<p>The mean transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></math> of hadrons has been observed experimentally and in numerical simulations to have a power-law dependence on the hadronic multiplicity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> in ultracentral relativistic heavy-ion collisions: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow><mo>∝</mo><msup><mi>N</mi><msub><mi>b</mi><mi>UC</mi></msub></msup></mrow></math>. It has been put forward that this exponent <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mi>UC</mi></msub></math> is the speed of sound of quark-gluon plasma measured at a temperature determined from <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></math>. We study step by step the connection between (i) the energy and entropy of hydrodynamic simulations and (ii) experimentally measurable observables. We show that an argument based on energy and entropy should yield an exponent equal to the pressure over energy density <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo>/</mo><mi>ɛ</mi></mrow></math>, rather than the speed of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>c</mi><mi>s</mi><mn>2</mn></msubsup></math>; however, we also observe that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> are not sufficiently accurate proxies for the energy and entropy to make this possible in practice. From simulations, we find that the exponent <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mi>UC</mi></msub></math> is significantly different whether the “effective volume” is strictly constant or not, a condition that cannot be enforced experimentally. Additional tests using a modified equation of state find that the exponent <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mi>UC</mi></msub></math> exhibits a variable degree of correlations with the speed of sound and with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo>/</mo><mi>ɛ</mi></mrow></math>, but is not an accurate measurement of either quantity in general.</p>

United States

Lorenzo Gavassino

Henry Hirvonen

Jean-Francois Paquet

Mayank Singh

Brazil

Gabriel Soares Rocha

Feasibility of measuring the speed of sound of the quark-gluon plasma from the multiplicity and mean <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> of ultracentral heavy-ion collisions

<p>Fluctuations between charged and neutral kaons measured by the ALICE Collaboration in Pb-Pb collisions at the CERN Large Hadron Collider (LHC) exceed conventional explanations. Previously it was shown that if the scalar condensate is accompanied by an electrically neutral isospin-1 field then the combination can produce large equilibrium fluctuations where <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>〈</mo><mover accent="true"><mi>u</mi><mo>¯</mo></mover><mi>u</mi><mo>〉</mo></mrow><mo>≠</mo><mrow><mo>〈</mo><mover accent="true"><mi>d</mi><mo>¯</mo></mover><mi>d</mi><mo>〉</mo></mrow></mrow></math>. Hadronizing strange and antistrange quarks might then strongly fluctuate between charged (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>u</mi><mover accent="true"><mi>s</mi><mo>¯</mo></mover></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi><mover accent="true"><mi>u</mi><mo>¯</mo></mover></mrow></math>) and neutral (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mover accent="true"><mi>s</mi><mo>¯</mo></mover></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi><mover accent="true"><mi>d</mi><mo>¯</mo></mover></mrow></math>) kaons. Here, we estimate the times for the condensates to achieve their equilibrium probability distributions within causal volumes in high energy heavy ion collisions. This is achieved by modeling the temperature dependence of the condensates, mesonic collective excitations, decay rates of the associated fields, and employing the Langevin and Fokker-Planck equations. Within this model, we find that the equilibration times are short compared with the expansion time, making disoriented isospin condensates a viable explanation for the anomalous fluctuations observed at the LHC.</p>

Olivia Chabowski

Joseph I. Kapusta

Relaxation times for disoriented isospin condensates in high energy heavy ion collisions

Quantum chromodynamics (QCD) is expected to have a first order phase transition between the confined hadron gas and the deconfined quark gluon plasma at high baryon densities. This will result in phase boundary effects in the metastable and unstable regions. It is important to include these effects in phenomenological models of heavy ion collisions to identify experimental signatures of a phase transition. This requires building intuition on phase separation in rapidly expanding fluids. In this work we present the covariant equations of relativistic hydrodynamics with a phase boundary, provide prescriptions to extend the equation of state to metastable and unstable regions, and show the effects of spinodal separation in a Bjorken flow.

