Hard Thermal Loop Research Articles

Soft-gluon exchange matters: Isotropic screening in QCD kinetic theory

QCD kinetic theory simulations are a prominent tool for studying the nonequilibrium initial stages in heavy-ion collisions. Despite their success, all implementations rely on approximations of the hard thermal loop (HTL) screened matrix elements in the collision terms. In this paper, we present our results for different isotropic screening prescriptions in the elastic collision term for gluons. In particular, we go beyond the simple Debye-like screening form that is used in all current implementations and apply the isotropic HTL matrix element instead. For isotropic systems, the evolution is nearly unchanged, but when studying the equilibration process in a Bjorken expanding plasma, we find qualitative and quantitative differences in a range of moments of the distribution function, such as a decrease in the maximum pressure anisotropy by up to 50%. In contrast, we find no significant qualitative impact on the jet quenching parameter or on the late-time hydrodynamization dynamics of anisotropic plasmas, but observe systematically smaller values of η/s by about 10% that coincide with perturbative calculations at small couplings. Our study reveals that the choice of the screening prescription can lead to large corrections at early times, but is less important close to equilibrium. Published by the American Physical Society 2024

Correlation function of flavored fermion in holographic QCD

By using the gauge-gravity duality, we investigate the correlation function of flavored fermion in the Dp/Dp+4 model as top-down approaches of holographic QCD for p=4,3. The bulk spinor, as the source of the flavored fermion in QCD, is identified to the worldvolume fermion on the flavor Dp+4-branes and the standard form of its action can be therefore obtained by the T-duality rules in string theory. Keeping this in hand, we afterwards generalize the prescription for two-point correlation function in the AdS/CFT dictionary into general D-brane backgrounds and apply it to the case of p=4,3, i.e., the D4/D8 and D3/D7 approaches, respectively. Resultantly, our numerical calculation with the bubble background always displays discrete peaks in the correlation functions which imply the bound states created by the flavored fermions as the confinement in QCD. With the black brane background, the on-shell condition illustrated by the correlation function covers basically the dispersion curves of fermion obtained by the hard thermal loop approximation in the hot medium. Finally, we interpret the flavored fermions in the bubble background as baryons by taking into account a baryon vertex, then find the two-point correlation function is able to fit the lowest baryon spectrum. In this sense, we conclude remarkably that our top-down approach in this work could reveal the fundamental properties of QCD both in the confined and deconfined phases. Published by the American Physical Society 2024

Chemical freeze-out parameters via a functional renormalization group approach

We study the freeze-out parameters in a QCD-assisted effective theory that accurately captures the quantum and in-medium effects of QCD at low energies. The functional renormalization group approach is implemented in our work to incorporate the nonperturbative quantum, thermal, and density fluctuations. By analyzing the calculated baryon number susceptibility ratios χ2B/χ1B and χ3B/χ2B, we determine the chemical freeze-out temperatures and baryon chemical potentials in cases of hard thermal or dense loop improved μ-dependent gluon potential and μ-independent gluon potential. We calculate the χ4B/χ2B(κσ2) and χ6B/χ2B along the freeze-out line for both cases. It is found that κσ2 exhibits a nonmonotonic behavior in a low collision energy region and approaches one for lower collision energy. χ6B/χ2B shows a similar complicated behavior in our calculation. Published by the American Physical Society 2024

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

Power corrections to the photon polarization tensor in a hot and dense medium of massive fermions

We compute the O(k2) terms (power corrections) of the photon polarization tensor in a hot and dense medium of particles with a small but finite mass, i.e., 0<m≪T, μ. We perform our calculations within the hard thermal loop approximation in the real-time formalism, and evaluate the first nonzero mass corrections. For a renormalization scale Λ¯∼T, these mass contributions determine the temperature dependence of the power corrections. These results have direct implications in the computation of electric and magnetic susceptibilities of hot and dense media in equilibrium. We address such implications and make comparisons with previous results. Published by the American Physical Society 2024

Initial-state and final-state effects on hadron production in small collision systems

