We find, within the pQCD dipole model for DIS processes, a rapid increase with energy of the scale of parton momenta in the current fragmentation region in the limit $s\to \infty$ and fixed $Q^2$ . We explain the equivalence between the dispersion representation over $Q^2$ for LT pQCD zero angle amplitude of $γ^*+T\to γ^*+T$ scattering at large energies and the $k_t$ factorization, and use it to evaluate the scales of the hard processes in the current fragmentation region. We derive within the black disc (BD) regime the modified Gribov formula for the total cross-section of the DIS. We evaluate the coherence length of the processes relevant for the BD regime and find that it increases with energy as $\sim s^{0.6}$ i.e. significantly slower than in the parton model ($1/2m_Nx$ - the Ioffe length) as well as in pQCD. In the BD regime we estimate the gluon densities, local in the coordinate space, and find that they do not decrease with the energy. We discuss briefly how the new pQCD phenomena may reveal itself in the proton-proton collisions at LHC
We prove $k_T$ factorization theorem in perturbative QCD (PQCD) for exclusive processes by considering $πγ^*\to γ(π)$ and $B\toγ(π) l\barν$. The relevant form factors are expressed as the convolution of hard amplitudes with two-parton meson wave functions in the impact parameter $b$ space, $b$ being conjugate to the parton transverse momenta $k_T$. The point is that on-shell valence partons carry longitudinal momenta initially, and acquire $k_T$ through collinear gluon exchanges. The $b$-dependent two-parton wave functions with an appropriate path for the Wilson links are gauge-invariant. The …
We discuss real time simulations of high energy nuclear collisions in a classical effective theory of QCD at small x. At high transverse momenta, our results match the lowest order predictions of pQCD based mini-jet calculations. We discuss novel non-perturbative behaviour of the small x modes seen at small transverse momenta.
We study three-hadron azimuthal angular correlations in high energy proton-proton and central nucleus-nucleus collisions at RHIC and LHC at mid-rapidity. We use the LO parton matrix elements for 2 \rightarrow 3 processes and include the effect of parton energy loss in the Quark-Gluon Plasma using the modified fragmentation function approach. For the case when the produced hadrons have either same or not too different momenta, we observe two away side peaks at 2pi/3 and 4pi/3. We consider the dependence of the angular correlations on energy loss parameters that have been used in studies of sing…
We calculate rapidity and transverse momentum distributions of charmonium formed in high energy heavy ion collsions from incoherent recombination of charm quarks. The results are very sensitive to the corresponding distributions of the charm quarks, and thus can serve as a probe of the state of matter produced in the heavy ion collision. At one extreme we generate a set of charm pair momenta directly from pQCD amplitudes, which are appropriate if one can neglect interaction of the quarks with the medium. At the other extreme we generate momenta of charm quarks in thermal equilibrium with the e…
Nuclear modification factors for pion production in AuAu and CuCu collisions are analyzed at very high transverse momenta. At p_T > 10 GeV/c, the R_{AA}(p_T) is determined mostly by the initial state nuclear modifications (e.g. EMC effect) and the non-Abelian jet-energy loss in the final state. At high momenta these effects together are strong enough to suppress R_{AA}(p_T) to below 1 at RHIC energies. We display results using HKN shadowing in our pQCD improved parton model. Result of a similar calculation at LHC energies for PbPb collisions are also displayed. Based on dN/dy estimates, a larg…
The dipole and the DGLAP approximations are combined with the $k_t$ factorization theorem to demonstrate the fundamental property of pQCD: smaller is the size of the colorless quark-gluon configurations in the fragmentation region, more rapid is the increase of its interaction with the target as a function of energy. First, we show that the transverse momenta of the quark(antiquark) within the $q\bar{q}$ pair, produced in the fragmentation region by the strongly virtual photon, increase with the decrease of x for fixed $Q^2$. As practical consequence of these effects we show that the cross sec…
The multiplicity distribution of the gluons produced at the high energy is evaluated in BFKL approach. The distribution has Poisson form that can explain experimentally observed KNO scaling.
