Effective Gluon Research Articles

Reentrant Condensation of Polyelectrolytes Induced by Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects.

We explore the reentrant condensation of polyelectrolytes triggered by multivalent salts, whose phase-transition mechanism remains under debate. We propose a theory to study the reentrant condensation, which separates the electrostatic effect into two parts: a short-range electrostatic gluonic effect because of sharing of multivalent ions by ionic monomers and a long-range electrostatic correlation effect from all ions. The theory suggests that the electrostatic gluonic effect governs reentrant condensation, requiring a minimum coupling energy to initiate the phase transition. This explains why diluted salts with selective multivalency trigger a polyelectrolyte phase transition. The theory also uncovers that strong adsorption of multivalent ions onto ionic monomers causes low-salt concentrations to induce both collapse and reentry transitions. Additionally, we highlight how the incompatibility of uncharged polyelectrolyte moieties with water affects the polyelectrolyte phase behaviors. The obtained results will contribute to the understanding of biological phase separations if multivalent ions bound to biopolyelectrolytes play an essential role.

The nuclear shadowing effect of gluon at small x

The ratio of nuclear gluon distribution functions xgA/Axg in the saturation region at small x (i.e., x≲10−3) for light and heavy nuclei is investigated and compared with the HIJING2.0 model. The moments of the nuclear gluon distribution per nucleon, <xA>g/A, on a wide range of the scale μ with charm contribution are considered and compared with the parametrization groups. The importance of the binding energy for nuclei is also considered.

Nonlinear Schwinger mechanism in QCD, and Fredholm alternatives theorem

We present a novel implementation of the Schwinger mechanism in QCD, which fixes uniquely the scale of the effective gluon mass scale and streamlines considerably the procedure of multiplicative renormalization. The key advantage of this method stems from the nonlinear nature of the dynamical equation that generates massless poles in the longitudinal sector of the three-gluon vertex. An exceptional feature of this approach is an extensive cancellation involving the components of the integral expression that determines the gluon mass scale; it is triggered once the Schwinger–Dyson equation of the pole-free part of the three-gluon vertex has been appropriately exploited. It turns out that this cancellation is driven by the so-called Fredholm alternatives theorem, which operates among the set of integral equations describing this system. Quite remarkably, in the linearized approximation this theorem enforces the exact masslessness of the gluon. Instead, the nonlinearity induced by the full treatment of the relevant kernel evades this theorem, allowing for the emergence of a nonvanishing mass scale. The numerical results obtained from the resulting equations are compatible with the lattice findings, and may be further refined through the inclusion of the remaining fundamental vertices of the theory.

The complex heavy quarkonium potential with the Gribov–Zwanziger action

Gribov–Zwanziger prescription in Yang–Mills theory improves the infrared dynamics. In this work, we study the static potential of a heavy quark-antiquark pair with the HTL resummed perturbation method within the Gribov–Zwanziger approach at finite temperature. The real and imaginary parts of the heavy quarkonium complex potential are obtained from the one-loop effective static gluon propagator. The one-loop effective gluon propagator is obtained by calculating the one-loop gluon self-energies containing the quark, gluon, and ghost loop. The gluon and ghost loops are modified in the presence of the Gribov parameter. We also calculate the decay width from the imaginary part of the potential. We also discuss the medium effect of heavy quarkonium potential with the localized action via auxiliary fields.

Heavy quark diffusion coefficients in magnetized quark-gluon plasma

We evaluate the heavy quark momentum diffusion coefficients in a hot magnetized medium for the most general scenario of any arbitrary values of the external magnetic field. We choose to work with the systematic way of incorporating the effect of the magnetic field, by using the effective gluon and quark propagators, generalized for a hot and magnetized medium. To get gauge independent analytic form factors valid through all Landau levels, we apply the hard thermal loop technique for the resummed effective gluon propagator. The derived effective hard thermal loop gluon propagator and the generalized version of Schwinger quark propagator subsequently allow us to analytically evaluate the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Within the static limit we also explore another way of incorporating the effect of the magnetic field, i.e. through the magnetized medium modified Debye mass and compare the results to justify the need for structural changes. Published by the American Physical Society 2024

Yukawa potential under weak magnetic field

Weak magnetic field induced corrections for the Yukawa potential due to one pion exchange between two constituent quarks (nucleons) are presented. For that, the constant magnetic field effect on the pion propagator and on the pion form factor are taken into account. An effective gluon propagator parametrized with an effective gluon mass (Mg∼0.5 GeV) is considered. In the limit of magnetic field that is weak with respect to the constituent quark mass and pion mass, analytical and semianalytical expressions can be obtained. Different types of contributions are found, isotropic or anisotropic, dependent on the pion mass and also on the constituent quark and effective gluon masses. Overall the corrections are of the order of 2% to 5% of the Yukawa potential at distances close to 2 fm, and they decrease slower than the Yukawa potential. The anisotropic corrections are considerably smaller than the isotropic components. A sizable splitting between results due to the magnetic field dependent neutral or charged pion mass is found. Published by the American Physical Society 2024

