<p>The detection of the chiral magnetic effect (CME) in relativistic heavy-ion collisions remains challenging due to substantial background contributions that obscure the expected signal. In this Letter, we present a novel machine learning approach for constructing optimized observables that significantly enhance CME detection capabilities. By parametrizing generic observables constructed from flow harmonics and optimizing them to maximize the signal-to-background ratio, we systematically develop CME-sensitive measures that outperform conventional methods. Using simulated data from the anomalous viscous fluid dynamics framework, our machine learning observables demonstrate up to 90% higher sensitivity to CME signals compared to traditional <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi></math> correlators, while maintaining minimal background contamination. The constructed observables provide physical insight into optimal CME detection strategies and offer a promising path forward for experimental searches of the CME at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.</p>

Japan

Yuji Hirono

United States

Kazuki Ikeda

Dmitri E. Kharzeev

China

Ziyi Liu

Shuzhe Shi

Optimal observables for the chiral magnetic effect from machine learning

We study the properties of quarkonia inside a bulk-viscous quark gluon plasma. The non-equilibrium nature of the medium is encoded in the deformed distribution functions of thermal quarks and gluons, with which we compute the dielectric permittivity within the hard thermal loop approximation at one-loop. The modified dielectric permittivity is used to calculate the in-medium heavy quark potential, and using the potential we compute spectral functions, which reflect the physical properties of heavy quarkonia. We discuss how the bulk viscous effect influences quantities such as binding energies and thermal widths. Based on those properties, we discuss the implications of the bulk viscous effect on the physical observables such as ψ′ to J/ψ ratio and the nuclear modification factor, R  AA . In particular, we argue that the nuclear modification factors of excited and ground states show different sensitivities to the bulk viscous nature of a plasma, which is potentially useful for the critical point search.

South Korea

Lata Thakur

Spectral functions of heavy quarkonia in a bulk-viscous quark gluon plasma

We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry-breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.

Yoshimasa Hidaka

Ryo Yokokura

Counting Nambu-Goldstone Modes of Higher-Form Global Symmetries

We study the properties of heavy quarkonia in a quark gluon plasma in the presence of bulk viscous effects. Within the hard thermal loop approximation at one-loop, the dielectric permittivity of a quark gluon plasma is computed, where the bulk viscous effect enters through the deformation of the distribution functions of thermal quarks and gluons. Based on the modified dielectric permittivity, we compute the in-medium heavy quark potential, that includes non-pertubative string-like terms as well as the perturbative Coulombic term. We discuss how the bulk viscous effect modify the real and imaginary parts of the in-medium potential. Several prescriptions are examined as to how to include the string-like non-perturbative potentials. Using the deformed potential, we compute the wave functions, binding energies, and decay widths of heavy quarkonia in a bulk viscous medium, and study their sensitivity to the strength of the bulk viscous effect. An estimate of the melting temperatures is given.

India

Najmul Haque

Heavy quarkonia in a bulk viscous medium

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

Italy

Luca Del Zanna

Dmitri Kharzeev

Germany

Marcus Bleicher

Magnetic fields in heavy ion collisions: flow and charge transport

We study a (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> gauge theory with <math><mi>N</mi></math>-flavor fundamental scalar fields, whose color-flavor locked (CFL) phase has topologically stable non-Abelian vortices. The <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> charge of the scalar fields must be <math><mi>N</mi><mi>k</mi><mo>+</mo><mn>1</mn></math> for some integer <math><mi>k</mi></math> in order for them to be in the representation of <math><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> gauge group. This theory has a <math><msub><mi>Z</mi><mrow><mi>N</mi><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math> one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the CFL phase is topologically ordered if <math><mi>k</mi><mo>≠</mo><mn>0</mn></math>. We also find that the world sheet of topologically stable vortices in CFL phase can generate this one-form symmetry.

Muneto Nitta

Yuya Tanizaki

Topological order in the color-flavor locked phase of a (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> gauge-Higgs system

We discuss the low-energy dynamics of superfluidity with topological order in (3 + 1) spacetime dimensions. We generalize a topological BF theory by introducing a non-square K matrix, and this generalized BF theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed ’t Hooft anomaly between discrete higher-form symmetries. We apply this framework to the color-flavor locked phase of dense QCD, which shows anyonic particle-vortex statistics while no topological order appears. An explicit example of superfluidity with topological order is discussed.

Effective gauge theories of superfluidity with topological order

We study relativistic hydrodynamics with chiral anomaly and dynamical electromagnetic fields, namely chiral magnetohydrodynamics (CMHD). We formulate CMHD as a low-energy effective theory based on a generalized derivative expansion. We demonstrate that the modification of ordinary magnetohydrodynamics (MHD) due to chiral anomaly can be obtained from the second law of thermodynamics and is tied to the chiral magnetic effect. We further study the real-time properties of a chiral fluid by solving linearized CMHD equations. We discover a remarkable “transition” at an intermediate axial chemical potential <math><msub><mi>μ</mi><mi>A</mi></msub></math> between a stable chiral fluid at low <math><msub><mi>μ</mi><mi>A</mi></msub></math> and an unstable chiral fluid at high <math><msub><mi>μ</mi><mi>A</mi></msub></math>. We summarize this transition in a “phase diagram” in terms of <math><msub><mi>μ</mi><mi>A</mi></msub></math> and the angle of the wave vector relative to the magnetic field. In the unstable regime, four collective modes carry both magnetic and fluid helicity, in contrary to MHD waves, which are unpolarized. Half of the helical modes grow exponentially in time, indicating the instability, while the other half become dissipative.

Koichi Hattori

Ho-Ung Yee

Yi Yin

Magnetohydrodynamics with chiral anomaly: Phases of collective excitations and instabilities

Quark-hadron continuity is a scenario in which hadronic matter is continuously connected to a color superconductor without phase transitions as the baryon chemical potential increases. This scenario is based on Landau’s classification of phases, since they have the same symmetry breaking pattern. We address the question of whether this continuity is true as quantum phases of matter, which requires treatment beyond the Ginzburg-Landau description. To examine the topological nature of a color superconductor, we derive a dual effective theory for U(1) Nambu-Goldstone (NG) bosons and vortices of the color-flavor locked phase and discuss the fate of emergent higher-form symmetries. The theory has the form of a topological BF theory coupled to NG bosons, and fractional statistics of test quarks and vortices arise as a result of an emergent <math><msub><mi>Z</mi><mn>3</mn></msub></math> two-form symmetry. We find that this symmetry cannot be spontaneously broken, indicating that quark-hadron continuity is still a consistent scenario.

Quark-Hadron Continuity beyond the Ginzburg-Landau Paradigm

We study the motion of vortex filaments in chiral media and find a semiclassical analog of the anomaly-induced chiral magnetic effect. The helical solitonic excitations on vortices in a parity-breaking medium are found to carry additional energy flow along the vortex in the direction dictated by the sign of chirality imbalance; we call this new transport phenomenon the chiral propulsion effect. The dynamics of vortex filaments in the parity-breaking background is described by a modified version of the localized induction equation. We analyze the linear stability of simple vortex solutions and study the effects of chiral media on the excitation spectrum and the growth rate of the unstable modes. We also show that, if the equation of motion of the filament is symmetric under the simultaneous reversal of parity and time, planar-shape solutions cannot transport energy.