Strong Color Fields Research Articles

Spin polarization and correlation of quarks from the glasma

We investigate the interaction of strong color fields in the glasma stage of high-energy nuclear collisions with the spins of quarks and antiquarks. We employ the perturbative solution of the quantum kinetic theory for the spin transport of (massive) quarks in a background color field governed by the linearized Yang-Mills equation and derive expressions for the quark-spin polarization and quark-antiquark spin correlation at small momentum in terms of field correlators. For the Golec-Biernat W\"usthoff dipole distribution the quark-spin polarization vanishes, but the out-of-plane spin correlation of quarks and antiquarks is nonzero. Our order-of-magnitude estimate of the correlation far exceeds that caused by vorticity effects, but does not fully explain the data for vector meson alignment. We identify possible mechanisms that could further increase the predicted spin correlation.

Diffusion of heavy quarks in the early stage of high-energy nuclear collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

We study the diffusion of charm and beauty in the early stage of high energy nuclear collisions at RHIC and LHC energies, considering the interaction of these heavy quarks with the evolving Glasma by means of the Wong equations. In comparison with previous works, we add the longitudinal expansion as well as we estimate the effect of energy loss due to gluon radiation. We find that heavy quarks diffuse in the strong transverse color fields in the very early stage (0.2-0.3 fm/c) and this leads to a suppression at low $p_T$ and enhancement at intermediate low $p_T$. The shape of the observed nuclear suppression factor obtained within our calculations is in qualitative agreement with the experimental results of the same quantity for $D-$mesons in proton-nucleus collisions. We compute the nuclear suppression factor in nucleus-nucleus collisions as well, for both charm and beauty, finding a substantial impact of the evolving Glasma phase on these, suggesting that initialization of heavy quarks spectra in the quark-gluon plasma phase should not neglect the early evolution in the strong gluon fields.

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

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 approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_\perp$, and it deviates from the perturbative calculation at small $p_\perp$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_\perp$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

Topological charge fluctuations in the Glasma

The early-time evolution of the system generated in ultra-relativistic heavy ion collisions is dominated by the presence of strong color fields known as Glasma fields. These can be described following the classical approach embodied in the Color Glass Condensate effective theory, which approximates QCD in the high gluon density regime. In this framework we perform an analytical first-principles calculation of the two-point correlator of the divergence of the Chern-Simons current at proper time τ = 0+, which characterizes the early fluctuations of axial charge density in the plane transverse to the collision axis. This object plays a crucial role in the description of anomalous transport phenomena such as the Chiral Magnetic Effect. We compare our results to those obtained under the Glasma Graph approximation, which assumes gluon field correlators to obey Gaussian statistics. While this approach proves to be equivalent to the exact calculation in the limit of short transverse separations, important differences arise at larger distances, where our expression displays a remarkably slower fall-off than the Glasma Graph result (1/r4 vs. 1/r8 power-law decay). This discrepancy emerges from the non-linear dynamics mapping the Gaussianly-distributed color source densities onto the Glasma fields, encoded in the classical Yang-Mills equations. Our results support the conclusions reached in a previous work, where we found indications that the color screening of correlations in the transverse plane occurs at relatively large distances.

Multiplicity-dependent pT distributions of identified particles in pp collisions at 7 TeV within the HIJING/ BB¯ v2.0 model

Effects of strong longitudinal color fields (SCF) on the identified (anti)particle transverse momentum ($p_T$) distributions in $ pp$ collision at $\sqrt{s}$ = 7 TeV are investigated within the framework of the {\small HIJING/B\=B v2.0} model. The comparison with the experiment is performed in terms of the correlation between mean transverse momentum ($\langle p_t\rangle$) and multiplicity (N$_{ch}^*$) of charged particles at central rapidity, as well as the ratios of the $p_T$ distributions to the one corresponding to the minimum bias (MB) pp collisions at the same energy, each of them normalized to the corresponding charged particle density, for high multiplicity $\mbox{(HM, N$_{ch}>100$)}$ and low multiplicity $\mbox{(LM, N$_{ch}<100$)}$ class of events. The theoretical calculations show that an increase of the strength of color fields (as characterized by the effective values of the string tension $\kappa$), from $\kappa$ = 2 GeV/fm to $\kappa$ = 5 GeV/fm from LM to HM class of events, respectively, lead to a ratio at low and intermediate $p_T$ (i.e., \mbox{$ 1$GeV/{\it c} $< p_{T} < 6 $ GeV/{\it c}}) consistent with recent data obtained at LHC by the ALICE Collaboration.

