We investigate saturation effects in exclusive vector meson production in deep inelastic scattering, where we model fluctuations within the target protons as localized color-charge hot spots. Based on the color glass condensate framework and the dipole picture for vector meson production, we examine the dependencies of coherent and incoherent scattering cross sections on the momentum transfer. We draw conclusions on the effectiveness of our hot spot model and the strength of the suppression of the scattering cross sections caused by saturation effects. We find that saturation has mild effects in the given energy and charge-density ranges, but can also show that suppression becomes more prominent as the color-charge density inside the proton increases.

Germany

Spain

Oscar Garcia-Montero

Yannik Hoffmann

Sören Schlichting

Saturation effects in exclusive vector meson production in DIS

The relative abundances and kinematic distributions of hadrons containing (anti)charm quarks are key observables for deconfinement, heavy-quark diffusion and hadronization in heavy-ion collisions. The production of (anti)charm quarks is commonly associated to the initial hard scatterings in hadronic collisions. Based on previous studies on dilepton production, we evaluate the (anti)charm quark production from the pre-equilibrium phase. A non-negligible contribution to the overall charm quark production is found, albeit large theoretical uncertainties are limiting factors. We conclude that precise total charm production measurements combined with progress on charm production calculations from the initial hard scatterings can be used to infer information on the pre-equilibrium stage.

Switzerland

Maurice Coquet

France

Thomas Faure

Mika Spier

Michael Winn

Charm quark production in heavy-ion collisions as a signature of pre-equilibrium

So far a major source of uncertainty in the study of heavy-ion collisions arises from the early time dynamics which includes initial state and preequilibrium dynamics. The state-of-the-art framework, KøMPøST [Kurkela et al. <a href="http://dx.doi.org/10.1103/PhysRevC.99.034910">Phys. Rev. C 99, 034910 (2019)</a>; Kurkela et al. <a href="http://dx.doi.org/10.1103/PhysRevLett.122.122302">Phys. Rev. Lett. 122, 122302 (2019)</a>], employs nonequilibrium Green’s functions to propagate the initial energy-momentum tensor to the hydrodynamic phase, yet currently only treats transverse plane dynamics under boost-invariant conditions. In this work, we extend KøMPøST to include nonboost-invariant responses to initial conditions, essential for accurately capturing the longitudinal structures observed in heavy-ion collisions. Nonboost-invariant fluctuations on top of a homogeneous background are evolved using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> response functions calculated in kinetic theory. To assess kinetic theory’s transition towards hydrodynamic evolution, we systematically compare the out-of-equilibrium shear-stress tensor from KøMPøST-3D with estimates based on Navier-Stokes hydrodynamics. Subsequently, a comprehensive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> framework, mcdipper + KøMPøST-3D + CLVisc + SMASH, is utilized to simulate the complete spacetime evolution of heavy-ion collisions. The sensitivity of key observables, including longitudinal structure of anisotropic flow, to variations in the hydrodynamic initialization time is thoroughly investigated.

China

Finland

Xiaojian Du

Jie Zhu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> event-by-event preequilibrium dynamics in heavy-ion collisions

We perform a global analysis of deep-inelastic $\textit{e}$ + $\textit{p}$ scattering data from HERA and transverse energy distributions in $\textit{p}$ + $\textit{p}$ and $\textit{p}$ + Pb collisions, alongside charged hadron multiplicities in Pb+Pb collisions at $$ \sqrt{s_{\textrm{NN}}}=5.02 $$ TeV from ALICE. Using a saturation-based initial state model grounded in high-energy QCD, we determine the early-time non-equilibrium shear viscosity to entropy density ratio $\textit{η/s}$ of the quark-gluon plasma. Our results provide new insights into the early-time transport properties of nuclear matter under extreme conditions.

Anton Andronic

Nicolas Borghini

Christian Klein-Bösing

Renata Krupczak

United States

Hendrik Roch

Constraining hot and cold nuclear matter properties from heavy-ion collisions and deep-inelastic scattering

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.

Johannes V. Roth

Yunxin Ye

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.

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.