We investigate the scattering of a quark jet on a high-energy heavy nucleus using the time-dependent light-front Hamiltonian approach. We simulate a real-time evolution of the quark in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. We study the sub-eikonal effect by letting the quark jet carry realistic finite longitudinal momenta, and we find sizeable changes on the transverse coordinate distribution of the quark. We also observe the energy loss of the quark through gluon emissions in the $\ket{q}+\ket{qg}$ Fock space. This approach provides us with an opportunity to study scattering processes from non-perturbative aspects.
A light front treatment of the nuclear wave function is developed and applied, using the mean field approximation, to infinite nuclear matter. The nuclear mesons are shown to carry about a third of the nuclear plus momentum, p+; but their momentum distribution has support only at p+ =0, and the mesons do not contribute to nuclear deep inelastic scattering. This zero mode effect occurs because the meson fields are independent of space-time position.
We calculate the cross section for production of a soft photon and two hard jets in the forward rapidity region in proton-nucleus collisions at high energies. The calculation is performed within the hybrid formalism. The hardness of the final particles is defined with respect to the saturation scale of the nucleus. We consider both the correlation limit of small momentum imbalance and the dilute target limit where the momentum imbalance is of the order of the hardness of the jets. The results depend on the first two transverse-momentum-dependent (TMD) gluon distributions of the nucleus.
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 calculate the spectrum of energy loss differences due to gluon radiation in high energy hard forward processes in proton-nucleus collisions as compared to proton-proton collisions. We find that the nuclear induced energy loss scales linearly with the beam energy. We evaluate the spectrum and "typical" energy losses in a logarithmic and large $N_{c}$ approximation. The energy losses found appear large enough to be phenomenologically important.
An outlook on physics at the high energy frontier of nucleus-nucleus collisions is presented, on the basis of the new results presented at Quark Matter 2011 by the LHC and RHIC experiments.
Forward $J/ψ$ production and suppression in high energy proton-nucleus collisions can be an important probe of gluon saturation. In an earlier work we studied this process in the Color Glass Condensate framework and showed that using the Glauber approach to extrapolate the dipole cross section of a proton to a nucleus leads to results closer to experimental data than previous calculations in this framework. Here we investigate the centrality dependence of the nuclear suppression in this model and show a comparison of our results with recent LHC data.
The production of forward $J/ψ$ mesons in proton-nucleus collisions can provide important information on gluon saturation. In a previous work we studied this process in the Color Glass Condensate framework, describing the target using a dipole cross section fitted to HERA inclusive data and extrapolated to the case of a nuclear target using the optical Glauber model. In this work we study the centrality dependence of the nuclear suppression in this model and compare our results with recent LHC data for this observable.
We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ appr…
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…
We re-evaluate the nuclear suppression of forward $J/ψ$ production at high energy in the Color Glass Condensate framework. We use the collinear approximation for the projectile proton probed at large $x$ and an up to date dipole cross section fitted to HERA data to describe the target in proton-proton collisions. We show that using the Glauber approach to generalize the proton dipole cross section to the case of a nucleus target leads to a nuclear modification factor much closer to LHC data than previous estimates using the same framework.
