We obtain a novel result in QCD for long range rapidity correlations between gluons produced in the collision of saturated high energy hadrons or nuclei. This result, obtained in a high energy factorization framework, provides strong justification for the Glasma flux tube picture of coherent strong color fields. Our formalism can be applied to "near side ridge" events at RHIC and in future studies of long range rapidity correlations at the LHC.
We explore the relationship between the Glasma framework and the String Percolation Model by introducing a simple model for the rapidity distributions in nucleus-nucleus collisions. The model is solved for both symmetrical and asymmetrical collisions. The phenomenon of limiting fragmentation is briefly discussed.
Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described by CSS-based TMD factorization at moderate Bjorken $x_B\sim 1$ and by $k_T$-factorization at small $x_B$. A uniform description valid for all $x_B$ is provided by rapidity-only TMD factorization developed in a series of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by gluon fusion is extended to the one-loop level.
I discuss how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at small $x\ll 1$ to linear evolution at moderate $x\sim 1$.
A model of multiparticle production in hadronic collisions at ultra-relativistic energies, based on the assumption of independent string fragmentation, reproduces the rapidity spectra of $Λ$ and $\barΛ$ in sulphur-sulphur collisions reported by the NA35 Collaboration. This is achieved after a reconsideration of the intermediate multi-string states and the structure of the diquarks. Nuclear stopping power is also studied through the computation of the $p-\bar{p}$ rapidity spectra.
I define the proton-contributor reference frame in proton nucleus (p--A) collisions as the center of mass of the system formed by the proton and the participant nucleons of the nucleus. Assuming that the rapidity distribution of produced particles is symmetric in the proton-contributor reference frame, several measurements in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02 {\rm TeV}$ can be described qualitatively. These include rapidity distributions of charged particles, $J/ψ$ and Z bosons.
In a recent paper (arXiv:1403.5221), Kang et al.proposed the so-called "rapidity factorization" for the single inclusive forward hadron production in pA collisions. We point out that the leading small-x logarithm was mis-identified in this paper, and hence the newly added next-to-leading order correction term is unjustified and should be absent in view of the small-x factorization.
We illustrate how a generalization of the JIMWLK formalism which treats independently the direct and complex conjugate amplitudes can be used to describe semi-inclusive multiparticle production with rapidity correlations in pA collisions. The evolution equations that are obtained with this formalism are susceptible of numerical implementation as a Langevin process.
Central production cross-sections of hard dijets with 2,1 or 0 rapidity gap at Tevatron are analyzed in terms of diffractive (``a la Good-Walker'') and non diffractive fluctuations of the incident particles. The observed large factorization breaking and the unexpected high value of the 2 to 1 gap cross-section ratio are explained in terms of scattering with and between the incident particles.
We develop the pQCD description of diffraction excitation of heavy flavours in DIS and we derive the analytic formulas for the mass spectrum in leading log$m_f^{2}$. The result illustrates nicely non-factorization properties of the QCD pomeron. We predict a very steep rise of the charm content of diffraction dissociation of photons at small $x_{\Pom}$. We evaluate the contribution of open charm to scaling violations in the structure function of the pomeron.
The solutions of the Balitsky-Kovchegov evolution equations are studied numerically and compared with known analytical estimations. The rapidity and nuclear size dependences of the saturation scale are obtained for the cases of fixed and running coupling constant. These same dependences are studied in experimental data, on lepton-nucleus, deuteron-nucleus and nucleus-nucleus collisions, through geometric scaling and compared with the theoretical calculations.
We extend previous results (arXiv:0804.2630 [hep-ph]) on factorization in high-energy nucleus-nucleus collisions by computing the inclusive multigluon spectrum to next-to-leading order. The factorization formula is strictly valid for multigluon emission in a slice of rapidity of width ΔY< 1/α_s. Our results show that often neglected disconnected graphs dominate the inclusive multigluon spectrum and are essential to prove factorization for this quantity. These results provide a dynamical framework for the Glasma flux tube picture of the striking "ridge"-like correlation seen in heavy ion collis…
Soft threshold factorization has been used extensively to study hadronic collisions. It is derived in the limit where the momentum fractions $x_{a,b}$ of both incoming partons approach $x_{a,b}\to 1$. We present a generalized threshold factorization theorem for color-singlet processes, which holds in the weaker limit of only $x_a \to 1$ for generic $x_b$ (or vice versa), corresponding to the limit of large rapidity but generic invariant mass of the produced color singlet. It encodes the complete soft and/or collinear singular structure in the partonic momentum fractions to all orders in pertur…
We calculate the helicity amplitudes for scattering of a quark from both large and small $x$ gluons of a target proton or nucleus using spinor helicity formalism. We show that scattering from large $x$ gluons of the target results in non-zero spin asymmetry at intermediate $p_t$ as well as rapidity loss of the projectile quark. We comment on how this can also generate angular asymmetries in particle production in high energy collisions.