Heavy meson production in reactions with nuclei is an active new frontier to understand QCD dynamics and the process of hadronization in nuclear matter. Measurements in various colliding systems at RHIC and LHC, including Pb-Pb, Xe-Xe, O-O, p-Pb, and p-O, enable precision tests of the medium-size, temperature, and mass dependencies of the in-medium parton propagation and shower formation. We employ a coupled DGLAP evolution framework that takes advantage of splitting functions recently obtained in softcollinear effective theory with Glauber gluons (SCETG) and hard thermal loop (HTL) motivated collisional energy loss effects. With jet quenching effects constrained to the nuclear modification factor of charged hadrons in Pb-Pb collisions at 5.02 TeV, we present predictions for light and heavy-meson in Xe-Xe, O-O and p-Pb collisions at the LHC.We find that the nuclear modification scales non-trivially with the quark mass and medium properties. In particular, there can be sizeable collision-induced attenuation of heavy mesons in small systems such as oxygen-oxygen and high-multiplicity p-Pb events. Finally, we analyze the impact of different models of initial-state parton dynamics on the search for QGP signatures in small colliding systems.

Constraining the equation of state with heavy quarks in the quasi-particle model of QCD matter

In a quasi-particle model of QCD matter at finite temperature with thermal masses for quarks and gluons from hard thermal loops, the equation of state (EOS) can be described by an effective temperature dependence of the strong coupling g(T). Assuming the same effective coupling between the exchanged gluon and thermal partons, the EOS can also be related to parton energy loss. Based on the quasi-particle linear Boltzmann transport (QLBT) model coupled to a (3+1)-dimensional viscous hydrodynamic model of the quark-gluon plasma (QGP) evolution and a hybrid fragmentation-coalescence model for heavy quark hadronization, we perform a Bayesian analysis of the experimental data on D meson suppression RAA and anisotropy v2 at RHIC and the LHC. We achieve a simultaneous constraint on the QGP EOS and the heavy quark transport coefficient, both consistent with the lattice QCD results.

Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge

We compute the next-to-leading order (NLO) hard correction to the gluon self-energy tensor with arbitrary soft momenta in a hot and/or dense weakly coupled plasma in Quantum Chromodynamics. Our diagrammatic computations of the two-loop and power corrections are performed within the hard-thermal-loop (HTL) framework and in general covariant gauge, using the real-time formalism. We find that after renormalization our individual results are finite and gauge-dependent, and they reproduce previously computed results in Quantum Electrodynamics in the appropriate limit. Combining our results, we also recover a formerly known gauge-independent matching coefficient and associated screening mass in a specific kinematic limit. Our NLO results supersede leading-order HTL results from the 1980s and pave the way to an improved understanding of the bulk properties of deconfined matter, such as the equation of state.

Collective bulk excitations in the QGP: From the weakly non‐ideal case to the strong correlation limit

AbstractCollective bulk excitation propagating in the medium of a quark‐gluon plasma are studied. The quark‐gluon plasma medium is described with two different models to investigate the effect of binary collisions and shear viscosity to account for damping and non‐ideality. To find the dispersion relation the longitudinal dielectric functions of the quark‐gluon plasma are used within quantum hydrodynamics and transport equation approaches. The results were obtained numerically by finding the roots of the dispersion relations. Both models are compared with the hard thermal loop approximation as the ideal case for both models.

Two-loop hard thermal loops for vector bosons in general models

Hard thermal loops describe how soft gauge fields are screened and damped in hot plasmas. As such they are used to calculate transport coefficients, Sphaleron rates, equations of state, and particle production. However, most calculations are done using one-loop hard thermal loop self-energies. And two-loop contributions can be large. To that end this paper provides vector two-loop self-energies for generic models: any scalar, fermion, or vector representation; and all possible renormalizable terms. Several examples are given to showcase the results. Two-loop results for higher-point functions are also given.

NLO quark self-energy and dispersion relation using the hard thermal loop resummation

Using the hard-thermal-loop (HTL) resummation in real-time formalism, we study the next-to-leading order (NLO) quark self-energy and corresponding NLO dispersion laws. In NLO, we have replaced all the propagators and vertices with the HTL-effective ones in the usual quark self-energy diagram. Additionally, a four-point vertex diagram also contributes to the quark NLO self-energy. We calculate the usual quark self-energy diagram and the four-point vertex diagram separately. Using those, we express the NLO quark self-energy in terms of the three- and four-point HTL-effective vertex functions. Using the Feynman parametrization, we express the integrals containing the three- and four-point HTL effective vertex functions in terms of the solid angles. After completing the solid angle integrals, we numerically calculate the momentum integrals in the NLO quark self-energy and plot them as a function of the ratio of momentum and energy. Using the NLO quark self-energy, we plot the NLO correction to dispersion laws.

