We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton distributions are defined in terms of the unpolarized and polarized gluon PDFs and profile functions. The latter are related to gluon PDFs via differential equations.
We develop a quasiclassical theory of the synchrotron-like gluon radiation. Our calculations show that the parton energy loss due to the synchrotron gluon emission may be important in the jet quenching phenomenon if the plasma instabilities generate a sufficiently strong chromomagnetic field. Our gluon spectrum disagrees with that obtained by Shuryak and Zahed within the Schwinger's proper time method.
A simplest case, where a contribution to a color ordered multi-gluon amplitude, describing a three body partonic interaction, can split into two weakly correlated two-body gluon scattering amplitudes and may thus contribute to a Double Parton Interaction, is briefly discussed. We find that the color ordered amplitude is not enhanced in the typical configuration generated by a DPI, where the transverse momenta of final state gluons are compensated pairwise, while a dominant contribution to the multi-gluon amplitude is due to terms proportional to the fusion amplitude of two initial state gluons…
A typical contribution to a color ordered multi-gluon amplitude, which can split into two weakly correlated two-body gluon scattering amplitudes and may thus contribute to a Double Parton Interaction, is briefly discussed. We find that the color ordered amplitude is not enhanced in the typical configuration generated by a DPI, where the transverse momenta of final state gluons are compensated pairwise, while a dominant contribution to the multi-gluon amplitude is due to terms proportional to the fusion amplitude of two initial state gluons. Which corresponds to an amplitude effectively describ…
We study radiative parton energy loss in an expanding quark-gluon plasma with magnetic monopoles. We find that for realistic number density of thermal monopoles obtained in lattice simulations parton rescatterings on monopoles can considerably enhance energy loss for plasma produced in $AA$ collisions at RHIC and LHC energies. However, contrary to previous expectations, monopoles do not lead to the surface dominance of energy loss.
We outline arguments for the cancellation of soft singularities in transition probabilities and parton distributions with incoming partons and Wilson lines, and with observed jets or heavy colored particles in the final states. We show the cancellation of Glauber gluons and divergent phases, relating finite remainders to corrections that arise from restrictions on final states in factorized cross sections.
The gluon radiation induced by multiple scattering of a hard parton in expanding quark-gluon plasma is investigated. The radiative energy loss of hard parton jet is shown to decrease considerably when angular size of extracted jet goes up, but the fraction of loss survives even for the reasonable wide cone of angles due to the coherent effects taking into account the rescattering of the radiated gluons in the QCD medium. The possible application to the jet quenching phenomenon in heavy ion collisions at LHC energies is discussed.
We discuss how the UN2LOPS scheme for matching NNLO calculations to parton showers can be applied to processes with large higher-order perturbative QCD corrections. We focus on Higgs-boson production through gluon fusion as an example. We also present an NNLO fixed-order event generator for this reaction.
The propagation of hard partons through spatially extended matter leads to medium-modifications of their fragmentation pattern. Here, we review the current status of calculations of the corresponding medium-induced gluon radiation, and how this radiation affects hadronic observables at collider energies.
We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with focus on correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering (DPS) in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results gives insight to the strengths of correlations in different kinematical regions, which can help in constructing input DPDs in cro…
Motivated by the desire to understand the nucleon mass structure in terms of light-cone distributions, we introduce the twist-four parton distribution function $F(x)$ whose first moment is the gluon condensate in the nucleon. We present the equation of motion relations for $F(x)$ and discuss the possible existence of the delta function (`zero mode') contribution at $x=0$. We also perform one-loop calculations for quark and gluon targets.
We discuss the energy loss of energetic parton jets in quark-gluon plasma above the deconfinement temperature $T_c$ by the interaction with scalar and pseudoscalar glueballs. It is shown that the loss by this mechanism is quite important and may play the important role of the observed jet-quenching.
Employing a newly developed pQCD inspired parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic $gg \leftrightarrow ggg$ interactions are for the first time implemented obeying full detailed balance. The numerical results show that thermalization of gluons is mainly driven by the inelastic gluonic interactions and reaches equilibrium at $1\sim 2$ fm/c. In simulations for noncentral collisions considerable partonic elliptic flow $v_2$ is generated being comparable with the experimental data.
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 derive the complete Wilson renormalization group equation which governs the evolution of the gluon distribution and other gluonic observables at low $x$ and arbitrary density.
We calculate the classical gluon field of a fast projectile passing through a dense medium. We show that this allows us to calculate both the initial state gluon production in proton-nucleus collisions and the final state gluon radiation off a hard parton produced in nucleus-nucleus collisions. This unified description of these two phenomena makes the relation between the saturation scale $Q_s$ and the transport coefficient $\hat q$ more transparent. Also, we discuss the validity of the eikonal approximation for gluon propagation inside the nucleus in proton-nucleus collisions at RHIC energy.