Cathode tube effect: Heavy quarks probing the glasma in p -Pb collisions

We study the propagation of charm quarks in the early stage of high energy proton-lead collision, considering the interaction of these quarks with the evolving glasma by means of the Wong equations. Neglecting quantum fluctuations at the initial time, the glasma is made of longitudinal fields, but the dynamics leads to a quick formation of transverse fields; we estimate such a formation time as $\mathrm{\ensuremath{\Delta}}t\ensuremath{\approx}0.1\text{ }\text{ }\mathrm{fm}/\mathrm{c}$, which is of the same order of the formation time of heavy quark pairs ${t}_{\text{formation}}\ensuremath{\approx}\phantom{\rule{0ex}{0ex}}1/(2m)$. Limiting ourselves to the simple case of a static longitudinal geometry, we find that heavy quarks are accelerated by the strong transverse color fields in the early stage and this leads to a tilting of the $c$-quarks spectrum towards higher ${p}_{T}$ states. This average acceleration can be understood in terms of drag and diffusion of $c$-quarks in a hot medium and appears to be similar to the one felt by the electrons ejected by the electron cannon in a cathode tube: we dub this effect as cathode tube effect. The tilting of the spectrum affects the nuclear modification factor, ${R}_{\mathrm{pPb}}$, suppressing this below one at low ${p}_{T}$ and making it larger than one at intermediate ${p}_{T}$. We compute ${R}_{\mathrm{pPb}}({p}_{T})$ after the evolution of charm quarks in the gluon fields and we find that its shape is in qualitative agreement with the measurements of the same quantity for $D$-mesons in proton-lead collisions.

Single inclusive forward hadron production at next-to-leading order

We discuss single inclusive hadron production from a high energy quark scattering off a strong target color field in the Color Glass Condensate formalism. Recent calculations of this process at the next-to-leading order accuracy have led to negative cross sections at large transverse momenta. We identify the origin of this problem as an oversubtraction of the rapidity divergence into the Balitsky-Kovchegov evolution equation for the target. We propose a new way to implement the kinematical restriction on the emitted gluons to overcome this difficulty.

Two-gluon rapidity correlations of strong colour field in pp, pA and AA collisions

Using the CGC formalism, we calculate the two-gluon rapidity correlations of strong colour fields in pp, pA and AA collisions, respectively. If one trigger gluon is fixed at central rapidity, a ridge-like correlation pattern is obtained in symmetry pp and AA collisions, and a huge bump-like correlation pattern is presented in asymmetry pA collisions. It is demonstrated that long-range ridge-like rapidity correlations are caused by the stronger correlation with the gluon of colour source. These features are independent of the azimuthal angular of two selected gluon. They are qualitatively consistent with current observed data at LHC. The transverse momentum and incident energy dependence of the ridge and bump-like correlations are also systematically studied. The ridge is more likely observed at higher incident energy and lower transverse momentum of trigger gluon.

JIMWLK evolution for multi-particle production with rapidity correlations

We study multi-particle production with rapidity correlations in proton-nucleus collisions at high energy in the Color Glass Condensate framework. The high-energy evolution responsible for such correlations is governed by a generalization of the JIMWLK equation describing the simultaneous evolution of the strong nuclear color fields in the direct amplitude and the complex conjugate amplitude. This functional equation can be used to derive ordinary evolution equations for the cross-sections for particle production, but the ensuing equations appear to be too complicated to be useful in practice, including in the limit of a large number of colors Nc. We propose an alternative formulation based on a Langevin process, which is valid for generic Nc and is better suited for numerical implementations. For illustration, we present the stochastic equations which govern two gluon production with arbitrary rapidity separation.

Color Glass Condensate in Schwinger–Keldysh QCD

Within the Schwinger–Keldysh representation of many-body QCD, it is shown that the leading quantum corrections to the strong classical color field are “classical” in the sense that the fluctuation field still obeys the classical Jacobi-field equation, while the quantum effects solely reside in the fluctuations of the initial field configurations. Within this context, a systematic derivation of the JIMWLK renormalization group equation is presented. A clear identification of the correct form of gauge transformation rules and the correct form of the matter-field Lagrangian in the Schwinger–Keldysh QCD is also presented.

Exploring Gluonic Matter with Electron–Ion Collisions

Abstract Light and heavy nuclei probed in deep inelastic scattering and diffractive processes in the high-energy regime open a new precision window into fundamental questions in QCD. The proposed Electron–Ion Collider (EIC) is a new high-energy and high-luminosity electron–ion machine. The design offers unprecedented access to explore the nature of QCD matter and strong color fields. In particular, the new collider will allow us to reach and explore the regime where the gluon density saturates, one of the fundamental outstanding questions in QCD, and test the validity of the Color Glass Condensate approach. Selected key measurements in electron–ion collisions with an emphasis on probing and characterizing the gluonic matter are discussed.

