10 pages, 6 figures. Proceedings contribution to the XXXIII International (Online) Workshop on High Energy Physics "Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests", November 8-12, 2021
In covariant gauges, the gluonic mass gap in Yang-Mills theory manifests itself in the basic observation that the massless pole in the perturbative gluon propagator disappears in nonperturbative calculations, but the origin of this behavior is not yet fully understood. We summarize a recent study of the respective dynamics with Dyson-Schwinger equations in Landau-gauge Yang-Mills theory. We identify the parameter that distinguishes the massive Yang-Mills regime from the massless decoupling solutions, whose endpoint is the scaling solution. Similar to the PT-BFM scheme, we find evidence that mass generation in the transverse sector is triggered by longitudinal massless poles.
We report on how $J/ψ$- and $Υ$-pair production are promising processes to access the polarised and unpolarised gluon TMDs at the LHC. We present the formalism used, as well as resulting observables that could be extracted from data.
Exploiting the gauge-invariant properties of the PT-BFM truncation scheme for the gluon Schwinger-Dyson equation, we estimate the individual non-perturbative contribution of the "one-loop dressed" ghost loop to the gluon propagator. Using the available quenched lattice data for the gluon and the ghost propagators in d=4 and d=3, we determine how the overall shape of the gluon propagator is affected by the removal of the ghost loop, and what are the consequences on the phenomenon of gluon mass generation.
We show that studying the single top quark production via the $W$--gluon fusion process can provide unique information on: (i) the measurement of the decay width $\width$; (ii) probing the symmetry breaking mechanism by measuring the form factor of~\tbW; (iii) testing the Effective--$W$ Approximation prior to supercolliders; (iv) testing CP violation by observing different production rates of $\bar p p \ra t X $ and $\bar p p \ra \bar t X$; (v) testing CP violation from the almost hundred percent longitudinally polarized top quark decay; in addition to the measurement of the top quark mass. In…
Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings …
We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behaviour of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single va…
We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator A^2 in linear covariant gauges. We show that the formation of <A^2> is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.
We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of th…
Measurements involving the gluon spin density, Delta G=G++ - G+-, can play an important role in the quantitative understanding of proton structure. To demonstrate this, we show that the shape of the gluon asymmetry, A(x,t)=Delta G(x,t)/G(x,t), contains significant dynamical information about non-perturbative spin-orbit effects. It is instructive to use a separation A(x,t)=A_0^epsilon(x)+epsilon(x,t), where A_0^epsilon(x) is an approximately scale-invariant form that can be calculated within a given factorization prescription from the measured distributions Delta q(x,t), q(x,t) and G(x,t). Appl…
In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost con…
We review recent work on the effects of quark loops on the gluon propagator in the Landau gauge, relying mainly on the Schwinger-Dyson equations that describe the two-point sector of QCD. Particularly important in this context is the detailed study of how the standard gluon mass generation mechanism, which is responsible for the infrared finiteness of the quenched gluon propagator, is affected by the inclusions of dynamical quarks. This issue is especially relevant and timely, given the qualitative picture that emerges from recent unquenched lattice simulations. Our results demonstrate clearly…
Fixed points in QCD can appear when the number of quark flavors ($N_f$) is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass generation (DGM) does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $β$ functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical…
In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $β$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector…
A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborat…
We investigate gluon propagators and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \times$ U(1)$_8$ Landau gauge fixing in SU(3) lattice QCD. The Monte Carlo simulation is performed on $16^4$ at $β$=5.7, 5.8 and 6.0 and $32^4$ at $β=$5.8 and 6.0 at the quenched level. To calculate the propagators, we adopt a method to extract gauge fields from link-variables analytically in the SU(3) case. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\rm off} \simeq 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and the p…
Gluon mass generation is investigated for 4-dimensional $SU(N)$ Yang-Mills in conventional covariant and in background field gauges within an effective description that, through a parameterization, can be regarded as a massive gluon model, or as a Nambu-Jona-Lasinio-like expansion around a massive leading order while preserving the Yang-Mills Lagrangian. We employ a renormalization scheme that introduces the ratio of the gluon mass parameter $m$ to the saturation value of the gluon propagator. This, along with the mass $m(μ)$ and the strong coupling $α_s(μ)$, provided the fit parameters for co…
We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound-states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of…
We compute the contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations.
We show that the matrix element of a local quark-gluon operator in the photon state, $<γ(kλ)|\hat O| γ(kλ)>$, can be calculated in lattice QCD. The result is generalized to other quantities involving space-like photons, including the transition form factor $γγ^*\to π^0$ and the virtual-photon-nucleon Compton amplitude $<γ^*N |γ^*N>$ which can be used to define the generalized Drell-Hearn-Gerasimov and Bjorken sum rules.