DIS on a two nucleon system in the regge limit is considered. In this framework a review is given of a pQCD approach for the computation of the corrections to the inclusive one jet production cross section at finite number of colors and discuss the general results.
Next-to-leading order parton fragmentation functions into light mesons are presented. They have been extracted from real and simulated $e^+e^-$ data and used to predict inclusive single particle distributions at different machines.
I examines the applicability and possible need for a re-formulation of pQCD, as we know it, in the DIS limit of small $Q^2$ and $x$. Gluon saturation, implied by s-channel unitarity, and its possible experimental signatures are critically assessed.
LHC predictions for the charm and bottom nuclear modification factors using pQCD and AdS/CFT drag energy loss models are given. We show that a new observable, the double ratio of charm to bottom nuclear modification factors, allows for easy experimental distinction between the two classes of energy loss models.
We study the exclusive decays of $B\to K^{(*)}l^+l^-$ within the framework of the PQCD. We obtain the form factors for the $B\to K^{(*)}$ transitions in all allowed values of $q^2$, which agree with the lattice results. We find that our distributions of the decay rates and leptonic asymmetries are consistent with that given in the other QCD models in the literature.
We review some aspects of multiple interactions in High Energy QCD; we discuss in particular AGK rules and present some results concerning multiple interactions in the context of jet production.
We compare data on the proton structure function from SLAC experiments in the range of x between 0.7 and 0.97 in and near the resonance region with previous empirical fits to Deep Inelastic Scattering and with calculations from parton distribution functions. The data is in rough agreement with the empirical fits, but is an order of magnitude higher than the pQCD calculations at the highest x. This compares with the two orders of magnitude increase in the quark distributions at high x which seem to be necessary to explain the HERA high momentum transfer events.
This talk will discuss how to compute initial quantites in heavy ion collisions at RHIC (200 AGeV) and at LHC (5500 AGeV) using perturbative QCD (pQCD) by including the next-to-leading order (NLO) corrections and a dynamical determination of the dominant physical scale. The initial numbers are converted into final ones by assuming kinetic thermalization and adiabatic expansion.
The systematic treatment of heavy quark mass effects in DIS in current CTEQ global analysis is summarized. Applications of this treatment to the comparison between theory and experimental data on DIS charm production are described. The possibility of intrinsic charm in the nucleon is studied. The issue of determining the charm mass in global analysis is discussed.
A method of obtaining parton distributions directly from data is revealed in this series. In the process, the first step would be developing appropriate matrix solutions of the evolution equations in $x$ space. A division into commuting and non-commuting matrix solutions has been made. Here, well-developed commuting matrix solutions are presented. Results for finite LO evolution match those of standard LO sets. There is a real potential of doing non-parametric data analysis.