We review the origin, and salient features, of the breaking of the conventional linear $k_{\perp}$-factorization for an in-nucleus hard pQCD processes. A realization of the nonlinear $k_{\perp}$-factorization which emerges instead is shown to depend on color properties of the underlying pQCD subprocesses. We discuss the emerging universality classes and extend nonlinear $k_{\perp}$-factorization to AGK unitarity rules for the excitation of the target nucleus.
Nucleus-nucleus interaction is studied in the framework of the perturbative QCD with large number of colours and a fixed coupling constant. The pomeron tree diagrams are summed by an effective field theory. The classical field equations are solved by iteration procedure, which is found convergent in a restricted domain of not too high energies and atomic numbers. The found gluon distributions do not scale, have their maxima close to 2 GeV/c independent of rapidity and fall towards the central rapidity region. The cross-sections slowly grow with energy due to the contribution from peripheral co…
We present a partonic picture for diffractive onium-nucleus scattering in the large-number-of-color limit from which the distribution of rapidity gaps in a certain kinematic region can be deduced. This picture allows us to draw a parallel between diffractive dissociation and the genealogy of partonic evolution, the latter being essentially similar to a branching-diffusion process in which the branching is the parton splitting, and the diffusion occurs in the transverse momenta of the partons. In particular, we show that the rapidity gap distribution corresponds to the distribution of the split…
The cross sections for a variety of channels of proton-nucleus interaction associated with large gaps in rapidity are calculated within the Glauber-Gribov theory. We found inelastic shadowing corrections to be dramatically enhanced for such events. We employ the light-cone dipole formalism which allows to calculate the inelastic corrections to all orders of the multiple interaction. Although Gribov corrections are known to make nuclear matter more transparent, we demonstrate that in some instances they lead to an opaqueness. Numerical calculations are performed for the energies of the HERA-B e…
Single inclusive hadron production at forward rapidity in high energy p+A collisions is an important probe of the high gluon density regime of QCD and the associated small-$x$ formalism. We revisit an earlier one-loop calculation to illustrate the significance of the "rapidity factorization" approach in this regime. Such factorization separates the very small-$x$ unintegrated gluon density evolution and leads to a new correction term to the physical cross section at one-loop level. Importantly, this rapidity factorization formalism remedies the previous unphysical negative next-to-leading orde…
We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultra-relativistic and sources of non-abelian Weizsäcker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classic…
We study proton-lead collisions with a new model for the Fock states of the incoming proton. The number of collisions which the proton experiences selects the appropriate Fock state of the proton which generates a multiple of pp-like rapidity distributions. We take as input the pp maximum entropy distributions shifting the respective cm-rapidities and reducing the available energies. A comparison with existing data at 5 TeV is made and results for 8 TeV are presented. We also explore the high multiplicity data in this model.
We calculate the probability that the rapidity gaps in diffractive processes survive both eikonal and enhanced rescattering. We present arguments that enhanced rescattering, which violates soft-hard factorization, is not very strong. Accounting for NLO effects, there is no reason to expect that the black disc regime is reached at the LHC. We discuss the predictions for the survival of the rapidity gaps for exclusive Higgs production at the LHC.
The rapidity dependence of elliptic, $v_2$, and triangular, $v_3$, flow coefficients in proton-nucleus (p+A) collisions is predicted in hydrodynamics and in a multi-phase transport model (AMPT). We find that $v_n$ ($n=2,3$) on a nucleus side is significantly larger than on a proton side and the ratio between the two, $v_n^{\rm Pb}/v_n^{\rm p}$, weekly depends on the transverse momentum of produced particles.
We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data. For comparison, we also update the results for the nuclear modification factor for pion production in the same kinematics. We present predictions for future forward RHIC and LHC measurements at $\sqrt{s_{NN}}=200$ GeV and $\sqrt{s_{NN}}=8$ TeV.
