phase. The transport theoretical description of quarks and gluons is based on a dynamical quasiparticle model for partons matched to reproduce recent lattice QCD results in thermodynamic equilibrium. The transition from partonic to hadronic degrees of fre…
Diffractive parton distributions of the proton are determined from fits to diffractive data from HERA. In addition to the twist--2 contribution, the twist--4 contribution from longitudinally polarised virtual photons is considered, which is important in the region of small diffractive masses. A new prediction for the longitudinal diffractive structure function is presented which differs significantly from that obtained in the pure twist--2 analyses.
M. Melnitchouk et al. [hep-ex/9912001] misunderstand the model of Frankfurt and Strikman for nuclear binding effects in deep inelastic scattering (DIS). In addition, their comment is entirely irrelevant to the results of our article.
The impact of the recent very precise CLAS and COMPASS g_1/F_1 data on polarized parton densities and higher twist effects is discussed. We demonstrate that the low Q^2 CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function g1, while the large Q^2 COMPASS data influence mainly the strange quark and gluon polarizations which slightly decrease. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities.
We discuss the recent claim that hadron multiplicities measured at RHIC energies are directly described in terms of gluon degrees of freedom fixed from the initial conditions of central heavy ion collisions. The argument is based on the parton saturation scenario expected to be valid at high parton densities and on the assumption of conserved gluon number. Alternatively we conjecture that "bottom-up" equilibration before hadronization modifies this picture, due to nonconservation of the number of gluons.
We show that in the large N_c limit four-quark twist-4 distributions in the pion can be expressed in terms of twist-2 pion distribution amplitude. This allows us to compute the isospin-2 structure function of the pion F_2^{I=2}(x_B) in the large N_c limit. The method can be easily applied to other mesons as well.
Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau-Pomeranchuk-Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, $A\to \infty$, as assumed in previous studies. Due to the correlative nature of the twist-fo…
We discuss the calculation of the evolution kernels ΔW_ζ(X,Z) for the leading-twist nonforward parton distributions G_ζ(X,t) sensitive to parton helicities. We present our results for the kernels governing evolution of the relevant light-ray operators and describe a simple method allowing to obtain from them the components of the nonforward kernels ΔW_ζ(X,Z).
The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for the axial-vector quasi- and pseudodistributions.
We investigate the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in excellent agreement with deep inelastic scattering experimental data from HERA.
We define in a systematic way, based on the light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the pi0) up to twist 5. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 20 real GPDs, whose symmetry properties are explicitely given. The reduction of these GPDs to a minimal set is …
A re-analysis of the NMC and SLAC data leads to a great improvement in our knowledge of the valence d and u parton distribution functions at high x. Standard parton distributions with our modifications are in good agreement with QCD predictions for d/u at x=1, and with the CDHSW nu p and nubar p data, the HERA charged current cross section data, the collider high-P_t jet data, and the CDF W asymmetry data. With the inclusion of target mass and higher twist corrections, the modified PDF's also describe all DIS data up to x = 0.98 and down to Q^2 = 1 GeV^2.
In order to study twist-3 and transverse momentum dependent parton distributions, we use light-front time-ordered pQCD at order $α_s$ to calculate various distribution functions for a dressed quark target. This study enables us to investigate in detail the existing relations between twist-3 and transverse momentum dependent parton distributions. Our calculation shows explicitly that two versions of such relations, considered to be equivalent, occur in the literature which need to be distinguished. Moreover, we examine sum rules for higher twist distributions. While the Burkhardt-Cottingham sum…
We propose a formalism for calculating the event cross-section of parton interactions. In this formalism, we use the light-front bound-state wave function to expand scattering initial state. This leads to an expression of the cross-section in terms of square of wave functions which can be used to define the parton distribution functions. The probability interpretation of the partonic interactions among hadron-hadron scattering is naturally achieved. We apply this formalism to calculate the 4-particle final state cross-section for single parton, double parton and gluon splitting interactions. W…
We study the production of bottom quarks in $pp$ collisions at Large Hadron Collider energies using previously developed parton cascade model to explore the impact of Landau Pomeranchuk Midgal (LPM) effect on their dynamics. In contrast to the case for charm quarks reported recently, we find only a marginal impact of the suppression of multiple scatterings of partons due to the LPM effect on their production. It is felt that this happens as they are only produced in very hard collisions.