Low transverse momentum direct photon measurements have been carried out by the ALICE experiment at the CERN LHC in small collision systems (pp, $\sqrt{s}=2.76$ and 8 TeV and p--Pb, $\sqrt{s_\text{NN}}=5.02$ TeV) as well as in heavy-ion collisions (Pb--Pb, $\sqrt{s_\text{NN}}=2.76$ TeV). For the first time, also the multiplicity dependence of direct photon production was investigated in p--Pb collisions. Whereas in the small systems no significant thermal photon signal was observed, a $\sim15\%$ excess has been measured in central Pb--Pb collisions in the region of $p_{\rm T}<3$ GeV/$c$. A sig…
Within a pQCD inspired kinetic parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic gluonic interactions $gg \leftrightarrow ggg$ do play an important role: For various initial conditions it is found that thermalization and the close to ideal fluid dynamical behaviour sets in at very early times. Special emphasis is put on color glass condensate initial conditions and the `bottom up thermalization' scenario. Off-equilibrium $3\to 2$ processes make up the very beginning of the evolution leading to an in…
We study the dependence on photon virtuality $Q^2$ for the semihard quasi--elastic photoproduction of neutral vector mesons on a quark, gluon or real photon (at $s\gg p_{\bot}^2, Q^2; p_{\bot}^2 \gg μ^2 \approx (0.3$ GeV)$^2$). To this end we calculate the corresponding amplitudes (in an analytical form) in the lowest nontrivial approximation of the perturbative QCD. The amplitudes for the production of mesons consisting of light quarks vary very rapidly with the photon virtuality near $Q^2=0$. We estimate the bound of the pQCD validity region for such processes. For the process with mass shel…
The Mueller-Navelet di-jet production process represents an ultimate testfield of pQCD in the high-energy limit. Several experimental analyses carried out so far are in good agreement with theoretical predictions, based on collinear factorization and BFKL resummation of energy logarithms in the next-to-leading approximation, with the CMS experimental data at center-of-mass energy equal to 7 TeV. However, the question if the same data can be described also by fixed-order perturbative approaches has not yet been fully answered. We discuss how the use of partially asymmetric cuts in the transvers…
We present fully dynamic simulations of heavy ion collisions at RHIC energies within the perturbative QCD-based partonic transport model BAMPS, focusing on the simultaneous investigation of jet-quenching and elliptic flow. The model consistently features elastic and inelastic 2 -> 3 processes, the latter being based on the Gunion-Bertsch matrix element. We discuss first attempts to extend the model to include light quark degrees of freedom and study the energy loss of high energy gluons and quarks in a static partonic medium. The difference between gluons and quarks in inelastic processes is f…
The recent analysis of nuclear distortions in DIS off nuclei revealed a breaking of the conventional hard factorization for multijet observable. The related pQCD analysis of distortion effects for jet production in nucleus-nucleus collisions is as yet lacking. As a testing ground for such an analysis we consider the Abelian problem of higher order Coulomb distortions of the spectrum of lepton pairs produced in peripheral nuclear collisions. We report an explicit calculation of the contribution to the lepton pair production in the collision of two photons from one nucleus with two photons from …
Recent surprising discoveries of collective behaviour of low-$p_T$ particles in $pA$ collisions at LHC hint at the creation of a hot, fluid-like QGP medium. The seemingly conflicting measurements of non-zero particle correlations and $R_{pA}$ that appears to be consistent with unity demand a more careful analysis of the mechanisms at work in such ostensibly minuscule systems. We study the way in which energy is dissipated in the QGP created in $pA$ collisions by calculating, in pQCD, the short separation distance corrections to the well-known DGLV energy loss formulae that have produced excell…
We predict the dependence on energy of photo(electro) production processes: $γ(γ^*)+p\to V+ X$ with large rapidity gap at small x and large momentum $-t$ transferred to $V$ in pQCD. Here V is a heavy quarkonium ($J/ψ, Υ$) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer $t$, photon virtuality $Q^2$ and/or quarkonium mass. In the kinematical region $Q_0^2\le -t\ll Q^2+M^2_V$ the nontrivial energy dependence of the cros…
Perturbative QCD (pQCD) running coupling a(Q^2) (=alpha_s(Q^2)/pi) is expected to get modified at low spacelike momenta 0 < Q^2 < 1 GeV^2 so that, instead of having unphysical (Landau) singularities it remains smooth and finite there, due to infared (IR) fixed point. This behavior is suggested by: Gribov-Zwanziger approach, Dyson-Schwinger equations (DSE) and other functional methods, lattice calculations, light-front holographic mapping AdS/CFT modified by a dilaton background, and by most of the analytic (holomorphic) QCD models. All such couplings, A(Q^2), differ from the pQCD couplings a(Q…