We study the nonperturbative gluon and ghost propagators in d=3 Yang-Mills, using the Schwinger-Dyson equations of the pinch technique. The use of the Schwinger mechanism leads to the dynamical generation of a gluon mass, which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained are in very good agreement with the results of SU(2) lattice simulations.
We describe the phenomenon of dynamical gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which gives rise to effective vertices containing massless poles; these vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. In this particular approach, the gluon mass is directly related …
Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. The corresponding Bethe-Salpeter kernel is constructed from constraints by chiral symmetry. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as…
We have unambiguously established the dynamical source of the mass scale parameter (the mass gap) responsible for the large scale structure of the true QCD vacuum. At the microscopic, Lagrangian level it is the nonlinear fundamental four-gluon interaction. At the level of the corresponding equation of motion for the full gluon propagator, it is all the skeleton loop contributions into the gluon self-energy, which contain the four-gluon vertices. The key role of the four-gluon interaction is determined by the fact that this interaction survivies when all the gluon momenta involved go to zero, w…
We propose a new reformulation of Yang-Mills theory in which three- and four-gluon self-interactions are eliminated at the price of introducing a sufficient number of auxiliary fields. We discuss the validity of this reformulation in the possible applications such as dynamical gluon mass generation, color confinement and glueball mass calculation. We emphasize the transverse-gluon pair condensation as the basic mechanism for dynamical mass generation. The confinement is realized as a consequence of a fact that the auxiliary fields become dynamical in the sense that they acquire the kinetic ter…
Higgs bosons can be produced copiously at the LHC via gluon fusion induced by top and bottom quark loops, and can be enhanced strongly if extra heavy quarks exist. We present results for Higgs +zero-, one- and two-jet production at the LHC, in both the Standard Model and the 4th generation model, by evaluating the corresponding heavy quark triangle, box and pentagon Feynman diagrams. We compare the results by using the effective Higgs-gluon interactions in the limit of heavy quarks with the cross sections including the full mass dependences. NLO effects with full mass dependence are included i…
We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadr…
We present an explicit construction of the special part of the three gluon vertex, which incorporates the Schwinger mechanism into the Schwinger-Dyson equation of the gluon propagator, enabling the generation of a dynamical gluon mass. This vertex contains massless, longitudinally coupled poles, acting effectively as composite Nambu-Goldstone bosons, generated by the strong QCD dynamics. The basic ingredients required for this construction are the longitudinal nature of this vertex and the Slavnov-Taylor identities that it must satisfy, in order for gauge-invariance and BRST symmetry to remain…
The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains m…
We consider the transverse momentum dependent gluon distribution functions (called gluon TMDs) by studying the light-front gluon-gluon correlator, extending the results for unpolarized and vector polarized targets to also include tensor polarized targets -- the latter type of polarization is relevant for targets of spin $\ge1$. The light-front correlator includes process-dependent gauge links to guarantee color gauge invariance. As from the experimental side the gluon TMDs are largely unknown, we present positivity bounds for combinations of leading-twist gluon distributions that may be used t…
We analyze the possibilities for studying properties of dense QCD-matter, created in ultrarelativistic nuclear collisions, by hard QCD-production processes, so-called "hard" probes -- heavy quarkonia, hard jets, high mass dimuons. Special attention is paid to the potential of coming heavy ion experiments on Large Hadron Collider to observe the rescattering and energy losses of hard partons in quark-gluon plasma.
Recent large-volume lattice simulations have established that, in the Landau gauge, the gluon propagator is infrared-finite. The most natural way to explain this observed finiteness is the generation of a nonperturbative, momentum-dependent gluon mass. Such a mass may be generated gauge-invariantly by employing the Schwinger mechanism, whose main assumption is the dynamical formation of massless bound-state excitations. In this work we demonstrate that this key assumption is indeed realized by the QCD dynamics. Specifically, the Bethe-Salpeter equation describing the aforementioned massless ex…
We review the Pinch Technique - Background Field Method (PT-BFM) framework for formulating and solving the Schwinger-Dyson equations of Yang-Mills theories. In particular, we show how within this framework it is possible to write a new set of Schwinger-Dyson equations that (i) accommodate the dynamical gluon mass generation through Schwinger's mechanism, and (ii) have much better truncation properties than the the conventional equations. The resulting solutions show (in the Landau gauge) an infra-red saturating gluon propagator and ghost dressing function, in agreement with all lattice studies…
Schwinger operator method is applied for studying CP-odd pure gluonic effective Lagrangian in the Standard Model at three-loop level. The induced $θ$-term vanishes by the same reasons as EDMs of quark and W-boson to two-loop approximation. A simple way is found to demonstrate these cancellations. All other terms of the effective Lagrangian acquire non-vanishing contributions. The effective operator of dimension six, Weinberg operator, is calculated explicitly. The corresponding contribution to the EDM of neutron is much smaller than that comes from large distances.
