In this work we study the quark-meson model within a real-time formulation of the functional renormalization group (FRG) on the Schwinger-Keldysh contour. First, we discuss in detail the symmetry of thermal equilibrium for the fermionic sector of the Keldysh action. We take into account dissipation for the bosonic degrees of freedom in the spirit of the Caldeira-Leggett model by coupling the system to an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> invariant external heat bath. We study the effect of dissipation on static equilibrium properties, most prominently on the FRG flow of the effective potential and thus on the resulting phase diagram. We find that, unlike in classical systems, through the contributions from nonzero Matsubara modes the dissipative dynamics can in general have an effect on static observables. We investigate these effects within two phenomenological models for the temperature dependence of the pion damping to verify that they are quantitatively small. To estimate their largest possible influence, we consider limits where the damping constants approach infinity.

Germany

Johannes V. Roth

Yunxin Ye

Sören Schlichting

Lorenz von Smekal

Effects of dissipation on phase diagram and bosonic excitations in the quark-meson model

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study model H, the conjectured dynamic universality class of the quantum chromodynamics (QCD) critical point. We emphasize the structural similarities with model G, conjectured to be the dynamic universality class of the chiral phase transition in the limit of two massless quark flavors. Importantly, our formulation of the real-time FRG preserves all relevant symmetries throughout the FRG flow which, e.g., guarantees the nonrenormalization of the reversible mode couplings, as but one exact result. We derive nonperturbative RG flow equations for the kinetic coefficients of both, model G and H, in parallel, and discuss commonalities and differences in the resulting fixed-point structure and dynamic critical exponents, such as weak-scaling relations which hold in either case versus the characteristic strong scaling of model G which is absent in model H.

Universal critical dynamics near the chiral phase transition and the QCD critical point

We use quantum chromodynamics (QCD) kinetic theory to compute dilepton production coming from the pre-equilibrium phase of the quark-gluon plasma created in high-energy heavy-ion collisions. We demonstrate that the dilepton spectrum exhibits a simple scaling in terms of the specific shear viscosity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>η</mi><mo>/</mo><mi>s</mi></mrow></math> and entropy density <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>S</mi><mo>/</mo><mi>d</mi><mi>ζ</mi><mo>∼</mo><msubsup><mrow><mo stretchy="false">(</mo><mi>T</mi><msup><mi>τ</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></mrow><mi>∞</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msubsup></math>, which can be derived from dimensional analysis in the presence of a pre-equilibrium attractor. Based on this scaling we perform event-by-event calculations of in-medium dilepton production and determine the invariant mass range where the pre-equilibrium yield is the leading contribution.

Oscar Garcia-Montero

Philip Plaschke

Scaling of pre-equilibrium dilepton production in QCD kinetic theory

We compute baryon and electric charge deposition in high-energy heavy-ion collisions using the color glass condensate effective field theory, where at leading order, charge is deposited through multiple scatterings of valence quarks with a saturated gluon target. A simplified phenomenological formula is derived to describe charge deposition, from which the parametrical dependence with collisional energy and geometry can be extracted. We present an approximate analytical prediction of the so-called baryon stopping parameter <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>B</mi></msub></math>, which shows excellent agreement with the state-of-the art extractions of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>B</mi></msub></math> from experimental data. These results are further validated using the McDipper framework, by computing charge deposition at midrapidity across a range of collision energies <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>62.4</mn><mo>–</mo><mn>5020</mn><mspace width="0.16em"></mspace><mi>GeV</mi><mo>)</mo></mrow></math>.

Baryon stopping and charge deposition in heavy-ion collisions due to gluon saturation

We study the critical dynamics of a scalar field theory with <math altimg='si1.svg'><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.