Using the formalism of the light-cone wave function in perturbative QCD together with the hybrid factorization, we compute the cross-section for three particle production at forward rapidities in proton-nucleus collisions. We focus on the quark channel, in which the three produced partons -- a quark accompanied by a gluon pair, or two quarks plus one antiquark -- are all generated via two successive splittings starting with a quark that was originally collinear with the proton. The three partons are put on-shell by their scattering off the nuclear target, described as a Lorentz-contracted "sho…
Inclusive production of $J/ψ$ mesons, especially at forward rapidities, is an important probe of small-x gluons in protons and nuclei. In this paper we re-evaluate the production cross sections in the Color Glass Condensate framework, where the process is described by a large x gluon from the probe splitting into a quark pair and eikonally interacting with the target proton or nucleus. Using a standard collinear gluon distribution for the probe and an up to date dipole cross section fitted to HERA data to describe the target we achieve a rather good description of the cross section in proton-p…
We show that a special choice of light-cone gauge can greatly simplify the calculation of the classical color field created in the initial stages of nucleus-nucleus collisions. Within this gauge, we can in particular construct explicitly the conserved color current and calculate exactly the gauge field immediately after the collision. This field is used as a boundary condition in an iterative solution of the Yang-Mills equations in the forward light-cone. In leading order, which corresponds to a linearization of the Yang-Mills equation in the forward light-cone, we obtain a simple formula for …
We discuss the effects of initial collision geometry and centrality bin definition on correlation and fluctuation observables in nucleus-nucleus collisions. We focus on the forward-backward correlation coefficient recently measured by the STAR Collaboration in Au+Au collisions at RHIC. Our study is carried out within two models: the Glauber Monte Carlo code with a `toy' wounded nucleon model and the hadron-string dynamics (HSD) transport approach. We show that strong correlations can arise due to averaging over events in one centrality bin. We, furthermore, argue that a study of the dependence…
Using the color glass condensate formalism, we study the nuclear modification of forward $J/ψ$ and $D$ meson production in high energy proton-nucleus collisions at the LHC. We show that relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data leads to a smaller nuclear suppression than in the first study of these processes in this formalism and a better agreement with experimental data.
Single inclusive particle production at next-to-leading order in proton-nucleus collisions at forward rapidities: hybrid approach meets TMD factorization
The nuclear suppression of forward $J/ψ$ production in high energy proton-nucleus collisions can be used as a probe of gluon saturation at small $x$. In an earlier work we studied this suppression in minimum bias collisions in the Color Glass Condensate formalism, relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data. Here we study how the impact parameter dependence of this model can be used to compare our results with recent LHC data on the centrality dependence of this suppression.
The problem of understanding the nuclear effects observed in lepton-nucleus deep-inelastic-scattering (the EMC effect) is still with us. Standard nuclear models (those using only hadronic degrees of freedom) are not able to account for the EMC effect. Thus it is necessary to understand how the nuclear medium modifies quark wave functions in the nucleus. Possibilities for such modifications, represented by the quark meson coupling model, and the suppression of point-like-configurations are discussed, and methods to experimentally choose between these are reviewed.
The PHENIX experiment at BNL-RHIC recently reported the single transverse spin asymmetry $A_N$ for forward neutrons measured in polarized proton-nucleus collisions at $\sqrt{s_{NN}} = 200\,$GeV; $A_N$ in proton-aluminum and proton-gold collisions are -0.015 and 0.18, respectively, which are clearly different from $A_N=-0.08$ in proton-proton collisions. In this paper, we propose large $A_N$ for forward neutrons in ultraperipheral polarized proton-nucleus collisions as an explanation of the PHENIX measurements. The proposed model is demonstrated using two Monte Carlo simulations organized as fo…
Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but …
We show how the limiting fragmentation phenomenon can arise from the Color Glass Condensate model of high energy QCD. We consider the very forward rapidity region in relativistic heavy ion collisions and argue that in this region, nucleus-nucleus collisions are similar to proton-nucleus collisions (up to shadowing corrections). We then use the known results for proton-nucleus cross sections to show that it leads to the phenomenon of limiting fragmentation in the very forward region of heavy ion collisions as observed at RHIC.
We calculate nuclear suppression $R_{AA}$ of heavy quarks produced from the initial fusion of partons in nucleus-nucleus collisions at RHIC and LHC energies. We take the shadowing as well as the energy loss suffered by them while passing through Quark Gluon Plasma into account. We obtain results for charm and bottom quarks at several rapidities using different mechanisms for energy loss, to see if we can distinguish between them.
We study the real-time evolution of an electron influenced by intense electromagnetic fields using the time-dependent basis light-front quantization (tBLFQ) framework. We focus on demonstrating the non-perturbative feature of the tBLFQ approach through a realistic application of the strong coupling QED problem, in which the electromagnetic fields are generated by an ultra-relativistic nucleus. We calculate transitions of an electron influenced by such electromagnetic fields and we show agreement with light-front perturbation theory when the atomic number of the nucleus is small. We compare tBL…
We consider production of prompt photons in high energy gold-gold and deuteron-gold collisions in the forward rapidity region of RHIC ($y \sim 3.8$). In this kinematics, the projectile partons typically have large $x_{bj}$ while the target partons are mostly at very small $x_{bj}$ so that the primary partonic collisions involve valence quarks from the projectile and gluons from the target. We take the target nucleus to be a Color Glass Condensate while the projectile deuteron or nucleus is treated as a dilute system of partons. We show that the photon production cross section can be written as…
We consider dilepton production in high energy proton-nucleus (and very forward nucleus-nucleus) collisions. Treating the target nucleus as a Color Glass Condensate and describing the projectile proton (nucleus) as a collection of quarks and gluons as in the parton model, we calculate the differential cross section for dilepton production in quark-nucleus scattering and show that it is very sensitive to the saturation scale characterizing the target nucleus.