Counting linearly polarized gluons with lattice QCD

We outline an approach to calculate the transverse-momentum-dependent distribution of linearly polarized gluons inside an unpolarized hadron on the lattice with the help of large momentum effective theory. To achieve this purpose, we propose calculating a Euclidean version of the degree of polarization for a fast-moving hadron on the lattice, which is ultraviolet finite, and no soft function subtraction is needed. It indicates a practical way to explore the distribution of the linearly polarized gluons in a proton and the linearly polarized gluon effects in hadron collisions on the lattice. Published by the American Physical Society 2024

Baryon correlations in Pythia

We present the results from our investigation of angular correlations between baryons pairs in the Pythia8 event generator. We show how colour reconnection models and hadronization mechanisms influence such angular correlations and in particular address the effect of gluons on the baryon production mechanism in the Lund string fragmentation model. We conclude by discussing the new theoretical ideas in comparison with the ALICE pp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{pp} $$\\end{document} collision results for the baryon angular correlations. We propose a hypothesis for suppressing baryons produced in gluon jets and show how that may influence the angular correlations.

Scalar propagator in a background gluon field beyond the eikonal approximation

We investigate the path integral representation of the scalar propagator in a background gluon field, extending beyond the eikonal approximation by considering all gauge field components and incorporating its x− dependence. Utilizing the worldline formalism, we integrate the Schwinger proper time to express the scalar propagator in light-cone coordinates, facilitating a direct comparison with known results in the literature. The derived propagator captures the change of longitudinal momentum of the projectile within the medium. In the high-energy limit, our result simplifies to the effective gluon propagator employed in the BDMPS-Z formalism. Hence, we propose that our outcome serves as a foundational point for investigating corrections to the BDMPS-Z spectrum arising from the longitudinal momentum transfer of the radiated gluon with the medium, as well as for studying collisional energy loss phenomena. Lastly, by employing an expansion around the classical saddle point solution, we systematically derive an eikonal expansion in inverse powers of the boost parameter, encompassing corrections related to longitudinal momentum transfer and interactions of the projectile with the transverse component of the field.

Shadowing corrections to the evolution of singlet structure function

In this paper, a semi-analytical approach is introduced to address the solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) evolution equation for sea quark distribution. Here the effect of gluon shadowing on the behaviour of singlet structure function, , has been investigated, particularly in the regime of small-x and moderate-Q 2. The predicted values of singlet structure functions with shadowing corrections align well with different experimental data and existing parametrizations. It is very fascinating to observe signatures of gluon recombination within these predictions. Notably, as x decreases, the rapid growth of singlet structure function is eventually tamed by the shadowing or nonlinear term appeared in the QCD evolution due to gluon recombination. This taming behaviour of shadowing singlet structure function towards small-x become significant at the hot spots, at R = 2 GeV−1. Further the computed ratios of with shadowing, in comparison to those without shadowing, clearly indicate that towards smaller values of x and Q 2 the nonlinear effects gradually become prominent.

Glauber gluon effects in soft collinear factorization

Effects of Glauber gluons, which cause the elastic scattering process between different jets, are studied in the frame of soft-collinear effective theory. Glauber modes are added into the action before being integrated out, which is helpful in studies on the Glauber couplings of collinear and soft particles. It is proved that the final state interactions cancel out for processes inclusive enough. So are interactions with the light cone coordinates x + and x − greater than those of the hard collision. The eikonalization of Glauber couplings of active particles and absorption of these couplings into soft and collinear Wilson lines are discussed, which is related to the loop level definitions of Glauber gluons here. The active-spectator coherence is proved to be harmless to the inclusive summation of spectator-spectator and spectator-soft Glauber exchanges. Based on this result, spectator-spectator and spectator-soft Glauber exchanges cancel out in the processes considered here. Graphic aspects of the cancellation are also discussed to explain relations between the graphic and operator level cancellation of Glauber gluons.

Exclusive J/ψ photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale-choice and PDFs, and compare our results with ALICE, CMS and LHCb $J/\psi$ photoproduction data in Pb+Pb UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in p+p. The scale dependence in $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$ is significant, but we can find a scale-choice that reproduces the Pb+Pb UPC data both at 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner where the relative signs of the LO and NLO terms in the amplitude play a significant role.

Gluon condensates and effective gluon mass

Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an $SU(3)$ gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios.