We argue that the collinear factorization of the fragmentation functions in high energy hadron and nuclei collisions breaks down at transverse momenta kT < Qs/g due to high parton densities in the colliding hadrons and/or nuclei. We calculate, at next-to-leading order in projectile parton density and to all orders in target parton density, the double-inclusive cross section for production of a pair of gluons in the scalar J^(PC)=0^(++) channel. Using the low energy theorems of QCD we find the inclusive cross section for pi-meson production.
We derive the space-time distribution of energy and momentum deposited by a fast parton traversing a weakly coupled quark-gluon plasma by treating the fast part on as the source of an external color field perturbing the medium. We then use our result as a source term for the linearized hydrodynamical equations of the medium. We show that the solution contains a sonic Mach cone and a dissipative wake if the parton moves at a supersonic speed.
In relativistic heavy ion collisions, the cross section of heavy hadron production via the combination of a heavy quark with a light one from the quark-gluon matter can be factorized. It is the convolution of twist-4 combination matrix elements, the parameters corresponding to the parton distributions of the quark-gluon matter, as well as the hard partonic cross section of heavy quark production calculable in PQCD. These parton distributions and combination matrix elements are functions of a scaling variable which is the momentum fraction of the heavy quark w.r.t. the heavy hadron. In the same…
We present a study of proton GPDs in both momentum and position spaces using proton wavefunction obtained from AdS/ QCD. Here we consider the soft wall model. The results are compared with a phenomenological model of proton GPDs.
We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a gluon parent which splits into four collinear partons. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next- to-next-to-next-to-leading order (N$^3$LO) in the strong coupling constant. Combined with our earlier results for a quark parent, this completes the set of tree-level splitting amplitudes required at this order. We also study iterated collinear limits where a subset of the four collinear partons become themselves collinear.
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized compo…
We study the small-$x$ evolution equation for the gluon generalized parton distribution (GPD) $E_g$ of the nucleon. It is shown that $E_g$ at vanishing skewness exhibits the Regge behavior identical to the BFKL Pomeron, despite its association with nucleon helicity-flip processes. We also consider the effect of gluon saturation and demonstrate that $E_g$ gets saturated in the same way as its helicity-nonflip counterpart $H_g$. Our result has a direct impact on the modeling of $E_g$ as well as the small-$x$ contribution to nucleon spin sum rules.
We incorporate the perturbative evolution effects in the generalized parton distributions (GPDs) calculated in effective light-front quark model for the nucleon. The perturbative effects enters into formalism through the evolution of GPDs according to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-like (DGLAP) equation. We obtain the evolved GPDs in the momentum space and transverse impact parameter space. We observe that combining the light front quark model with the perturbative evolution effects, give the effective model for studying the phenomenological GPDs
Starting from the observation that soft rescattering of hard scattered partons from the colour charged remnant plays an important role in proton-proton collisions a similar model for soft scatterings in a quark-gluon plasma was constructed and implemented as a Monte Carlo event generator. The main emphasis was put on the question to what extend these soft scatterings can contribute to the energy loss that an energetic parton suffers, when it traverses a quark-gluon plasma. It was found that the soft scattering can account for up to 50% of the observed energy loss. Furthermore, it was investiga…
We consider a model of transverse momentum production in which non-perturbative smearing takes place throughout the perturbative evolution, by a simple modification to an initial state parton shower algorithm. Using this as the important non-perturbative ingredient, we get a good fit to data over a wide range of energy. Combining it with the non-perturbative masses and cutoffs that are a feature of conventional parton showers also leads to a reasonable fit. We discuss the extrapolation to the LHC.
Infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension matrix, which is also an essential ingredient for the resummation of large logarithms due to soft gluon emissions. We report a recent analytical calculation of the anomalous dimension matrix with both massless and massive partons at two-loop level, which describes the two-loop infrared singularities of any scattering amplitudes with an arbitrary number of massless and massive partons, and also enables soft gluon resummation at next-to-next-to-leading-logarithmic order. As an application, we calculate t…
The phenomenological success of PQCD is based on processes where the effects of the color field environment on parton propagation can be eliminated or is universal. In hard diffraction and quarkonium production the PQCD subprocess is the same as in fully inclusive scattering, but the sensitivity to reinteractions is different. I discuss how this may be exploited to give new information on the dynamics of hard collisions.