We derive an all-order factorization theorem for the narrow jet broadening event shape, a measure of the transverse momentum in jet events. This is a non-global observable which receives logarithmically enhanced contributions associated with the large rapidity difference between soft and collinear radiation and which is also sensitive to soft recoil effects. Our work is the first factorization analysis of an observable of this type and we show that with regard to the non-global nature, the rapidity logarithms do not constitute an essential complication since they can be tied to the jet functio…
A model for the production of large rapidity gaps being implemented in the Monte Carlo event generator PHOJET is discussed. In this model, high-mass diffraction dissociation exhibits properties similar to hadron production in non-diffractive hadronic collisions at high energies. Hard diffraction is described using leading-order QCD matrix elements together with a parton distribution function for the pomeron and pomeron-flux factorization. Since this factorization is imposed on Born graph level only, unitarity corrections lead to a non-factorizing flux function. Rapidity gaps between jets are o…
Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in
Saturation models -- colour glass condensate and string percolation -- impose a strict relation between the average transverse momentum, <P_T>, and the rapidity particle densities, dn/dy. By combining this relation with an appropriate evolution equation for dn/dy, and imposing energy-momentum conservation, we obtain a fair description of data, for generic AB collisions (hadron-hadron, hadron-nucleus and nucleus-nucleus) at all rapidities and (high) energies. Predictions are given for the LHC.
Finding an efficient and compelling regularization of soft and collinear degrees of freedom at the same invariant mass scale, but separated in rapidity is a persistent problem in high-energy factorization. In the course of a calculation, one encounters divergences unregulated by dimensional regularization, often called rapidity divergences. Once regulated, a general framework exists for their renormalization, the rapidity renormalization group (RRG), leading to fully resummed calculations of transverse momentum (to the jet axis) sensitive quantities. We examine how this regularization can be i…
We discuss azimuthal correlations in $dAu$ collisions at different rapidities and centralities and argue that experimentally observed depletion of the back-to-back peak can be quantitatively explained by gluon saturation in the Color Glass Condensate of the Gold nucleus.
Long-range correlations between multiplicities in different rapidity windows in hadron-nucleus collisions are analyzed. After recalling the standard results in the probabilistic model, we study them in the framework of perturbative QCD. Considering interacting BFKL pomerons in the form of fan diagrams coupled to a dilute projectile, analytic estimates are done for very large rapidities. The correlation strength results weakly depending on energy and centrality or nuclear size, and generically greater than unity. Finally, we turn to the Color Glass Condensate framework. For a saturated projecti…
We address the general features of event-by-event fluctuations of the multiplicity of gluons produced in the scattering of a dilute hadron off a large nucleus at high energy in the fragmentation region of the dilute hadron. We relate these fluctuations to the stochasticity of the number of quanta contained in the hadron at the time of the interaction. For simplicity, we address the ideal case in which the hadron is an onium, and investigate different kinematical regimes in rapidity and onium size. We show that at large rapidity, the multiplicity distribution exhibits an exponential tail in the…
With the help of a phenomenological approach outlined in the text in some detail, we have dealt here with the description of the plots on rapidity and pseudorapidity spectra of some hadron-secondaries produced in various nucleus-nucleus interactions at high energies. The agreement between the measured data and the attempted fits are, on the whole, modestly satisfactory excepting a very narrow central region in the vicinity of y=$η$=0. At last, hints to how the steps suggested in the main body of the text to proceed with the description of the measured data given in the plots could lead finally…
The perturbative QCD description of high-energy hadroproduction of two hard jets separated by a large rapidity gap void of emission (also called Mueller-Tang jets) is based on a factorization formula of BFKL type that represents exchanges of colour-singlet objects among the external particles. This formula resums to all perturbative orders a certain class of Feynman diagrams that are supposed to dominate the cross-section in the Regge limit. However, the explicit calculations at next-to-leading logarithmic order questions the validity of such factorization when an IR safe jet algorithm is used…