I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large light-cone momenta x; the breakdown of pQCD factorization theorems due to the lensing effects of initial- and final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniver…
As one of the key components of perturbative QCD theory, it is helpful to find a systematic and reliable way to set the renormalization scale for a high-energy process. The conventional treatment is to take a typical momentum as the renormalization scale, which assigns an arbitrary range and an arbitrary systematic error to pQCD predictions, leading to the well-known renormalization scheme and scale ambiguities. As a practical solution for such scale setting problem, the "Principle of Minimum Sensitivity" (PMS), has been proposed in the literature. The PMS suggests to determine an optimal scal…
Higher-order pQCD corrections play an important role in the reproduction of data at high transverse momenta in the energy range 20 GeV $ \leq \sqrt{s} \leq 200$ GeV. Recent calculations of photon and pion production in $pp$ collisions yield detailed information on the next-to-leading order contributions. However, the application of these results in proton-nucleus and nucleus-nucleus collisions is not straightforward. The study of nuclear effects requires a simplified understanding of the output of these computations. Here we summarize our analysis of recent calculations, aimed at handling the …
Through data analysis, we present new sets of nonperturbative fragmentation functions (FFs) for $Λ_c^+$ baryon both at leading and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the minimal subtraction factorization scheme with five massless quarks. The FFs are determined by fitting all available data of inclusive single $Λ_c^+$ baryon production in $e^+e^-$ annihilation taken by the OPAL Collaboration at CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties in the $Λ_c^+$ FFs as well as in the corresponding observables. …
A pQCD-based model for parton production and equilibration in ultrarelativistic heavy-ion collisions is reviewed. The model combines pQCD processes including initial and final state radiations together with string phenomenology for nonperturbative soft processes. Nuclear effects on the initial parton production, such as multiple parton scattering and nuclear shadowing of parton distribution functions are considered. Comparisons with existing data are made and further tests of the model to constrain model parameters are proposed. With the obtained space-time history of the parton production, ev…
The recent progress in the pQCD theroy of diffractive DIS (DDIS) is reviewed. We place emphasis on pQCD scales, diffractive factorization breaking, jet and charm production and new fundamental observables which are becomeing accessible with the Leading Proton Spectrometers of ZEUS and H1.
At very high energies, in the infinite momentum frame and in light cone gauge, a hard scale proportional to the high parton density arises in QCD. In an effective theory of QCD at small $x$, this scale is of order $α_Sμ$, where $μ$ is simply related to the gluon density at higher rapidities. The ab initio real time evolution of small $x$ modes in a nuclear collision can be described consistently in the classical effective theory and various features of interest can be studied non-perturbatively. In this paper, we discuss results from a real time lattice computation of the production of gluon j…
We study the reactions $γ^*(Q^2)p\toρ^0 p$ and $γ^*(Q^2)p\toγ^*(Q^2) p$ at large Q^2 and $W^2/Q^2$ and small momentum transfer, $κ^2_\perp$, to the nucleon where the pomeron exchange dominates. At large Q^2 the virtual photon selects a hard $q\bar q$ pair, thus selecting the hard pomeron component (the BFKL pomeron). The amplitudes for both transverse and longitudinal polarizations of the initial photon and outgoing $ρ$-meson (photon) are calculated in the framework of the BFKL pomeron exchange. Our calculations show that one cannot expect the early onset of the pure perturbative regime in the…
At sufficiently small $x$ where pQCD methods become insufficient we rewrote sum of dominant Feynman diagrams for single-scale hard processes in the form of the effective field theory where a quasiparticle corresponds to pQCD ladder. We explain that pQCD series are divergent at small $x$ since pQCD produces tachyon in effective field theory and because of degeneracy of vacua . Within the WKB approximation we found the hierarchy among quasiparticle interactions due to smallness of the QCD coupling constant which justifies restriction by the triple quasiparticle interaction in the Lagrangean of e…
