<p>The dipole cross-section behavior for protons and nuclei is analyzed with and without considering the heavy quark masses in the Bjorken variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> using the Kharzeev-Levin-Nardi (KLN) model of low <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> gluon distributions. The color glass condensate (CGC) effects in the color dipole model are influenced by the heavy quark masses in the Bjorken variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>&lt;</mo><msubsup><mi>Q</mi><mrow><mi>s</mi></mrow><mn>2</mn></msubsup></mrow></math>. These nonlinear saturation effects will be observable in the Large Hadron Electron Collider (LHeC) and the Electron-Ion Collider (EIC) at very small <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> values.</p>

Iran

G.R. Boroun

Effects of heavy quarks in the dipole cross section with the Kharzeev-Levin-Nardi model

The possible link between entanglement and thermalization, and the dynamics of hadronization are addressed by studying the real-time response of the massive Schwinger model coupled to external sources. This setup mimics the production and fragmentation of quark jets, as the Schwinger model and quantum chromodynamics (QCD) share the properties of confinement and chiral symmetry breaking. By using simulations of quantum dynamics on classical hardware, we study the entanglement between the produced jets, and observe the growth of the corresponding entanglement entropy in time. This growth arises from the increased number of contributing eigenstates of the reduced density matrix with sufficiently large and close eigenvalues. We also investigate the physical nature of these eigenstates, and find that at early times they correspond to fermionic Fock states. We then observe the transition from these fermionic Fock states to mesonlike bound states as a function of time. In other words, we observe how hadronization develops in real time. At late times, the local observables at midrapidity (such as the fermion density and the electric field) approach approximately constant values, suggesting the onset of equilibrium and approach to thermalization.

United States

Adrien Florio

David Frenklakh

Kazuki Ikeda

Dmitri Kharzeev

Vladimir Korepin

China

Shuzhe Shi

Kwangmin Yu

Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model

In this study, we explore the real-time dynamics of the chiral magnetic effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive Schwinger model. By introducing a chiral chemical potential μ 5 through a quench process, we drive the system out of equilibrium and analyze the induced vector currents and their evolution over time. The Hamiltonian is modified to include the time-dependent chiral chemical potential, thus allowing the investigation of the CME within a quantum computing framework. We employ the quantum imaginary time evolution (QITE) algorithm to study the thermal states, and utilize the Suzuki-Trotter decomposition for the real-time evolution. This study provides insights into the quantum simulation capabilities for modeling the CME and offers a pathway for studying chiral dynamics in low-dimensional quantum field theories.

Zhong-Bo Kang

Spain

Wenyang Qian

Fanyi Zhao

Real-time chiral dynamics at finite temperature from quantum simulation

Gauge invariance of QCD dictates the presence of string junctions in the wave functions of baryons. In high-energy inclusive processes, these baryon junctions have been predicted to induce the separation of the flows of baryon number and flavor. In this paper we describe this phenomenon using the analog-gas model of multiparticle production proposed long time ago by Feynman and Wilson and adapted here to accommodate the topological expansion in QCD. In this framework, duality arguments suggest the existence of two degenerate junction-antijunction glueball Regge trajectories of opposite   <math> <mi>C</mi> </math>  $$ \mathcal{C} $$ -parity with intercept close to 1/2. The corresponding results for the energy and rapidity dependence of baryon stopping are in reasonably good agreement with recent experimental findings from STAR and ALICE experiments. We show that accounting for correlations between the fragmenting strings further improves agreement with the data, and outline additional experimental tests of our picture at the existing (RHIC, LHC, JLab) and future (EIC) facilities.

