The large density of gluons, which is present shortly after a nuclear collision at very high energies, can lead to the formation of a condensate. We identify a gauge-invariant order parameter for condensation based on elementary nonperturbative excitations of the plasma, which are described by spatial Wilson loops. Using real-time lattice simulations, we demonstrate that a self-similar transport process towards low momenta builds up a macroscopic zero mode. Our findings reveal intriguing similarities to recent discoveries of condensation phenomena out of equilibrium in table-top experiments with ultracold Bose gases.

Germany

Jürgen Berges

Austria

Finland

Kirill Boguslavski

Mark Mace

Jan M. Pawlowski

Gauge-invariant condensation in the nonequilibrium quark-gluon plasma

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.

Gabriele Inghirami

South Korea

Yuji Hirono

Italy

Luca Del Zanna

United States

Dmitri Kharzeev

Marcus Bleicher

Magnetic fields in heavy ion collisions: flow and charge transport

We present a first principles study of chiral plasma instabilities and the onset of chiral turbulence in QED plasmas with strong gauge matter interaction (<math><msup><mi>e</mi><mn>2</mn></msup><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>64</mn></math>), far from equilibrium. By performing classical-statistical lattice simulations of the microscopic theory, we show that the generation of strong helical magnetic fields from a helicity imbalance in the fermion sector proceeds via three distinct phases. During the initial linear instability regime the helicity imbalance of the fermion sector causes an exponential growth (damping) of magnetic field modes with right- (left-) handed polarization, for which we extract the characteristic growth (damping) rates. Secondary growth of unstable modes accelerates the helicity transfer from fermions to gauge fields and ultimately leads to the emergence of a self-similar scaling regime characteristic of a decaying turbulence, where magnetic helicity is efficiently transferred to macroscopic length scales. Within this turbulent regime, the evolution of magnetic helicity spectrum can be described by an infrared power spectrum with spectral exponent <math><mi>κ</mi><mo>=</mo><mn>10.2</mn><mo>±</mo><mn>0.5</mn></math> and dynamical scaling exponents <math><mi>α</mi><mo>=</mo><mn>1.14</mn><mo>±</mo><mn>0.50</mn></math> and <math><mi>β</mi><mo>=</mo><mn>0.37</mn><mo>±</mo><mn>0.13</mn></math>.

Niklas Mueller

Sören Schlichting

India

Sayantan Sharma

Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas

Vladimir V. Skokov

Prithwish Tribedy

Raju Venugopalan

Corrigendum to “Systematics of azimuthal anisotropy harmonics in proton–nucleus collisions at the LHC from the Color Glass Condensate” [Phys. Lett. B 788 (2019) 161–165]

Simple power counting arguments in the dilute-dense framework of the Color Glass Condensate (CGC) Effective Field Theory predict that even and odd azimuthal anisotropy harmonics of two-particle correlations in proton–nucleus collisions at the LHC will respectively satisfy <math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>{</mo><mn>2</mn><mo>}</mo><mo>∝</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>ch</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> and <math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>{</mo><mn>2</mn><mo>}</mo><mo>∝</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>ch</mi></mrow></msub></math>, where <math><msub><mrow><mi>N</mi></mrow><mrow><mi>ch</mi></mrow></msub></math> denotes the number of charged particles. We show that these expectations are borne out qualitatively, and even quantitatively, within systematic uncertainties, for <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi>v</mi></mrow><mrow><mn>4</mn></mrow></msub></math> in comparisons with data from the ATLAS collaboration. We also observe that ATLAS data for the <math><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub></math> azimuthal harmonic are in excellent agreement with our qualitative expectation; quantitative comparisons are numerically challenging at present. The lessons from this study fully complement those gained by the recent comparison of the CGC dilute-dense framework [1] to data from the PHENIX collaboration on small system collisions at RHIC.