We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pion's gluon densities can be probed through the pion-nucleus induced $J/ψ$ production data. Our pion part…
A light-front treatment for the scalar and vector meson momentum distribution functions is developed using a model in which the nucleus is treated a static source of radius $R$. The limit $R\to \infty$ corresponds to infinite nuclear matter. In this limit, the scalar mesons are shown to carry a vanishing momentum fraction of the nuclear plus momentum $k^+$, but the vector mesons carry a significant fraction, all occuring at the experimentally inaccessible value of $k^+=0$. This confirms earlier work. A study of the $R$ dependence for sizes of real nuclei shows that a fraction of the scalar and…
Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton-nucleus and ultra-peripheral heavy ion collisi…
Recent experimental results have revealed a surprisingly rich structure of multiparticle azimuthal correlations in high energy proton-nucleus collisions. Final state collective effects can be responsible for many of the observed effects, but it has recently been argued that a part of these correlations are present already in the wavefunctions of the colliding particles. We evaluate the momentum space 2-particle cumulant azimuthal anisotropy coefficients v_n{2}, n=2,3,4 from fundamental representation Wilson line distributions describing the high energy nucleus. These would correspond to the fl…
We present a complete comparison of semi-inclusive $ν_μ$-$^{12}$C cross-section measurements by T2K and MINER$ν$A collaborations with the predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event generator GENIE and an unfactorized approach based on the relativistic distorted wave impulse approximation (RDWIA). Results, that include cross sections as function of the final muon and proton kinematics and correlations between both, show that the agreement with data obtained by the RDWIA approach, that accounts for final-state interactions, matches or improves GENIE-SuSAv2 pr…
We study nuclear modification factors for single $D$ meson and semileptonic decay lepton $l$ ($=e,μ$) production in minimum bias proton-nucleus (p$A$) collisions at the LHC in the color-glass-condensate (CGC) framework at leading order in strong coupling. In our numerical computations, transverse momentum ($k_\perp$) dependent multi-point Wilson line correlators are employed for describing target nucleus for p$A$ and proton for pp. The projectile proton is treated with unintegrated gluon distribution function, which is also $k_\perp$-dependent. The rapidity evolutions of these functions in the…
We obtain the pion and the kaon parton distribution functions from the eigenstates of a light front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolution, are consistent with the data from the FNAL-E615 experiment. The ratio of the up quark distribution of the kaon to that of the pion also agrees with the CERN-NA3 experiment. Supplemented by known parton distribution functions for the nucleons, we further o…
[Background] Meticulous modeling of neutrino-nucleus interactions is essential to achieve the unprecedented precision goals of present and future accelerator-based neutrino-oscillation experiments. [Purpose] Confront our calculations of charged-current quasielastic cross section with the measurements of MiniBooNE and T2K, and to quantitatively investigate the role of nuclear-structure effects, in particular, low-energy nuclear excitations in forward muon scattering. [Method] The model takes the mean-field (MF) approach as the starting point, and solves Hartree-Fock (HF) equations using a Skyrm…
We derive forward inclusive dijet production in the scattering of a dilute hadron off an arbitrary dense target, whose partons with small fraction of momentum x are described by a Color Glass Condensate. Both multiple scattering and non-linear QCD evolution at small-x are included. This is of relevance for measurements of two-particle correlations in the proton direction of proton-nucleus collisions at RHIC and LHC energies. The azimuthal angle distribution is peaked back to back and broadens as the momenta of the measured particles gets closer to the saturation scale.