The quark combination mechanism of hadron production is applied to nucleus-nucleus collisions at the CERN Super Proton Synchrotron (SPS) and BNL Alternating Gradient Synchrotron (AGS). The rapidity spectra of identified hadrons and their spectrum widths are studied. The data of $π^{-}$, $K^{\pm}$, $ϕ$, $Λ$, $\barΛ$, $Ξ^{-}$, and $\barΞ^{+}$ at 80 and 40 AGeV, in particular at 30 and 20 AGeV where the onset of deconfinement is suggested to happen, are consistently described by the quark combination model. However at AGS 11.6 AGeV below the onset the spectra of $π^{\pm}$, $K^{\pm}$ and $Λ$ can n…
In the present work, it is intended to calculate the unintegrated parton distribution functions (UPDFs) of the $^6{Li}$ nucleus, which depend not only on the longitudinal momentum fraction $x$ (the Bjorken variable) and the factorization scale $μ$ of partons, but also on their transverse momentum ($k_t$). Therefore, the KMR and MRW procedures are applied to generate the $k_t$-dependent parton distributions from the familiar integrated parton densities (PDFs), which were determined in our recent related work, using the constituent quark exchange model (CQEM) for the $^6Li$ nucleus. Then, the re…
Rapidity-dependent transverse momentum spectra of negatively charged pions measured at different rapidities in proton-proton collisions at the Super Proton Synchrotron (SPS) at various energies within its Beam Energy Scan (BES) program are investigated by using one- and two-component standard distributions where the chemical potential and spin property of particles are implemented. The rapidity spectra are described by a double-Gaussian distribution. At the stage of kinetic freeze-out, the event patterns are structured by the scatter plots in the three-dimensional subspaces of velocity, moment…
We study two-particle long-range rapidity correlations arising in the early stages of heavy ion collisions in the saturation/Color Glass Condensate framework, assuming for simplicity that one colliding nucleus is much larger than the other. We calculate the two-gluon production cross section while including all-order saturation effects in the heavy nucleus with the lowest-order rescattering in the lighter nucleus. We find four types of correlations in the two-gluon production cross section: (i) geometric correlations, (ii) HBT correlations accompanied by a back-to-back maximum, (iii) away-side…
The extension of the factorization theorems of perturbative QCD to power corrections associated with re-scattering in nuclear collisions is reviewed. The importance of hadron-nucleus collisions is discussed.
Motivated by understanding the background to Chiral Magnetic Effect in proton-nucleus collisions from first principles, we compute the three particle correlation in the projectile wave function. We extract the correlations between two quarks and one gluon in the framework of the Color Glass Condensate. This is related to the same-charge correlation of the conventional observable for the Chiral Magnetic Effect. We show that there are two different contributions to this correlation function. One contribution is rapidity-independent and as such can be identified with the pedestal; while the other…
We investigate consequences of local energy-momentum conservation for initial eccentricity coefficients in heavy ion collisions at not too high energies relevant for CERN SPS and RHIC BES. Different models of energy density available for pion production are considered. We study dependence of eccentricity coefficients on space-time rapidity for different impact parameters. The naive formula how to define eccentricities breaks with our initial conditions and must be corrected. We predict considerable eccentricities for $ε_{1,2,3,4}$ and specific dependence on space-time rapidity as well as on im…
Longitudinal hadron spectra from Proton-Proton (pp) and nucleus-nucleus (AA) collisions from $E_{lab}= 2$ AGeV to $\sqrt s=200$ AGeV are investigated. The widths of the rapidity spectra for various particle species increases monotonously with energy. The present calculation indicates no sign of a step like behaviour as excepted from the Kaon transverse mass systematics. For Pions, the transport simulation is consistent with a Landau type scaling of the rapidity widths, both in central AA reactions and in pp collisions. However, other hadron species do not follow the Landau scaling. The present…
In order to describe large transverse momentum ($p_T$) distributions observed in high energy nucleus-nucleus collisions, a stochastic model in the three dimensional rapidity space is introduced. The fundamental solution of the radial symmetric diffusion equation is Gaussian-like in radial rapidity. We can also derive a $p_T$ or radial rapidity distribution function, where a distribution of emission center is taken into account. It is applied to the analysis of observed large $p_T$ distributions of charged particles. It is shown that our model approaches to a power function of $p_T$ in the high…
We discuss the inclusive dilepton cross section for proton (quark)-nucleus collisions at high energies in the very forward rapidity region. Starting from the calculation in the quasi-classical approximation, we include low-x evolution effects in the nucleus and predict leading twist shadowing together with anomalous scaling behaviour.