Thomas Welle

Covariant formulation of spinodal decomposition in rapidly expanding quark gluon plasma

We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity <math><msub><mi>N</mi><mtext>tot</mtext></msub></math> and average energy <math><mrow><msub><mi>E</mi><mtext>tot</mtext></msub><mo>/</mo><msub><mi>N</mi><mtext>tot</mtext></msub></mrow></math> is related to the speed of sound <math><msub><mi>c</mi><mi>s</mi></msub></math> by <math><mrow><msubsup><mi>c</mi><mi>s</mi><mn>2</mn></msubsup><mo>=</mo><mi>d</mi><mo>ln</mo><mrow><mo>(</mo><msub><mi>E</mi><mtext>tot</mtext></msub><mo>/</mo><msub><mi>N</mi><mtext>tot</mtext></msub><mo>)</mo></mrow><mo>/</mo><mi>d</mi><mo>ln</mo><msub><mi>N</mi><mtext>tot</mtext></msub></mrow></math> if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity <math><mi>N</mi></math> and energy <math><mi>E</mi></math> introduce corrections between <math><msubsup><mi>c</mi><mi>s</mi><mn>2</mn></msubsup></math> and <math><mrow><mi>d</mi><mo>ln</mo><mo>(</mo><mi>E</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>/</mo><mi>d</mi><mo>ln</mo><mi>N</mi></mrow></math> that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freeze-out temperature <math><msub><mi>T</mi><mi>FO</mi></msub></math> over the maximum initial temperature of the fluid <math><msub><mi>T</mi><mn>0</mn></msub></math>; the nonthermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions.

Jean-François Paquet

Analytical insights into the interplay of momentum, multiplicity, and the speed of sound in heavy-ion collisions

The magnitude of fluctuations between charged and neutral kaons measured by the ALICE Collaboration in heavy-ion collisions at the LHC exceeds conventional explanation. Here it is shown that if the scalar condensate, which is typically associated with chiral symmetry, is accompanied by an <math><mrow><mi>isospin</mi><mo>=</mo><mn>1</mn></mrow></math> field, then the combination can produce large fluctuations where <math><mrow><mrow><mo>〈</mo><mover><mi>u</mi><mo>¯</mo></mover><mi>u</mi><mo>〉</mo></mrow><mo>≠</mo><mrow><mo>〈</mo><mover><mi>d</mi><mo>¯</mo></mover><mi>d</mi><mo>〉</mo></mrow></mrow></math>. Hadronizing strange and antistrange quarks might then strongly fluctuate between charged (<math><mrow><mi>u</mi><mover><mi>s</mi><mo>¯</mo></mover></mrow></math> or <math><mrow><mi>s</mi><mover><mi>u</mi><mo>¯</mo></mover></mrow></math>) and neutral (<math><mrow><mi>d</mi><mover><mi>s</mi><mo>¯</mo></mover></mrow></math> or <math><mrow><mi>s</mi><mover><mi>d</mi><mo>¯</mo></mover></mrow></math>) kaons.

Scott Pratt

Disoriented isospin condensates may be the source of anomalous kaon correlations measured in Pb-Pb collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV

Measurements of the dynamical correlations between neutral and charged kaons in central Pb-Pb collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV by the ALICE Collaboration display anomalous behavior relative to conventional heavy-ion collision simulators such as AMPT, EPOS, and HIJING. We consider other conventional statistical models, none of which can reproduce the magnitude and centrality dependence of the correlations. The data can be reproduced by coherent emission from domains, which grow in number and volume with increasing centrality. We show that the energy released by condensation of strange quarks may be sufficient to explain the anomaly.

Confronting anomalous kaon correlations measured in Pb-Pb collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV

The drag and diffusion coefficients are studied within the framework of Fokker-Planck dynamics for the case of a charm quark propagating in an expanding quark-gluon plasma. The space-time evolution of the nuclear matter created in the relativistic heavy-ion collision is modeled using music, a <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn><mi>D</mi></mrow></math> relativistic viscous hydrodynamic approach. The effect of viscous corrections to the heavy quark transport coefficients is explored by considering scattering processes with thermal quarks and gluons in the medium. It is observed that the momentum diffusion of the heavy quarks is sensitive to the shear and bulk viscosity to entropy ratios. The collisional energy loss of the charm quark in the viscous quark-gluon plasma is analyzed.

Canada

India

Manu Kurian

Vinod Chandra

Sangyong Jeon

Charles Gale

Charm quark dynamics in quark-gluon plasma with 3 <math><mo>+</mo></math> 1D viscous hydrodynamics

The particle content of the Singh-Hagen model (SH) in <math id="M2"><mi>D</mi></math> dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding source terms, we provide a unitarity analysis in <math id="M3"><mi>D</mi></math> dimensions. In addition, we have also analyzed the positivity of the massless Hamiltonian.