Forward particle correlations in the color glass condensate

Multiparticle correlations, such as forward dihadron correlations in pA collisions, are an important probe of the strong color fields that dominate the initial stages of a heavy ion collision. We describe recent progress in understanding two-particle correlations in the dilute-dense system, e.g. at forward rapidity in deuteron-gold collisions. This requires evaluating higher point Wilson line correlators from the JIMWLK equation, which we find well described by a Gaussian approximation. We then calculate the dihadron correlation, including both the "elastic" and "inelastic" contributions, and show that our result includes the double parton scattering contribution.

Anisotropic flows from colour strings: Monte Carlo simulations

By direct Monte-Carlo simulations it is shown that the anisotropic flows can be successfully described in the colour string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Quenching of produced particles in the strong colour field of the string is the basic mechanism for this anisotropy. The concrete realization of this mechanism is borrowed from the QED. Due to dependence of this mechanism on the external field strength the found flows grow with energy, with values for $v_2$ at LHC energies greater by ~15% than at RHIC energies.

Comparing Two Different Initial Conditions AAMQS and Quartic Action in Illustrating the Effect of Valence Color Charges in High-EnergypACollisions at Forward Rapidity

The inclusive particle productions in proton-proton (pp) and deuton-gold (d+Au) collisions at forward rapidity at the Relativistic Heavy Ion Collider (RHIC) energy are studied in the framework of the color glass condensate (CGC) theory by using two different initial conditions: AAMQS (Albacete-Armesto-Milhano-Quiroga-Salgado) and quartic action. Then, the results obtained by the two different initial conditions in illustrating the effect of valence color charges in high-energy proton-nucleus (pA) collisions at forward energy are compared. Meanwhile, the inclusive particle productions inpAcollisions at forward rapidity at the Large Hadron Collider (LHC) energies are predicted. The main dynamical input in our calculations is the use of solutions of the running coupling Balitsky-Kovchegov equation tested in electron-proton (ep) collision data. Particle production is computed via the hybrid formalisms to obtain spectra and yields. These baseline predictions are useful for testing the current understanding of the dynamics of very strong color fields against the upcoming LHC data.

Hyperon/meson ratios in rare high-multiplicityppcollisions at energies available at the Large Hadron Collider, and potential signatures for mini-quark-gluon plasma formation

We use the framework of the HIJING/B\=B v2.0 model to simulate high-multiplicity (HM) $p+p$ collision events at the Large Hadron Collider (LHC) to study observables sensitive to possible collective phenomena, such as strong longitudinal color fields (SLCF) modeled by an enhanced string tension ($\kappa$). We focus on the hyperon/meson yield ratios at center-of-mass (c.m.) energy $\sqrt{s}$ = 7 TeV, in the transverse momentum region, $1 < p_T < 4 $ GeV/{\it c}. For minimum bias events these ratios are well described assuming an energy dependence $\kappa = \kappa(s)= \kappa_{0} (s/s_{0})^{0.04} {\rm GeV/fm}$ ($\kappa_{0}$= 1 GeV/fm), giving a value $\kappa = 2$ GeV/fm at $\sqrt{s}$ = 7 TeV. We compare minimum bias (MB) events to simulated HM events assuming that $\kappa(MB)=2$ GeV/fm could grow to an extreme value of $\kappa(HM)=5$ GeV/fm that saturates the strangeness suppression factor. With this assumption the model predicts a very strong enhancement of (multi)strange baryon/meson ratios in HM events. If observed, such an enhancement could be also interpreted as a possible signature for formation in HM $p+p$ collision events of a deconfined but out of local thermal equilibrium {\em mini quark-gluon plasma} (mQGP).

Production of K∗(892)0 and ϕ(1020) in pp collisions at $\sqrt{s}=7\ \mathrm{TeV}$

The production of K$^{*}$(892)$^{0}$ and $\phi$(1020) in pp collisions at $\sqrt{s}=7$ TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra d$^{2}$N/d$y$d$p_{\rm T}$ at midrapidity $|y|<0.5$ in the range $0<p_{\rm T}<6$ GeV/$c$ for K$^{*}$(892)$^{0}$ and $0.4<p_{\rm T}<6$ GeV/$c$ for $\phi$(1020) are reported and compared to model predictions. Using the yield of pions, kaons, and Omega baryons measured previously by ALICE at $\sqrt{s}=7$ TeV, the ratios K$^{*}$/K$^{-}$, $\phi$/K$^{*}$, $\phi$/K$^{-}$, $\phi/\pi^{-}$, and ($\Omega$ + $\overline{\Omega}$)/$\phi$ are presented. The values of the K$^{*}$/K$^{-}$, $\phi$/K$^{*}$ and $\phi$/K$^{-}$ ratios are similar to those found at lower centre-of-mass energies. In contrast, the $\phi/\pi^{-}$ ratio, which has been observed to increase with energy, seems to saturate above 200 GeV. The ($\Omega$ + $\overline{\Omega}$)/$\phi$ ratio in the $p_{\rm T}$ range $1$-$5$ GeV/$c$ is found to be in good agreement with the prediction of the HIJING/BB v2.0 model with a strong colour field.