Italy

Giancarlo Rossi

CERN

France

Gabriele Veneziano

Baryon-number — flavor separation in the topological expansion of QCD

The recently introduced concept of timelike entanglement entropy has sparked a lot of interest. Unlike the traditional spacelike entanglement entropy, timelike entanglement entropy involves tracing over a timelike subsystem. In this work, we propose an extension of timelike entanglement entropy to Euclidean space (“temporal entanglement entropy”), and relate it to the renormalization group (RG) flow. Specifically, we show that tracing over a period of Euclidean time corresponds to coarse-graining the system and can be connected to momentum space entanglement. We employ Holography, a framework naturally embedding RG flow, to illustrate our proposal. Within cutoff holography, we establish a direct link between the UV cutoff and the smallest resolvable time interval within the effective theory through the irrelevant  $$T\overline{T }$$  deformation. Increasing the UV cutoff results in an enhanced capability to resolve finer time intervals, while reducing it has the opposite effect. Moreover, we show that tracing over a larger Euclidean time interval is formally equivalent to integrating out more UV degrees of freedom (or lowering the temperature). As an application, we point out that the temporal entanglement entropy can detect the critical Lifshitz exponent z in non-relativistic theories which is not accessible from spatial entanglement at zero temperature and density.

Sebastian Grieninger

Temporal entanglement entropy as a probe of renormalization group flow

The production of jets should allow testing the real-time response of the QCD vacuum disturbed by the propagation of high-momentum color charges. Addressing this problem theoretically requires a real-time, nonperturbative method. It is well known that the Schwinger model [QED in (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>) dimensions] shares many common properties with QCD, including confinement, chiral symmetry breaking, and the existence of vacuum fermion condensate. As a step in developing such an approach, we report here on fully quantum simulations of a massive Schwinger model coupled to external sources representing quark and antiquark jets as produced in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation. We study, for the first time, the modification of the vacuum chiral condensate by the propagating jets and the quantum entanglement between the fragmenting jets. Our results indicate strong entanglement between the fragmentation products of the two jets at rapidity separations <math><mi>Δ</mi><mi>η</mi><mo>≤</mo><mn>2</mn></math>, which can potentially exist also in QCD and can be studied in experiments.

Real-Time Nonperturbative Dynamics of Jet Production in Schwinger Model: Quantum Entanglement and Vacuum Modification

We start by considering the production rates of sphalerons with different sizes <math><mi>ρ</mi></math> in the symmetric phase, <math><mi>T</mi><mo>&gt;</mo><msub><mi>T</mi><mrow><mi>EW</mi></mrow></msub></math>. At small <math><mi>ρ</mi></math>, the distribution is cut off by the growing mass <math><mi>M</mi><mo>∼</mo><mn>1</mn><mo>/</mo><mi>ρ</mi></math>, and at large <math><mi>ρ</mi></math> by the magnetic screening mass. In the broken phase, <math><mi>T</mi><mo>&lt;</mo><msub><mi>T</mi><mrow><mi>EW</mi></mrow></msub></math>, the scale is set by the Higgs vacuum expectation value <math><mi>v</mi><mo>(</mo><mi>T</mi><mo>)</mo></math>. We introduce the concept of “sphaleron freeze-out” whereby the sphaleron production rate matches the Hubble Universe expansion rate. At freeze-out the sphalerons are out of equilibrium. Sphaleron explosions generate sound and even gravity waves, when a nonzero Weinberg angle makes them nonspherical. We evaluate the magnitude of <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation during the sphaleron explosions. We assess its magnitude using the Standard Model Cabbibo-Kobayashi-Maskawa (CKM) quark matrix, first for nonzero and then zero Dirac eigenstates. We find that its magnitude is maximal at the sphaleron freeze-out condition with <math><mi>T</mi><mo>≈</mo><mn>130</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We proceed to estimate the amount of <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation needed to generate the observed magnitude of baryon asymmetry of the Universe, and find that it is about an order of magnitude above our CKM-based estimates. We also relate the baryon asymmetry to the generation of <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> magnetic chirality, which is expected to be conserved and perhaps visible in polarized intergalactic magnetic fields.