We study production of two pairs of jets in %hard hadron--hadron collisions in view of extracting contribution of {\em double hard interactions} of three and four partons ($3\to4$, $4\to4$). Such interactions, in spite of being power suppressed at the level of the total cross section, become comparable with the standard hard collisions of two partons, $2\to4$, in the {\em back-to-back kinematics} when the transverse momentum imbalances of two pairing jets are relatively small. We express differential and total cross sections for two-dijet production in double parton collisions through the gene…
To obtain more precise parton distribution functions (PDFs) it is important to include data on inclusive high transverse energy jet production in the global parton analyses. These data have high statistics and the NNLO terms in the perturbative QCD (pQCD) description are now available. Our aim is to reduce the uncertainty in the comparison of the jet data with pQCD. To ensure the best convergence of the pQCD series it is important to choose the appropriate factorization scales, $μ_F$. We show that it is possible to absorb and resum in the incoming PDFs and fragmentation function ($D$) an essen…
We investigate the Lambda_b polarization problem in the inclusive semileptonic decays of a polarized Lambda_b baryon, using the modified perturbative QCD formalism which includes Sudakov suppression. According to HQEFT, we show that, at the leading order in the 1/M_b expansion, the polarized and unpolarized distribution functions become one single universal distribution function. To explore the mechanisms which determine the spin properties of a polarized Lambda_b baryon, we construct four formalisms which are the naive quark model (QM), the modified quark model (MQM), the naive parton model (…
Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the s…
Parametrizations of fragmentation functions (FFs) from $e^+$-$e^-$ and p-p collisions are combined with a parton spectrum model in a pQCD folding integral to produce minimum-bias {\em fragment distributions}. A model of in-medium FF modification is included. Calculated fragment distributions are compared with {\em hard components} from p-p and Au-Au $p_t$ spectra. Data are well described by pQCD over a large kinematic region for a range of Au-Au centralities.
I discuss the theoretical status of the `soft' pomeron and its place in describing generic diffractive processes. The role of perturbative QCD (pQCD) corrections is considered, in particular in the context of quasi-elastic vector meson production at high $Q^2$. In those processes where short distances are dominant, the `hard' (pQCD) pomeron is expected to reveal itself, such a process may well be that of diffractive vector meson production at high-$t$ and I discuss this.
We compare calculations of jet quenching observables at sqrt s = 2.76 ATeV to preliminary LHC data from weak-coupling pQCD and strong-coupling AdS/CFT drag energy loss models. Rigorously constrained to sqrt s = 200 AGeV RHIC pi^0 suppression data and introducing no free parameters, the pQCD-based WHDG model simultaneously describes qualitatively the suppression of light hadrons and quantitatively the azimuthal anisotropy (over many centrality classes) of light hadrons and the suppression of D mesons at LHC. The drag predictions shown here--qualitatively constrained to RHIC data--compare poorly…
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.
Quenching of gluonic jets and heavy quark production in Au+Au collisions at RHIC can be understood within the pQCD based 3+1 dimensional parton transport model BAMPS including pQCD bremsstrahlung $2 \leftrightarrow 3$ processes. Furthermore, the development of conical structures induced by gluonic jets is investigated in a static box for the regimes of small and large dissipation.
Future prospects of hard diffraction at HERA a reviewed. A selection of processes which can be calculated in pQCD is given, with emphasis on the separation of soft and hard diffraction. The main focus will be put on the energy dependence of diffractive processes and signatures for the hard pQCD pomeron. Problems in the experimental detection of these processes and the expected significance of future measurements at HERA are discussed.
LPS provides access to new fundamental observables: the diffraction cone and azimuthal asymmetries. Diffraction cone has a unique rise of $B_T$ from the exclusive limit to excitation of continuum $M^2 \approx Q^2$ which is in striking contrast to experience with real photoproduction and hadronic diffraction. Azimuthal asymmetry is large and pQCD calculable at large $β$ and can be measured with LPS. It allows testing of the pQCD prediction of $L/T >> 1$.
The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize $B_c$ meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous $J/ψ$ and $ψ'$ production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons.