Azimuthal Collimation of Long Range Rapidity Correlations by Strong Color Fields in High Multiplicity Hadron-Hadron Collisions

The azimuthal collimation of dihadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the color glass condensate (CGC) effective theory [A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi, and R. Venugopalan, Phys. Lett. B 697, 21 (2011).] by N(c)(2) suppressed multiladder QCD diagrams that are enhanced α(S)(-8) due to gluon saturation in hadron wave functions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger dihadron yields and predict further systematics of these yields with varying trigger p(T) and charged hadron multiplicity. Radial flow generated by rescattering is strongly limited by the structure of the p+p dihadron correlations. In contrast, radial flow explains the systematics of identical measurements in heavy ion collisions.

Baryon anomaly and strong color fields in Pb + Pb collisions at 2.76ATeV at the CERN Large Hadron Collider

With the HIJING/B$\ifmmode\bar\else\textasciimacron\fi{}B$ v2.0 heavy ion event generator, we explore the phenomenological consequences of several high parton density dynamical effects predicted in central Pb+Pb collisions at the Large Hadron Collider (LHC) energies. These include (1) jet quenching due to parton energy loss ($dE/dx$), (2) strangeness and hyperon enhancement due to strong longitudinal color field (SCF), and (3) enhancement of baryon-to-meson ratios due to baryon-antibaryon junction (J$\ifmmode\bar\else\textasciimacron\fi{}J$) loops and SCF effects. The saturation/minijet cutoff scale ${p}_{0}(s,A)$ and effective string tension $\ensuremath{\kappa}(s,A)$ are constrained by our previous analysis of LHC $p+p$ data and recent data on the charged multiplicity for Pb+Pb collisions reported by the ALICE collaboration. We predict the hadron flavor dependence (mesons and baryons) of the nuclear modification factor ${R}_{AA}({p}_{T})$ and emphasize the possibility that the baryon anomaly could persist at the LHC up to ${p}_{T}\ensuremath{\sim}10$ GeV, well beyond the range observed in central Au+Au collisions at RHIC energies.

The initial spectrum of fluctuations in the little bang

High parton densities in ultra-relativistic nuclear collisions suggest a description of these collisions wherein the high energy nuclear wavefunctions and the initial stages of the nuclear collision are dominated by classical fields. This underlying paradigm can be significantly improved by including quantum fluctuations around the classical background fields. One class of these contributes to the energy evolution of multi-parton correlators in the nuclear wavefunctions. Another dominant class of unstable quantum fluctuations grow rapidly with proper time $\tau$ after the collision. These secular terms appear at each loop order; the leading contributions can be resummed to all loop orders to obtain expressions for final state observables. The all-order result can be expressed in terms of the spectrum of fluctuations on the initial proper time surface. We compute, in $A^\tau=0$ gauge, the essential elements in this fluctuation spectrum--the small quantum fluctuation modes in the classical background field. With our derivation in QCD, we have all the ingredients to compute inclusive quantities in heavy ion collisions at early times including i) all--order leading logs in Bjorken $x_{1,2}$ of the two nuclei, ii) all strong multiple scattering contributions, and iii) all-order leading secular terms. In the simpler analogous formalism for a scalar $\phi^4$ theory, numerical analysis of the behavior of the energy-momentum tensor is strongly suggestive of early hydrodynamic flow in the system. In QCD, in addition to studying the possible early onset of hydrodynamic behavior, additional important applications of our results include a) the computation of sphaleron transitions off-equilibrium, and b) "jet quenching", or medium modification of parton spectra, in strong color fields at early times.

CMS ridge effect at LHC as a manifestation of bremsstrahlung of gluons off quarks accelerated in a strong color field

The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with 1 GeV<p T <3 GeV. To understand the effect several possibilities have been discussed. In the letter we propose a simple qualitative mechanism which corresponds to gluon bremsstrahlung of quarks moving with acceleration defined by the string tension. The smallness of azimuthal angle difference Δφ along with large Δη at large multiplicities in this interval of p T are natural in this mechanism. The mechanism predicts also bremsstrahlung photons with mean values of p T ≈2.9 and 0.72 GeV.