Systematics of azimuthal anisotropy harmonics in proton–nucleus collisions at the LHC from the Color Glass Condensate

We demonstrate that the striking systematics of two-particle azimuthal Fourier harmonics <math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> and <math><msub><mi>v</mi><mn>3</mn></msub></math> in ultrarelativistic collisions of protons, deuterons, and helium-3 ions off gold nuclei measured by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC) is reproduced in the color glass condensate effective field theory. This contradicts the claim in C. Aidala et al. (PHENIX Collaboration), arXiv:1805.02973, that their data rule out initial state-based explanations. The underlying systematics of the effect, as discussed previously in K. Dusling, M. Mace, R. Venugopalan, Phys. Rev. D 97, 016014 (2018); Phys. Rev. Lett. 120, 042002 (2018); Proc. Sci., QCDEV2017 (2018) 039, arise from the differing structure of strong color correlations between gluon domains of size <math><mn>1</mn><mo>/</mo><msub><mi>Q</mi><mi>S</mi></msub></math> at fine (<math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mo>⊥</mo></mrow></msub><mo>⪆</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math>) or coarser (<math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mo>⊥</mo></mrow></msub><mo>⪅</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math>) transverse momentum resolution. Further tests of the limits of validity of this framework can be carried out in light-heavy ion collisions at both RHIC and the Large Hadron Collider. Such measurements also offer novel opportunities for further exploration of the role of the surprisingly large short-range nuclear correlations measured at Jefferson Lab.

Hierarchy of Azimuthal Anisotropy Harmonics in Collisions of Small Systems from the Color Glass Condensate

Qualitative features of multiparticle correlations in light-heavy ion (<math><mi>p</mi><mo>+</mo><mi>A</mi></math>) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include (i) the ordering of the magnitudes of the azimuthal angle <math><mi>n</mi></math>th Fourier harmonics of two-particle correlations <math><msub><mi>v</mi><mi>n</mi></msub><mo>{</mo><mn>2</mn><mo>}</mo></math>, (ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>, and (iii) the energy dependence of four-particle symmetric cumulants measuring correlations between different Fourier harmonics. Similar patterns are seen in an Abelian version of the model, where we observe <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>6</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>8</mn><mo>}</mo></math> of two, four, six, and eight particle correlations. While such patterns are often interpreted as signatures of collectivity arising from hydrodynamic flow, our results provide an alternative description of the multiparticle correlations seen in <math><mi>p</mi><mo>+</mo><mi>A</mi></math> collisions.

Kevin Dusling

Multiparticle Collectivity from Initial State Correlations in High Energy Proton-Nucleus Collisions

In K. Dusling et al. [arXiv:1705.00745.], an initial-state “parton model” of quarks scattering off a dense nuclear target was shown to qualitatively reproduce the systematics of multiparticle azimuthal anisotropy cumulants measured in proton/deuteron-nucleus (<math><mi>p</mi><mi>A</mi></math>) collisions at the Relativistic Heavy Ion Collider and the LHC. The systematics included (i) the behavior of the four-particle cumulant <math><msub><mi>c</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>, which generates a real four-particle second Fourier harmonic <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>; (ii) the ordering <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>6</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>8</mn><mo>}</mo></math> for two-, four-, six-, and eight-particle Fourier harmonics; and (iii) the behavior of so-called symmetric cumulants SC(2,3) and SC(2,4). These features of azimuthal multiparticle cumulants were previously interpreted as a signature of hydrodynamic flow; our results challenge this interpretation. We expand here upon our previous study and present further details and novel results on the saturation scale and transverse momentum (<math><msub><mi>p</mi><mo>⊥</mo></msub></math>) dependence of multiparticle azimuthal correlations. We find that the dependence of <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo></math> and <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math> on the number of color domains in the target varies with the <math><msub><mi>p</mi><mo>⊥</mo></msub></math> window explored. We extend our prior discussion of symmetric cumulants and compute as yet unmeasured symmetric cumulants. We investigate the <math><msub><mi>N</mi><mi>c</mi></msub></math> dependence of <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo></math> and <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>. We contrast our results, which include multiple scatterings of each quark off the target, to the Glasma graph approximation, where each quark suffers at most two-gluon exchanges with the target. We find that coherent multiple scattering is essential to obtain a positive definite <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>. We provide an algorithm to compute expectation values of arbitrary products of the “dipole” lightlike Wilson line correlators.

Parton model description of multiparticle azimuthal correlations in <math><mi>p</mi><mi>A</mi></math> collisions

With an explicit example, we show that Jordan frame and the conformally transformed Einstein frames clearly lead to different physics for a non-minimally coupled theory of gravity, namely Brans–Dicke theory, at least at the quantum level. The example taken up is the spatially flat Friedmann cosmology in Brans–Dicke theory.

Narayan Banerjee

Barun Majumder

A question mark on the equivalence of Einstein and Jordan frames