We present the first NLO pQCD study of coherent exclusive $J/ψ$ photoproduction in ultraperipheral heavy-ion collisions (UPCs) at the LHC. Taking the generalized parton distributions (GPDs) in their forward limit, as parton distribution functions (PDFs), we quantify the NLO contributions in the rapidity-differential cross section, show that the real part of the amplitude must not be neglected, study the gluon and quark contributions, chart the scale-choice and PDF uncertainties, and compare the NLO results with LHC and HERA data. We show that the scale dependence is significant but a scale cho…
With the advent of TeV-energy colliding machines, such as the Large Hadron Collider (LHC), the possibility has opened up to test predictions of Quantum Chromodynamics (QCD) and, more in general, of the Standard Model (SM), in new, and so far unexplored, kinematical regimes. Among the many reactions that can be investigated at LHC, the Higgs production is one of the most important and challenging for the entire high-energy physics Community. Beside usual studies in the Higgs sector, it has recently been highlighted how differential Higgs distributions can be effectively used as ``stabilizers'' …
We introduce an event-by-event pQCD + saturation + hydro ("EKRT") framework for high-energy heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD (pQCD) using saturation to control soft particle production, and describe the space-time evolution of the QCD matter with viscous hydrodynamics, event by event (EbyE). We compare the computed centrality dependence of hadronic multiplicities, p_T spectra and flow coefficients v_n against LHC and RHIC data. We compare also the computed EbyE probability distributions…
Within the framework of perturbative QCD approach, we study the charmless two-body decays into final states involving one axial-vector (A), $a_1(1260)$ or $b_1(1235)$, and one vector (V), namely $ρ(ω,ϕ)$. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Except the decays $\bar B^0\to a^{0}_1ρ^0(ω)$, other tree-dominated decays $B\to a_1ρ(ω)$ have larger branching ratios, at the order of $10^{-5}$. (b)Except the decays $\bar B\to b^+_1ρ^-$ and $B^-\to b^0_1ρ^-$, other $B\to b_1ρ(ω)$ de…
In the current paper, we argue that the ground state of a hadron contains a significant perturbative quantum chromodynamics (pQCD) core as the result of color gauge invariance and of the values of chiral and gluon vacuum condensates. The evaluation within the method of dispersion sum rules (DSR) of the vacuum matrix elements of the correlator of local currents with the proper quantum numbers leads to the value of the radius of the pQCD core of a nucleon of about 0.4--0.5 fm. The selection of the initial and final states allows to select processes in which the pQCD core of the projectile gives …
Motivated by the striking modifications of jets observed both at RHIC and the LHC, significant progress towards the understanding of jet dynamics within QGP has occurred over the last few years. In this talk, I review the recent theoretical developments in the study of medium-induced jet evolution and energy loss within a perturbative framework. The main mechanisms of energy loss and broadening will be firstly addressed with focus on leading particle calculations beyond the eikonal approximation. Then, I will provide an overview of the modifications of the interference pattern between the diff…
Hadrons inclusively produced with large pT in high-energy collisions originate from the jets, whose initial virtuality and energy are of the same order, what leads to an extremely intensive gluon radiation and dissipation of energy at the early stage of hadronization. Besides, these jets have a peculiar structure: the main fraction of the jet energy is carried by a single leading hadron, so such jets are very rare. The constraints imposed by energy conservation enforce an early color neutralization and a cease of gluon radiation. The produced colorless dipole does not dissipate energy anymore …
Semi-hard processes in the large COM energy limit offer us an exclusive chance to test the dynamics behind strong interactions in kinematical sectors so far unexplored. In the Regge limit, fixed-order calculations in pQCD based on collinear factorisation miss the effect of large energy logs, which are so large to compensate the small QCD coupling $α_s$ and must therefore be accounted for to all perturbative orders.. The BFKL approach represents the most powerful tool to resum to all orders these large logs both in the LLA and in the NLA. The inclusive hadroproduction of forward jets with high …