We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are determined solely by standard nuclear geometry and by electron-proton deep inelastic scattering data, which is fit using the running coupling BK equation. We show that it is possible to obtain a good fit of the HERA inclusive cross section also without an anomalous dimension in the initial condition. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in DIS also for the single inclusive cros…
Forward trijet production in proton-nucleus collisions: gluon initiated channel
SUBATECH UMR 6457 (IMT Atlantique, Universite de Nantes, IN2P3/CNRS)（SUBATECH UMR 6457 (IMT大西洋学院，南特大学，IN2P3/CNRS)）；Department of Physics, Temple University（天普大学物理系）；RIKEN-BNL Research Center, Brookhaven National Laboratory（理研-布鲁克海文国家实验室研究中心）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）
The remarkable observations in the pion induced and charge exchange reactions on a nucleus are the significant shift and broadening of the $Δ(1232)$-peak relative to free pion nucleon scattering. For the forward going massless leptons, the weak process $(ν_l,l)$ on a nucleon, according to Adler's partially conserved axial current theorem, is connected to the pion nucleon scattering. This mechanism is also applicable to the nucleus. Therefore, the modification of the $Δ$-peak in a nucleus can be seen in the $(ν_l,l)$ reaction since it is connected to the pion nucleus scattering. To investigate …
We present a study of coherent pion production in neutrino-nucleus interactions using the formalism based on partially conserved axial current theorem which connects the neutrino-nucleus cross section to the pion-nucleus elastic scattering cross section. Pion-nucleus elastic scattering cross section is calculated using Glauber model which takes three inputs, nuclear densities, pion-nucleon cross section and $α_{πN}$ which is the ratio of real to imaginary part of $πN$ forward scattering amplitude, for which the parametrizations are obtained from measured data. We calculate the differential and…
Quantum information entropy is calculated from the nucleon nucleus forward scattering amplitudes. Using a representative set of nuclei, from $^4$He to $^{208}$Pb, and energies, $T_{lab} < 1$\,[GeV], we establish a linear dependence of quantum information entropy as functions of logarithm nuclear mass $A$ and logarithm projectile energy $T_{lab}$.
In this paper we calculate the contribution to rapidity and angular correlations of the first Pomeron loop diagram in the dense partonic environment. This diagram is expected to give the largest contribution to the density variation mechanism of the angular correlations. We show that this diagrams leads to sizable contributions to the rapidity correlation functions of the order of $σ_{in} /\Lb πR^2\Rb$ where $σ_{in}$ is the inelastic cross section and $R$ is the size of the typical dipole inside the proton saturation scale. Therefore, the correlations do not depend on the saturation scale. We …
We show that particle production in proton-nucleus (pA) collisions in the Color Glass Condensate model can be related to Deep Inelastic Scattering of leptons on protons/nuclei (DIS). The common building block is the quark antiquark (or gluon-gluon) dipole cross section which is present in both DIS and pA processes. This correspondence in a sense generalizes the standard leading twist approach to pA collisions based on collinear factorization and perturbative QCD, and allows one to express the pA cross sections in terms of a universal quantity (dipole cross section) which, in principle, can be …
We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu--Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion str…
We consider hadron production in deuteron gold collisions at RHIC in the forward rapidity region. Treating the target nucleus as a Color Glass Condensate and the projectile deuteron as a dilute system of valence quarks, we obtain good agreement with the BRAHMS minimum bias data on charged hadron production in the forward rapidity ($y=3.2$) and low $p_t$ region. We provide predictions for neutral pion production in minimum bias deuteron gold collisions in the forward rapidity region, $y=3.8$, measured by the STAR collaboration at RHIC.
The theoretical treatment of alpha decay by Gamow is revisited by investigating the quantum time scales in tunneling. The time spent by an alpha particle in front of the barrier and traversing it before escape is evaluated using microscopic alpha nucleus potentials. The half-life of a nucleus is shown to correspond to the time spent by the alpha knocking in front of the barrier. Calculations for medium and super heavy nuclei show that from a multitude of available tunneling time definitions, the transmission dwell time gives the bulk of the lifetime of the decaying state, in most cases.