We perform a comparison of the radiative and collisional parton energy losses in an expanding quark-gluon plasma. The radiative energy loss is calculated within the light-cone path integral approach. The collisional energy loss is calculated using the Bjorken method with an accurate treatment of the binary collision kinematics. Our numerical results demonstrate that for RHIC and LHC conditions the collisional energy loss is relatively small in comparison to the radiative one. We find an enhancement of the heavy quark radiative energy loss as compared to that of the light quarks at high energie…
We derive the medium-induced, coherent gluon radiation spectrum associated with the hard forward scattering of an energetic parton off a nucleus, in the saturation formalism and within the Gaussian approximation for the relevant correlators of Wilson lines. The calculation reproduces the simple expression for the spectrum previously obtained in the opacity expansion formalism, and rigorously specifies its validity range. The connection between the calculations in the opacity expansion and saturation formalisms is made apparent. This study may serve as a first step in order to implement consist…
Holographic soft-wall model is successful in the phenomenology of hadrons. Here with the use of generalized parton distributions (GPDs) obtained from AdS/QCD, perturbative effects are entered into the formalism. Perturbations are incorporated in the formalism through the evolution of GPDs according to the DGLAP like equations. Evolved proton GPDs are compared with a phenomenological model to show that we can get good improvements of the holographic model. It seems that combining the holographic soft-wall model with perturbative effects to some extent, gives the correct physics of GPDs.
We examine the significance of $2 \rightarrow 2$ partonic collisions as the suppression mechanism of high-energy partons in the strongly interacting medium formed in ultrarelativistic heavy ion collisions. For this purpose, we have developed a Monte Carlo simulation describing the interactions of perturbatively produced, non-eikonally propagating high-energy partons with the quarks and gluons from the expanding QCD medium. The partonic collision rates are computed in leading-order perturbative QCD (pQCD), while three different hydrodynamical scenarios are used to model the medium. We compare o…
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
We study the generalized parton distributions (GPDs) of pion for non-zero skewness by considering the leading $| q \bar{q} \rangle$ Fock state component. Inspired from AdS/QCD light-front wave functions, we calculate the pion GPDs. By taking the Fourier transforms we obtain the results for impact-parameter dependent parton distribution functions (ipdpdf) and for GPDs in longitudinal boost-invariant space. We also calculate the charge density and gravitational form factor of the pion. The pion unpolarized transverse momentum distribution (TMD) have also been calculated. The results provide rich…
Being able to distinguish parton pair type in a dijet event could significantly improve the search for new particles that are predicted by the theories beyond the Standard Model at the Large Hadron Collider. To explore whether parton pair types manifesting themselves as a dijet event could be distinguished on an event-by-event basis, I performed a simulation based study considering observable jet variables. I found that using a multivariate approach can filter out about 80% of the other parton pairs while keeping more than half of the quark-quark or gluon-gluon parton pairs in an inclusive QCD…
New data, especially HERA measurements of the proton structure function at small $x$, allow the opportunity to improve our knowledge of the gluon and quark distribution functions. We perform a global analysis which incorporates these new precise data, and which extends down to $Q^2 = 1.5\; GeV^2$. We discuss the sensitivity to the value of $α_s$ and the improvement in the determination of the gluon. We compare the predictions of the single jet inclusive cross section with recent measurements from the Fermilab Tevatron.
We gauge the impact of soft-gluon resummation on quark distributions by performing a simple fit of Deep Inelastic Scattering structure function data using next-to-leading order (NLO) and next-to-leading-logarithmic (NLL)-resummed coefficient functions. We make use of NuTeV charged-current data, as well as New Muon Collaboration (NMC) and Bologna-CERN-Dubna-Munich-Saclay (BCDMS) neutral-current results, which probe large values of x. Our results suggest that the inclusion of resummation effects in global fits of parton distributions is both feasible and desirable, in order to achieve at large x…
We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1 percent over a range…
We evaluate the medium suppression of light hadron spectra in $pp$ collisions at RHIC and LHC energies in the scenario with formation of a mini quark-gluon plasma. We find a significant suppression effect. For $p_{T}\sim 10$ GeV we obtained the reduction of the spectra by $\sim [20-30,25-35,30-40]$ % at $\sqrt{s}=[0.2, 2.76,7]$ TeV. We also discuss how this phenomenon may change the predictions for the nuclear modification factors for $AA$ and $pA$ collisions.