The generalized parton distributions and the generalized distribution amplitudes give access to a deeper understanding of the quark and gluon content of hadrons. In this short review, we select some new developments of their interesting connections with the physics information that one can extract from exclusive reactions at medium and high energies.
We propose possible signatures of `exogamous' combinations between partons in the different W+ and W- hadron showers in e+e- -> W+W- events with purely hadronic final states. Within the space-time model for hadronic shower development that we have proposed previously, we find a possible difference of about 10 % between the mean hadronic multiplicity in such purely hadronic final states and twice the hadronic multiplicity in events in which one W decays hadronically and the other leptonically, i.e., <N_had(2W)> \ne 2 <N_{had}(W)>, associated with the formation of hadronic clusters by `exogamous…
The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.
We extend the counting of generalized form factors presented in PRD63(2000) by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity flip) operator is given in terms of generalized form factors.
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.
Beauty and charm quarks are ideal probes of pertubative Quantum Chromodymanics in proton-proton collisions, owing to their large masses. In this paper the role of multi-parton interactions in the production of doubly-heavy hadrons is studied using simulation samples generated with Pythia, a Monte Carlo event generator. Comparisons are made to the stand-alone generators BcVegPy and GenXicc. New methods of speeding up Pythia simulations for events containing heavy quarks are described, enabling the production of large samples with multiple heavy-quark pairs. We show that significantly higher pro…
For the first time, differential cross sections for the production of W-bosons in conjunction with up to three jets, computed at next-to leading order in QCD and including parton shower corrections, are presented and compared to recent experimental data from the Large Hadron Collider.
We study the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA.
We have re-analyzed the world data on inclusive polarized DIS including the very precise CLAS proton and deuteron data, as well as the latest COMPASS data on the asymmetry $A_1^d$, and have studied the impact of these data on polarized parton densities and higher twist effects. We demonstrate that the low $Q^2$ CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function $g_1$, while the large $Q^2$ COMPASS data influence mainly the strange quark density. In our new analysis we find that a negative polarized gluon density, or one that changes sign as a…
In the literature it is assumed that the parton to hadron fragmentation function cannot be studied by using the lattice QCD method because of the sum over the (unobserved) outgoing hadronic states. However, in this paper we find that since the hadron formation from the partons can be studied by using the lattice QCD method, the parton to hadron fragmentation function can be studied by using the lattice QCD method by using the LSZ reduction formula for the partonic processes.
We present recent results on the first moments of parton distributions using gauge configurations generated with two degenerate flavors of light twisted mass quarks with pion mass fixed approximately to its physical value. We also present a first study of the vector parton distribution function using a twisted mass ensemble at pion mass of 373 MeV.
In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors i…
We determine diffractive parton distributions of the proton from DGLAP based fits to HERA data including the twist--4 contribution from longitudinal polarized virtual photons, which is known to be important in the region of large beta. The biggest impact of this contribution is on the diffractive gluon distribution and on the diffractive longitudinal structure function to be determined from HERA data.
We discuss hadron production in heavy ion collisions at RHIC. We argue that hadrons at transverse momenta P_T < 5 GeV are formed by recombination of partons from the dense parton phase created in central collisions at RHIC. We provide a theoretical description of the recombination process for P_T > 2 GeV. Below P_T = 2 GeV our results smoothly match a purely statistical description. At high transverse momentum hadron production is well described in the language of perturbative QCD by the fragmentation of partons. We give numerical results for a variety of hadron spectra, ratios and nuclear sup…
Dynamical gluon effects in twist-3 generalized parton distributions of the proton
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