One-loop squared amplitudes for hadronic tW production at next-to-next-to-leading order in QCD

We present the analytic results of one-loop squared amplitudes for tW production at a hadron collider. The calculation is performed using the method of differential equations. After renormalization, we have checked that the infrared divergences agree with the general structure predicted by anomalous dimensions. The finite remainder contributes to the next-to-next-to-leading order hard function, one of the essential gradients in the factorization formula of the cross section near the infrared region, which can be used in resummation of all-order soft gluon effects or a differential next-to-next-to-leading order calculation based on the phase space slicing method.

Evidence for Nonlinear Gluon Effects in QCD and Their Mass Number Dependence at STAR.

The STAR Collaboration reports measurements of back-to-back azimuthal correlations of di-π^{0}s produced at forward pseudorapidities (2.6<η<4.0) in p+p, p+Al, and p+Au collisions at a center-of-mass energy of 200GeV. We observe a clear suppression of the correlated yields of back-to-back π^{0} pairs in p+Al and p+Au collisions compared to the p+p data. The observed suppression of back-to-back pairs as a function of transverse momentum suggests nonlinear gluon dynamics arising at high parton densities. The larger suppression found in p+Au relative to p+Al collisions exhibits a dependence of the saturation scale Q_{s}^{2} on the mass number A. A linear scaling of the suppression with A^{1/3} is observed with a slope of -0.09±0.01.

Heavy quark dynamics in a strongly magnetized quark-gluon plasma

We present a calculation of the heavy quark momentum diffusion coefficients in a quark-gluon plasma under the presence of a strong external magnetic field, within the Lowest Landau Level (LLL) approximation. In particular, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator, generalized for a hot and magnetized medium. Using the derived effective HTL gluon propagator and the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients as well as the energy losses for charm and bottom quarks beyond the static limit. We also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Understanding J/ψ and ψ′ production using a modified version of Non-Relativistic Quantum Chromodynamics

There is serious disagreement between the predictions of Non-Relativistic Quantum Chromodynamics (NRQCD) and the data on J/ψ polarisation which has persisted for almost a quarter of a century. We find that if we account for the effect of perturbative soft gluons on the intermediate charm-anticharm octet states in NRQCD then the polarisation problem can be resolved. In addition, this model, when used to fit the Run 1 data on J/ψ and ψ′ production from the CDF experiment at Tevatron, gives good fits and yields values of (energy-independent) non-perturbative parameters. These, in turn, can be used to make parameter-free predictions for J/ψ and ψ′ data from the CMS experiment at the Large Hadron Collider and the predictions are in excellent agreement with the CMS data.

Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field

Unusual constituent quark axial current couplings to light vector mesons, $\rho$ and $\omega$, are derived in the vacuum and under weak magnetic field by considering a quark-antiquark interaction mediated by a non perturbative gluon exchange. Similarly, light axial mesons are found to couple anomalously with the constituent quark vector current. These interactions are of the type of the Wess-Zumino-Witten terms, being strongly anisotropic and dependent on the vector (or axial) meson polarization. They also provide axial (vector) form factors for the vector (axial) mesons and are quite small, suppressed nearly by $1/{M^*}^2$ with respect to the vector mesons minimal coupling to the quark vector current. Some three leg meson vertices are also presented: $\pi-\rho-A_1$ and $V_1V_2 A$ (where $V_1,V_2$ are vector mesons and $A$ an axial meson). A vector and axial-vector mesons mixing is identified at non zero magnetic field which however can contribute only in the presence of a third particle or in a medium. Numerical results are presented for different effective gluon propagators.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Gluons, light and heavy quarks in the instanton vacuum

In this paper, we put our focus towards describing the nonperturbative effects in the properties of hadrons made from the light-heavy and the heavy–heavy quarks in the framework of Instanton Liquid Model (ILM) of QCD vacuum. The main features of ILM and its applicability in the heavy quark sector are briefly discussed. The properties of gluonic systems, the light and heavy quark correlators in the instanton background are also analyzed. We demonstrate that the consideration of both, perturbative and nonperturbative, gluon effects in the instanton background for a single heavy quark leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. For the interacting heavy quark and heavy anti-quark, the potential consists of the direct instanton-induced part and the one-gluon exchange (OGE) perturbative part. OGE interactions are screened at large distances due to the nonperturbative dynamics. The estimation of instanton contributions in the phenomenological Cornell-type potential model is presented. In relation to the experimental data, the charmonium properties, the role of instanton effects in their spectra and transitions are discussed. The main features of heavy-light quark systems in the instanton generated background are also discussed. As an example, we consider the process of pion emissions by the exited heavy quarkonium. We show that there is a sizable correction ([Formula: see text]) to the dipole approximation for the process [Formula: see text].