Edward Shuryak

Ismail Zahed

Sphalerons, baryogenesis, and helical magnetogenesis in the electroweak transition of the minimal standard model

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity $$\sigma $$ <math><mi>σ</mi></math>  and the chiral magnetic conductivity $$\sigma _{\chi }$$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math> . We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial $$\sigma _\chi $$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math>  can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like $$v_1$$ <math><msub><mi>v</mi><mn>1</mn></msub></math>  or $$\langle \sin \phi \rangle $$ <math><mrow><mo>⟨</mo><mo>sin</mo><mi>ϕ</mi><mo>⟩</mo></mrow></math> . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Finland

Gabriele Inghirami

Mark Mace

South Korea

Yuji Hirono

Luca Del Zanna

Germany

Marcus Bleicher

Magnetic fields in heavy ion collisions: flow and charge transport

We show that in order to obtain a successful description of the transverse momenta distribution for charged particles in ion-ion collisions, one must include a thermal emission term. The temperature of this emission <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>th</mi></mrow></msub></mrow></math> turns out to be proportional to the saturation scale, <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>th</mi></mrow></msub><mo>=</mo><mn>1.8</mn><msub><mrow><mi>Q</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>/</mo><mn>2</mn><mi>π</mi></mrow></math>. The formalism for the calculation of the transverse momenta spectra in color glass condensate/saturation approach is developed, in which two stages of the process are seen: creation of the color glass condensate, and hadronization of the gluon jets. Our calculations are based on the observation that even for small values of <math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>, the main contribution in the integration over the dipole sizes stems from the kinematic region in the vicinity of the saturation momentum, where theoretically, we know the scattering amplitude. Nonperturbative corrections need to be included in the model of hadronization. This model incorporates the decay of a gluon jet with effective mass <math><msubsup><mi>m</mi><mi>eff</mi><mn>2</mn></msubsup><mo>=</mo><mn>2</mn><msub><mi>Q</mi><mi>s</mi></msub><msub><mi>μ</mi><mrow><mi>soft</mi></mrow></msub></math> where <math><msub><mi>μ</mi><mrow><mi>soft</mi></mrow></msub></math> denotes the soft scale, with the fragmentation functions at all values of the transverse momenta. We use the Kharzeev-Levin-Nardi model which, provides a simple way to estimate the cross sections for the different centrality classes. Comparing the results of this paper with the transverse distribution in the proton-proton scattering, we see two major differences. First, a larger contribution of the thermal radiation term is needed, in accord with higher parton densities of the produced color glass condensate. Second, even changing the model for the hadronization, without a thermal radiation term, we fail to describe the <math><msub><mi>p</mi><mi>T</mi></msub></math> spectrum. Consequently, we conjecture that the existence of the thermal radiation term is independent of the model of confinement.

Israel

E. Gotsman

Chile

E. Levin

Thermal radiation and inclusive production in the Kharzeev-Levin-Nardi model for ion-ion collisions

We investigate the charge-dependent flow induced by magnetic and electric fields in heavy-ion collisions. We simulate the evolution of the expanding cooling droplet of strongly coupled plasma hydrodynamically, using the iEBE-VISHNU framework, and add the magnetic and electric fields as well as the electric currents they generate in a perturbative fashion. We confirm the previously reported effect of the electromagnetically induced currents [Gursoy et al., Phys. Rev. C 89, 054905 (2014)], that is a charge-odd directed flow <math><mrow><mi>Δ</mi><msub><mi>v</mi><mn>1</mn></msub></mrow></math> that is odd in rapidity, noting that it is induced by magnetic fields (à la Faraday and Lorentz) and by electric fields (the Coulomb field from the charged spectators). In addition, we find a charge-odd <math><mrow><mi>Δ</mi><msub><mi>v</mi><mn>3</mn></msub></mrow></math> that is also odd in rapidity and that has a similar physical origin. We furthermore show that the electric field produced by the net charge density of the plasma drives rapidity-even charge-dependent contributions to the radial flow <math><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></math> and the elliptic flow <math><mrow><mi>Δ</mi><msub><mi>v</mi><mn>2</mn></msub></mrow></math>. Although their magnitudes are comparable to the charge-odd <math><mrow><mi>Δ</mi><msub><mi>v</mi><mn>1</mn></msub></mrow></math> and <math><mrow><mi>Δ</mi><msub><mi>v</mi><mn>3</mn></msub></mrow></math>, they have a different physical origin, namely the Coulomb forces within the plasma.

Netherlands

Umut Gürsoy

Eric Marcus

Krishna Rajagopal

Chun Shen

Charge-dependent flow induced by magnetic and electric fields in heavy ion collisions