We show that for hadronic transverse energy $E_T$ in hadron-hadron collisions, the classic Collins-Soper-Sterman (CSS) argument for the cancellation of Glauber gluons breaks down at the level of two Glauber gluons exchanged between the spectators. Through an argument that relates the diagrams with these Glauber gluons to events containing additional soft scatterings, we suggest that this failure of the CSS cancellation actually corresponds to a failure of the `standard' factorisation formula with hard, soft and collinear functions to describe $E_T$ at leading power. This is because the observa…
We present a phenomenological unpolarized Parton Distribution Functions for diquarks based on a soft-wall light front AdS/QCD quark-diquark nucleon model. From a probed model consistent with the Drewll-Yan-West relation and quark counting rule, we have performed a fit of some free parameters using known phenomenological quark PDF data. The model considers the entire set of possible diquarks within the nucleon valence, in the present work we focus on the spin-0 $ud_0$, spin-1 $ud_1$ and spin-1 $uu_1$ diquarks into the valence of protons. The diquark PDFs obtained are able to used in proton-prot…
We present a numerical analysis of helicity independent nucleon generalized parton distributions (GPDs) using the known formalism based on inclusion of higher Fock states in the soft-wall approach of the anti-de Sitter/QCD model. We calculate the momentum space GPDs by matching the electromagnetic form factors in the AdS model to the sum rules in QCD. We investigate their Mellin moments, transverse impact parameter GPDs, transverse mean square radius, and transverse width. We further extend this work to investigate the charge and anomalous magnetization densities for both unpolarized and trans…
The evolution of orbital angular momentum distributions within the radiative parton model is studied. We use different scenarios for the helicity weighted parton distributions and consider a broad range of input distributions for orbital angular momentum. In all cases we are lead to the conclusion that the absolute value of the average angular momentum per parton peaks at relatively large $x\approx 0.1$ for perturbatively accessible scales. Furthermore, in all scenarios considered here the average orbital angular momentum per parton is several times larger for gluons than for quarks which favo…
We note that the phenomenon of perturbative saturation leads to transverse momentum broadening in the spectrum of partons produced in hadronic collisions. This broadening has a simple interpretation as parton level Cronin effect for systems in which saturation is generated by the "tree level" Glauber-Mueller mechanism. For systems where the broadening results form the nonlinear QCD evolution to high energy, the presence or absence of Cronin effect depends crucially on the quantitative behavior of the gluon distribution functions at transverse momenta kt outside the so called scaling window. We…
We study the leading twist gluon generalized parton distributions (GPDs) and the gluon angular momentum inside the proton within a light-cone spectator model. Using the light-cone wave functions derived from the model, we provide the expressions of these distributions at the particular kinematical point $ξ=0$ in the overlap representation. The numerical results of the $H^g$, $E^g$, $\tilde{H}^g$, $H_T^g$ and $E_T^g$ as functions of $x$ at different $Δ_T$ are presented. Particularly, $H^g$, $\tilde{H}^g$ at non-zero $Δ_T$ are different from their forward counterparts, the unpolarized distributi…
Using the AdS/CFT correspondence and the eikonal approximation, we evaluate the elastic parton-parton scattering amplitude at large $N$ and strong coupling $g^2N$ in N=4 SYM. We obtain a scattering amplitude with a Regge behavior that unitarizes at large $\sqrt{s}$.
We determine the valence parton distribution function of the pion by performing a new analysis of data for the Drell-Yan process $π^- N\to μ^+μ^-X$. Compared to previous analyses, we include next-to-leading-logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions $x$ than obtained in previous next-to-leading order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations.
We study the evolution of parton distributions down to low scales by considering several of their Mellin moments. For the initial conditions, we use a broad array of current parton density fits. Confirming earlier findings in the literature, we conclude that current determinations of parton distributions are incompatible with the idea that gluon or antiquark densities are generated by purely perturbative radiation as it is encoded in the DGLAP evolution equations.
Hadrons interaction at high energies is carried out by one color gluon exchange. All quarks and gluons contained in colliding hadrons take part in interaction and production of particles. The contribution of multiple parton interactions is negligible. Multiple hadrons production at high energies occurs only in three types of processes. The first process is hadrons production in gluon string, the second is hadrons production in two quark strings and the third is hadrons production in three quark strings. In proton-proton interaction production of only gluon string and two quark strings is possi…
We consider the radiation of three soft gluons in a generic process for multiparton hard scattering in QCD. In the soft limit the corresponding scattering amplitude has a singular behaviour that is factorized and controlled by a colorful soft current. We compute the tree-level current for triple soft-gluon emission from both massless and massive hard partons. The three-gluon current is expressed in terms of maximally non-abelian irreducible correlations. We compute the soft behaviour of squared amplitudes and the colour correlations produced by the squared current. The radiation of one and two…
Double parton distribution functions (dPDFs), entering the double parton scattering (DPS) cross section, are unknown fundamental quantities encoding new interesting properties of hadrons. Here, the pion dPDFs are investigated within different holographic QCD quark models in order to access their basic features. Results of the calculation,s obtained within the AdS/QCD soft-wall approach, have been compared with predictions of lattice QCD evaluations of the pion two-current correlation functions. The present analysis confirms that double parton correlations, affecting dPDFs, are very important a…
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
Generalized parton distributions of a deuteron in an AdS/QCD hard-wall model
Institute of Physics, Ministry of Science and Education（阿塞拜疆科学与教育部物理研究所）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）；Center for Theoretical Physics, Khazar University（哈扎尔大学理论物理中心）；Western Caspian University（西里海大学）