The coherent $η$ meson energy $E_η$ distribution spectra in the proton nucleus reaction have been calculated to investigate the $π^0 - η$ mesons' interference, in addition to the study of resonance $N^*$ dynamics in the nucleus. The elementary reaction occurring in the nucleus is assumed to proceed as $ pN \to pN^* $; $ N^* \to Nη$. Born terms in the intermediate state is also considered. In a scalar-isovector nucleus, this reaction occurs because of $π^0$ and $η$ meson exchange interactions for the forward going proton and $η$ meson; other meson exchange potentials do not contribute in this p…
We consider the J/Psi production in proton (deuteron) -- nucleus collisions at high energies. We argue that the production mechanism in this case is different from that in pp collisions due to gluon saturation in the nucleus and formation of the Color Glass Condensate. At forward rapidities (in the proton fragmentation region), the production of J/Psi is increasingly suppressed both as a function of rapidity and centrality. On the other hand, at backward rapidities at RHIC (in the fragmentation region of the nucleus) the coherent effects lead to a modest enhancement of the production cross sec…
The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, 1+1 dimensional bag model, three-dimensional harmonic oscillator and the Hulthén potential. The latter provide simplified versions of momentum distributions and form factors of relevance to experiments. …
We consider one loop corrections to single inclusive particle production in parton-nucleus scattering at high energies, treating the target nucleus as a Color Glass Condensate. We prove by explicit computation that in the leading log Q^2 approximation, these corrections lead to collinear factorization and DGLAP evolution of the projectile parton distribution and hadron fragmentation functions. At leading logarithmic level, and in single-inclusive cross sections, only two-point functions of Wilson lines in the adjoint and fundamental representations (Mueller's dipoles) arise, which can be obtai…
We study one pion production in both charged and neutral current neutrino nucleus scattering for neutrino energies below 2 GeV. We use a theoretical model for one pion production at the nucleon level that we correct for medium effects. The results are incorporated into a cascade program that apart from production also includes the pion final state interaction inside the nucleus. Besides, in some specific channels coherent pion production is also possible and we evaluate its contribution as well. Our results for total and differential cross sections are compared with recent data from the MiniBo…
We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. It is important that the transf…
We apply a Color Glass Condensate+Non-Relativistic QCD (CGC+NRQCD) framework to compute $J/ψ$ production in deuteron-nucleus collisions at RHIC and proton-nucleus collisions at the LHC. Our results match smoothly at high $p_\perp$ to a next-to-leading order perturbative QCD + NRQCD computation. Excellent agreement is obtained for $p_\perp$ spectra at RHIC and LHC for central and forward rapidities, as well as for the normalized ratio $R_{pA}$ of these results to spectra in proton-proton collisions. In particular, we observe that the $R_{pA}$ data is strongly bounded by our computations of the …
We study the impact of the description of the knockout nucleon wave function on electron- and neutrino-induced quasielastic and single-pion production cross sections. We work in a fully relativistic and quantum mechanical framework, where the relativistic mean-field model is used to describe the target nucleus. The focus is on Pauli blocking and the distortion of the final nucleon, these two nuclear effects are separated and analyzed in detail. We find that a proper quantum mechanical treatment of these effects is crucial to provide the correct magnitude and shape of the inclusive cross sectio…
Background: 12C has been and is still widely used in neutrino-nucleus scattering and oscillation experiments. More recently, 40Ar has emerged as an important nuclear target for current and future experiments. Liquid argon time projection chambers (LArTPCs) possess various advantages in measuring electroweak neutrino-nucleus cross sections. Concurrent theoretical research is an evident necessity. Purpose: 40Ar is larger than 12C, and one expects nuclear effects to play a bigger role in reactions. We present inclusive differential and total cross section results for charged-current neutrino scat…
We investigate inclusive prompt photon and semi-inclusive prompt photon-hadron production in high energy proton-nucleus collisions using the Color Glass Condensate (CGC) formalism which incorporates non-linear dynamics of gluon saturation at small x via Balitsky-Kovchegov equation with running coupling. For inclusive prompt photon production, we rewrite the cross-section in terms of direct and fragmentation contributions and show that the direct photon (and isolated prompt photon) production is more sensitive to gluon saturation effects. We then analyze azimuthal correlations in photon-hadron …