Leon J. Sieke

Mattis Harhoff

Universal non-equilibrium scaling of cumulants across a critical point

The collective dynamics around the second-order $\textit{O}$(4) chiral phase transition in QCD with two massless quark flavors can be understood by appealing to universality. We present a novel formulation of the real-time functional renormalization group (FRG) that describes the stochastic hydrodynamic equations of motion for systems in the same dynamic universality class, which corresponds to Model G in the Halperin-Hohenberg classification. Our approach preserves all relevant symmetries of such systems with reversible mode couplings, which establishes the real-time FRG as a valuable tool complementary to classical-statistical simulations. As a first application we show that our approach is consistent with dynamic scaling relations and reproduces the non-trivial value $\textit{z}$ = $\textit{d/}$2 for the dynamic critical exponent in $\textit{d}$ spatial dimensions. Moreover, we extract a novel dynamic scaling function that describes the universal momentum and temperature dependence of the diffusion coefficient of iso-(axial-)vector charge densities in the symmetric phase.

Johannes Roth

Lorenz Smekal

Dynamic critical behavior of the chiral phase transition from the real-time functional renormalization group

We modify the anomalous hydrodynamic equations of motion to account for dissipative effects due to quantum chromodynamic (QCD) sphaleron transitions. By investigating the linearized hydrodynamic equations, we show that sphaleron transitions lead to nontrivial effects on vector and axial charge transport phenomena in the presence of a magnetic field. Due to the dissipative effects of sphaleron transitions, a wave number threshold <math><msub><mi>k</mi><mrow><mi>CMW</mi></mrow></msub></math> emerges characterizing the onset of chiral magnetic waves. Sphaleron damping also significantly impacts the time evolution of both axial and vector charge perturbations in a QCD plasma in the presence of a magnetic field. Based on our analysis of the linearized hydrodynamic equations, we also investigate the dependence of the vector charge separation on the sphaleron transition rate, which may have implications for the experimental search for the chiral magnetic effect in heavy ion collisions.

United States

Lillian de Bruin

Sphaleron damping and effects on vector and axial charge transport in high-temperature QCD plasmas

We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting nonperturbative features as a function of time due to correlated momentum kicks it receives from the medium, eventually going over to a diffusive regime. We extract the momentum diffusion coefficient for a mass range describing charm and bottom quarks and find sizable discrepancies from the heavy-quark limit.

India

Harshit Pandey

Sayantan Sharma

Heavy-Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium

We present a succinct formulation of the energy-momentum tensor of the glasma characterizing the initial color fields in relativistic heavy-ion collisions in the color glass condensate effective theory. We derive concise expressions for the <math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi>D</mi></mrow></math> dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with nontrivial longitudinal correlations. Utilizing Monte Carlo integration, we calculate in unprecedented detail non-trivial rapidity profiles of early time observables at RHIC and LHC energies, including transverse energy densities and eccentricities. For our setup with broken boost invariance, we carefully discuss the placement of the origin of the Milne frame and interpret the components of the energy-momentum tensor. We find longitudinal flow that deviates from standard Bjorken flow in the <math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi>D</mi></mrow></math> case and provide a geometric interpretation of this effect. Furthermore, we observe a universal shape in the flanks of the rapidity profiles regardless of collision energy and predict that limiting fragmentation should also hold at LHC energies.

Austria

Andreas Ipp

Markus Leuthner

David I. Müller

Kayran Schmidt

Finland

Pragya Singh

Energy-momentum tensor of the dilute <math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi>D</mi></mrow></math> glasma

We present a new three-dimensional resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the <math><msub><mi>k</mi><mo>⊥</mo></msub></math>-factorized color glass condensate (CGC) hybrid approach. The McDipper framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge, and baryon densities) both in the midrapidity and forward (backward) regions of the collision. This event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the relevant conserved charges can be computed directly. In the present work we have included the leading-order contributions to the light flavor parton densities. As a feature, the model can be systematically improved in the future by adding next-to-leading-order calculations (in the CGC hybrid framework) and extending to lower energies by including subeikonal corrections to the channels included. We present relevant observables, such as the eccentricities and flow decorrelation, as tests of this new approach.