Classical off-shell currents

We consider tree-level off-shell currents of two massive particles and n massless bosons in the classical limit, which can be fused into the classical limit of n + 2 scattering amplitudes. We show that dressing up the current with coherent wave-functions associated with the massive particles leads to the recently proposed Worldline Quantum Field Theory (WQFT) path integral. The currents thus constructed encode solutions of classical equations of motion so they can be applied to contexts where the classical limit is relevant, including hard thermal loops. We give several examples of these currents in scalar, gauge and gravitational theories.

Estimation of the diffusion coefficient of heavy quarks in light of Gribov-Zwanziger action

The heavy quark momentum diffusion coefficient (κ) is one of the most essential ingredients for the Langevin description of heavy quark dynamics. In the temperature regime relevant to the heavy ion collision phenomenology, a substantial difference exists between the lattice estimations of κ and the corresponding leading order (LO) result from the hard thermal loop (HTL) perturbation theory. Moreover, the indication of poor convergence in the next-to-leading order (NLO) perturbative analysis has motivated the development of several approaches to incorporate the non-perturbative effects in the heavy quark phenomenology. In this work, we estimate the heavy quark diffusion coefficient based on the Gribov-Zwanziger prescription. In this framework, the gluon propagator depends on the temperature-dependent Gribov mass parameter, which has been obtained self-consistently from the one-loop gap equation. Incorporating this modified gluon propagator in the analysis, we find a reasonable agreement with the existing lattice estimations of κ within the model uncertainties.

Hamiltonian formalism for Fermi excitations in a plasma with a non-Abelian interaction

The Hamiltonian theory for the collective longitudinally polarized colorless gluon excitations (plasmons) and for collective quark–antiquark excitations with abnormal relation between chirality and helicity (plasminos) in high-temperature quark–gluon plasma (QGP) is developed. For this purpose, Zakharov’s formalism for constructing the wave theory in nonlinear media with dispersion is used. A generalization of the Poisson superbracket involving both commuting and anticommuting variables to the case of a continuous medium is performed and the corresponding Hamilton equations are presented. The canonical transformations including simultaneously both bosonic and fermionic degrees of freedom of the collective excitations in QGP are discussed and a complete system of the canonicity conditions for these transformations is written out. An explicit form of the effective fourth-order Hamiltonians describing the elastic scattering of plasmino off plasmino and plasmino off plasmon is found and the Boltzmann-type kinetic equations describing the processes of elastic scattering are obtained. A detailed comparison of the effective amplitudes defined within the (pseudo)classical Hamiltonian theory, with the corresponding matrix elements calculated early in the framework of high-temperature quantum chromodynamics in the so-called hard thermal loop approximation, is performed. This enables one to obtain, in particular, an explicit form of the vertex and coefficient functions in the effective amplitudes and in the canonical transformations, correspondingly, and also to define the validity of a purely pseudoclassical approach in the Hamiltonian description of the dynamics of quark–gluon plasma. The problem of determining the higher-order coefficient functions in the canonical transformations of fermionic and bosonic normal variables is considered. With the help of the coefficient functions obtained, the totally symmetric effective amplitudes of the elastic scattering of plasmino off plasmon and plasmino off plasmino are written out.

All Order Resummed Leading and Next-to-Leading Soft Modes of Dense QCD Pressure.

The cold and dense QCD equation of state at high baryon chemical potential μ_{B} involves at order α_{s}^{2} an all-loop summation of the soft mode m_{E}∼α_{s}^{1/2}μ_{B} contributions. Recently, the complete soft contributions at order α_{s}^{3} were calculated using the hard thermal loop formalism. By identifying massive renormalization group properties of the hard thermal loop theory, we resum to all orders α_{s}^{p}, p≥3 the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions that show visible deviations from the state-of-the art results, and noticeably reduce residual scale dependence. Our results should help to reduce uncertainties in extending the equation of state in the intermediate μ_{B} regime, relevant in particular for the phenomenology of neutron stars.