We present a pedagogical overview of the nonperturbative mechanism that endows gluons with a dynamical mass. This analysis is performed based on pure Yang-Mills theories in the Landau gauge, within the theoretical framework that emerges from the combination of the pinch technique with the background field method. In particular, we concentrate on the Schwinger-Dyson equation satisfied by the gluon propagator and examine the necessary conditions for obtaining finite solutions within the infrared region. The role of seagull diagrams receives particular attention, as do the identities that enforce…
In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory we pay particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This causes a large bulge in the propagator at small momentum. Mass is defined through $m^{-2}=Δ(p=0)$, where $Δ(p)$ is the scalar function for the gluon propagator in some chosen gauge, it is not a pole mass and is generally gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We truncate the PT equations with a new method called the vertex paradigm that automatically…
The quark's behaviour while influenced by a strong stochastic gluon field is analyzed. An approximate procedure for calculating the effective Hamiltonian is developed and the corresponding ground state within the Hartree-Fock-Bogolyubov approach is found. The comparative analysis of various Hamiltonian models is given and transition to the chiral limit in the Keldysh model is discussed in detail.
We discuss the possibility of generation of baryon inhomogeneities in a quark-gluon plasma phase due to moving Z(3) interfaces. By modeling the dependence of effective mass of the quarks on the Polyakov loop order parameter, we study the reflection of quarks from collapsing Z(3) interfaces and estimate resulting baryon inhomogeneities in the context of the early universe. We argue that in the context of certain low energy scale inflationary models, it is possible that large Z(3) walls arise at the end of the reheating stage. Collapse of such walls could lead to baryon inhomogeneities which may…
In this work we investigate the possibility of generation of primordial magnetic field in the early universe near the QCD phase transition epoch via the collapse of $Z(3)$ domains. The $Z(3)$ domain walls arise in the deconfined phase of the QCD (above $T\sim 200$ MeV) and their collapse leads to a net quark concentration near the wall boundary due to non-trivial reflection of quarks. We look at the response of leptons to this quark excess and find that leptons do not cancel the electric charge concentration due to the quarks. The wall collapse and a net charge concentration can lead to the ge…
We investigate the possibility of studying E$_6$ phenomenology at high energy hadron colliders. The production of heavy leptons pairs {\it via} a gluon-gluon fusion mechanism is discussed. An enhancement in the parton level cross-section is expected due to the heavy (s)fermion loops which couple to the gluons.
The gluon mass generation is a purely non-perturbative effect, and the natural framework to study it in the continuum are the Schwinger-Dyson equations (SDEs) of the theory. At the level of the SDEs the generation of such a mass is associated with the existence of infrared finite solutions for the gluon propagator. From the theoretical point of view, the dynamical gluon mass generation has been traditionally plagued with seagull divergences. In this work, we will review how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization…
By studying the $η_c$ exclusive decay to double glueballs, we introduce a model to mimic phenomenologically the gluon-pair-vacuum interaction vertices, namely the $0^{++}$ model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly $η_c \to f_0(1500)η(1405)$, $η_b\to f_0(1500)η(1405)$ and $η_b\to f_0(1710)η(1405)$ processes. Among them $f_0(1500)$ and $f_0(1710)$ are well-known scalars possessing large glue components and $η(1405)$ is a potential candidate for pseudoscalar glueball. The preliminary calculation results indicate that these processes are…
We study a manifestly gauge invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in $d=3$ Yang-Mills. The use of the well-known Schwinger mechanism, in the Landau gauge, leads to the dynamical generation of a mass for the gauge boson (gluon in $d=3$), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of $SU(2)$ lattice simulations.
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
As a topic of "quantum color dynamics", we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended c…
We review recent progress of understanding and resolving instabilities driven by mismatch between the Fermi surfaces of the pairing quarks in 2-flavor color superconductor. With the increase of mismatch, the 2SC phase exhibits chromomagnetic instability as well as color neutral baryon current instability. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. The Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF sta…
The two flavour AdS/QCD, with chiral and gluon condensates, sets in the description of the pion family and its mass spectra. Using gravity-dilaton-gluon backgrounds, entropic Regge-like trajectories for the pion family are then derived. They relate the $π$ mesons underlying configurational entropy to both the pions excitation wave mode number and the pions experimental mass spectra, yielding a reliable prediction for the mass spectra of higher excitation pion modes, to be experimentally detected.