We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data and extended to nuclei with an optical Glauber procedure that introduces no additional parameters beyond the basic nuclear geometry. We present predictions for future forward RHIC and LHC measurements. The predictions are also compared to updated results for the nuclear modification factors for pion…
The number of particles detected in a nucleus-nucleus collision strongly depends on the impact parameter of the collision. Therefore, multiplicity fluctuations, as well as rapidity correlations of multiplicities, are dominated by impact parameter fluctuations. We present a method based on Bayesian inference which allows for a robust reconstruction of fluctuations and correlations at fixed impact parameter. We apply the method to ATLAS data on the distribution of charged multiplicity and transverse energy. We argue that multiplicity fluctuations are smaller at large rapidity than around central…
We study Higgs boson production from gluon-gluon fusion at mid-rapidity in high energy proton-nucleus collisions. For this process the presently still little known gluon distribution function $h_1^{\perp g}$ gives a numerically relevant contribution. We show by explicite calculation that using CGC (color glass condensate) model input the result obtained in the naive k_t factorization approach matches the result obtained in the TMD factorization framework for a dilute medium. We also verify the earlier finding that the k_t factorization formalism for Higgs production breaks down in a dense medi…
We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We cannot describe simultaneously mid and forward rapidity data measured at the LHC when using the KMR UGDF with the same normalization parameter. Furthermore we get somewhat too hard distribution in $J/ψ$ transverse momentum. Correcting the standard KMR distributions for saturation ef…
We calculate spectrum of diffractively produced gluons in onium-heavy nucleus collisions at high energies. We show that it exhibits a characteristic dependence on nucleus atomic number A and energy/rapidity. We argue that this dependence offers a unique possibility for determining the low-x structure of nuclear matter. Applications to RHIC, LHC and EIC experimental programs are discussed.
We revisit the rapidity dependence of the average transverse momentum $\left\langle p_{T}\right\rangle$ in a $pp$ and $pA$ collision, using the high energy factorization (HEF). We update previous predictions for the $\left\langle p_{T}\right\rangle$ both in central and forward rapidity region using parton densities following from extended BK and BFKL evolution equations to account for corrections of higher orders as well as one obtained by Sudakov resummation. Furthermore, we demonstrate that in the mid rapidity region the saturation based formalisms predict increase of the transversal momentu…
We study diffractive hard dijet production, with one or two rapidity gaps, at high energies. We emphasize that both hard and Regge factorization are broken in these processes. We show that a multi-Pomeron-exchange model for screening effects gives a specific pattern for the breakdown of factorization, which is in good agreement with diffractive dijet data collected at the Tevatron.
We present the calculation of the forward jet vertex associated to a rapidity gap (coupling of a hard pomeron to the jet) in the BFKL formalism at next-to-leading order (NLO). Real emission contributions are computed via Lipatov's effective action. The NLO jet vertex turns out to be finite within collinear factorization and allows, together with the NLO non-forward gluon Green's function, to perform NLO studies of jet production in diffractive events (e.g. Mueller-Tang dijets).
The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton).
New evidence for the rapidity evolution in Mueller-Navelet dijet production: BFKL, Sudakov, and RG-invariance
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（鲍里索夫理论物理实验室，核物理研究所）；Physics Department, Ben-Gurion University of the Negev（内盖夫本-古里安大学物理系）；Samara National Research University（萨马拉国立研究大学）
In nuclear collisions, a sizable fraction of the available energy is carried away by baryons. As the baryon number is conserved, the net-baryon $B-\bar{B}$ retains information on the energy-momentum carried by the incoming nuclei. A simple and consistent model for net-baryon production in high energy proton-proton and nucleus-nucleus collisions is presented. The basic ingredients of the model are valence string formation based on standard PDFs with QCD evolution and string fragmentation via the Schwinger mechanism. The results of the model are presented and compared with data at different cent…
I give a pedagogical survey of the nuclear collective effects associated with gluon saturation and their impact on particle production in high-energy proton (or deuteron)-nucleus collisions at RHIC. At central rapidity, the theory predicts a Cronin peak due to independent multiple scattering off the valence quarks in the nucleus. At forward rapidities, the peak flattens out and disappears very fast, because of the correlations induced through quantum evolution in the nuclear gluon distribution at small x. Also, the ratio R_{pA} between the particle yield in proton-nucleus and proton-proton col…
Nucleus-nucleus scattering is studied in the local Reggeon Field Theory in the quasi-classical approximation with non-eikonal boundary conditions corresponding to the Glauber picture at low energies. Comparison with the commonly used eikonal boundary conditions shows that the new conditions make both the action and nucleus-nucleus total cross-sections lower by $3÷5$ %. They also substantially change the behaviour of the solutions of the equations of motion at low energies. Using expressions for the double inclusive cross-sections derived earlier in the Reggeon Field Theory \cite{CM} long-range…