Dual QCD thermodynamics at finite temperature and chemical potential

A Dual QCD formulation for [Formula: see text] color gauge has been developed in terms of dual gauge potentials, building on our previously published study for the [Formula: see text] case with zero bario-chemical potential [H. C. Chandola, G. Punetha and H. Dehnen, Nucl. Phys. A 945, 226 (2016).] and taking into account the local as well as topological structure of the color gauge group into its dynamics. For the purpose of examining the nonperturbative characteristics of QCD, the dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been examined. The thermal behavior of the nonperturbative QCD vacuum has been investigated for exploring the dynamics of quark-hadron phase transition at finite chemical potential. Related thermodynamic quantities and equation of state (EoS) to characterize quark matter have also been discussed within the framework of dual QCD-based hadronic bag which guarantees the critical parameters and the associated critical points for quark-hadron phase transition. These thermodynamic quantities are expected to play important roles in understanding the order of quark-hadron phase transition and are likely to predict the features of a first-order quark-hadron phase transition for finite chemical potential. Moreover, we have investigated the bulk properties of quark matter by constructing the free energy change and the associated surface tension for quark-hadron phase transition. For consistency and compatibility check, we have also compared our results with state-of-the-art three-loop Hard Thermal Loop perturbative results and available lattice QCD results and in the process found reasonable agreements.

Impact of EMC effect on D meson modification factor in equilibrating QGP

In this article we employ the nuclear EMC effect to extract the parton distribution functions (PDFs) inside the Lead (Pb) and Gold (Au) nuclei. Extracted PDFs are utilized to obtain the transverse momentum dependent (TMD) ones, using the computing codes like Pythia 8 or MCFM-10. Through this procedure TMDPDFs for charm and bottom quarks in Au at $\sqrt{s_{NN}}=200\;GeV$, Pb at $\sqrt{s_{NN}}=2.76\;TeV$ and $\sqrt{s_{NN}}=5.02\;TeV$ are calculated. To evaluate the validity of results and investigate the influence of nuclear EMC effect, the numerated TMDs are used as input to estimate heavy quark modification factor $R_{AA}$ at transverse plane $P_T$. This observable is calculated through numerical solution of the Fokker-Planck equation. For this purpose we need to extract the drag and diffusion coefficients, using the hard thermal loop correction. It is done in the frame work of the relativistic hydrodynamics up to the third order approximation of gradient expansion. The results are compared with same solutions when the input PFDs are considered inside the unbounded protons where the nuclear effect is not included. The comparison indicates a significant improvement of computed $R_{AA}$ with available experimental data when the EMC effect is considered.

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.

Scheme dependence of two-loop hard thermal loop perturbation theory resummed SYM4,4 thermodynamics

The resummed thermodynamics of ${\cal N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions ($\text{SYM}_{4,4}$) has been calculated previously to two loop order within hard thermal loop perturbation theory (HTLpt) using the canonical dimensional regularization (DRG) scheme. Herein, we revisit this calculation using the regularization by dimensional reduction (RDR) scheme. Since the RDR scheme manifestly preserves supersymmetry it is the preferred scheme, however, it is important to assess if and by how much the resummed perturbative results depend on the regularization scheme used. Comparing predictions for the scaled entropy obtained using the DRG and RDR schemes we find that for $\lambda \lesssim 6$ they are numerically very similar. We then compare the results obtained in both schemes with the strict perturbative result, which is accurate up to order $\lambda^2$, and a generalized Pad\'{e} approximant constructed from the known large-$N_c$ weak- and strong-coupling expansions. Comparing the strict perturbative expansion of the two-loop HTLpt result with the perturbative expansion to order $\lambda^2$, we find that both the DRG and RDR HTLpt calculations result in the same scheme-independent predictions for the coefficients at order $\lambda$, $\lambda^{3/2}$, and $\lambda^2 \log\lambda$, however, at order $\lambda^2$ there is a residual regularization scheme dependence.

Static quark-antiquark interactions at nonzero temperature from lattice QCD

We study the interactions of a static quark-antiquark pair at nonzero temperature using realistic $2+1$ flavor lattice QCD calculations. The study consists of two parts. The first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a hard-thermal-loop-inspired fit for the correlation function, Pad\'e rational approximation and the Bayesian reconstruction. We find that our high-statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well-defined ground state spectral peak.