We summarise results on the infrared behaviour of Landau gauge QCD from the Green's functions approach and lattice calculations. Approximate, nonperturbative solutions for the ghost, gluon and quark propagators as well as first results for the quark-gluon vertex from a coupled set of Dyson-Schwinger equations are compared to quenched and unquenched lattice results. Almost quantitative agreement is found for all three propagators. Similar effects of unquenching are found in both approaches. The dynamically generated quark masses are close to `phenomenological' values. First results for the quar…
The exact nonperturbative confining solutions of the SU(3)-Yang-Mills equations recently obtained by author in Minkowski spacetime with the help of the black hole theory techniques are analysed and on the basis of them the gluon propagator corresponding to linear confinement at large distances (small momenta) is constructed in a nonperturbative way. At small distances (large momenta) the resulting propagator passes on to the standard (nonperturbative) gluon propagator used in the perturbative quantum chromodynamics (QCD). The results suggest some scenario of linear confinement for mesons and q…
We investigate the effect of a small, gauge-invariant mass of the gluon on the anomalous chromomagnetic moment of quarks (ACM) by perturbative calculations at one loop level. The mass of the gluon is taken to have been generated via a topological mass generation mechanism, in which the gluon acquires a mass through its interaction with an antisymmetric tensor field $B_{μν}$. For a small gluon mass $(<10$ MeV), we calculate the ACM at momentum transfer $q^2=-M_Z^2$. We compare those with the ACM calculated for the gluon mass arising from a Proca mass term. We find that the ACM of up, down, stra…
In this work, we investigate the effects of the ghost sector on the dynamical mass generation for the gauge boson of a pure Yang-Mills theory. The generation of a dynamical mass for the gluon is realized by the Schwinger mechanism, which is triggered by the existence of longitudinally coupled massless poles in the fundamental vertices of the theory. The appearance of such poles occurs by purely dynamical reasons and is governed by a set of Bethe-Salpeter equations. In previous studies, only the presence of massless poles in the background-gauge three-gluon vertex was considered. Here, we inclu…
The Gluon and Ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find t…
Quantum Diffusion Model for Quark and Gluon Jet Generation
University of Glasgow（格拉斯哥大学）；Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学）；EPFL（洛桑联邦理工学院）；Technische Universität Dortmund（多特蒙德工业大学）；CERN（欧洲核子研究组织）；University of Florida（佛罗里达大学）；University of Kansas（堪萨斯大学）；University of Alabama（阿拉巴马大学）
A measurement for studying the mass dependence of the dilepton interferometry in relativistic heavy-ion collision experiments as a tool to characterize the quark-gluon phase is proposed. In calculations involving dileptons, we show that the mass dependence of radii extracted from the virtual photon (dilepton) interferometry provide access to the development of collective flow with time. It is argued that the non-monotonic variation of HBT radii with invariant mass of the lepton pairs signals the formation of quark gluon plasma in heavy ion collisions. Our proposal of experimentally measuring t…
I review recent developments in the phenomenological study of the quark-gluon plasma (QGP) transport properties based on a personal selection of results that were presented at Quark Matter 2019. The constraints on the temperature dependence of QGP shear and bulk viscosity are summarized. I discuss new theory advancements towards more realistic 3D dynamical simulations of heavy-ion collisions at finite baryon density. The challenges and opportunities of applying hydrodynamics to small collision systems are highlighted.
We apply the Bogoliubov compensation principle to QCD. The non-trivial solution of compensation equations for a spontaneous generation of the anomalous three-gluon interaction leads to the determination of parameters of the theory, including behavior of the gauge coupling $α_s(Q^2)$ without the Landau singularity, the gluon condensate $V_2\,\simeq\,0.01\,GeV^4$, mass of the lightest glueball $M_G\,\simeq\,1500\,MeV$ in satisfactory agreement with the phenomenological knowledge. The results strongly support the applicability of N.N. Bogoliubov compensation approach to gauge theories of the Stan…
We employ Padé approximants in the study of the analytic structure of the four-dimensional $SU(2)$ Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at $p_{\rm pole}^2 = \left[(-0.37 \,\pm\, 0.05_{\rm stat}\,\pm\, 0.08_{\rm sys}) \pm i\,(0.66\, \pm\, 0.03_{\rm stat}\, \pm\, 0.02_{\rm sys}…
It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent to the one-plane wave LOFF state. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. We show this Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We…
