We study some interesting aspects of the spectral properties of SU(3) gauge theory, both with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By calculating the eigenstates of a massless overlap Dirac operator on the gauge configurations, we implement a gauge-invariant method to study spectral properties of non-Abelian gauge theories. We have unambiguously categorized Dirac eigenvalues into different regimes based on a quantity defined in terms of the ratios of nearest neighbor spacings. While majority of these eigenstates below the magnetic scale are similar to those of random matrices belonging to the Gaussian Unitary ensemble at temperatures much higher than the chiral crossover transition in QCD, a few among them start to become prominent only near the crossover. These form fractal-like clusters with the median value for their fractal dimensions hinting at the universality class of the chiral transition in QCD. We further demonstrate that momentum modes below the magnetic scale in a particular non-equilibrium state of QCD are classically chaotic and estimate an upper bound on the thermalization time ∼ 1.44 fm/c by matching this magnetic scale with that of a thermal state at ∼ 600 MeV.

India

Harshit Pandey

Ravi Shanker

Sayantan Sharma

Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories

<p>We calculate the spatial Wilson line correlator for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> flavor QCD using highly improved staggered quark discretization for fermions and in quenched QCD for a wide range of temperatures, from the chiral crossover temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>pc</mi></mrow></msub><mo>≃</mo><mn>156</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> or the deconfinement temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≃</mo><mn>300</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, respectively, up to 2 GeV. Extracting the spatial string tension for different lattice cutoffs and by performing a continuum extrapolation of this observable, we show that the soft (magnetic) gluons interact nonperturbatively even at temperatures <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≳</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We provide incriminating evidences to demonstrate that dimensionally reduced effective theories can describe these soft quark and gluon quasi-particles for both quenched and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> flavor QCD, at temperatures <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mo>≳</mo><mn>5</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>pc</mi></mrow></msub></mrow></math>. We also show for the first time the imprints of the nonperturbative pseudopotential in the properties of mesonic screening masses for temperatures ranging from 0.8 to 164 GeV in the quark-gluon plasma.</p>

Germany

Dibyendu Bala

Olaf Kaczmarek

United States

Peter Petreczky

Swagatam Tah

Spatial String Tension and Its Effects on Screening Correlators in a Thermal QCD Plasma

We measure the maximal Lyapunov exponent <math altimg='si1.svg'><msub><mrow><mi>&#955;</mi></mrow><mrow><mi>L</mi></mrow></msub></math> of physical states in a SU(2) gauge theory consisting of soft momentum modes both in and out-of-thermal equilibrium conditions using ab-initio lattice techniques. We have implemented different algorithms to appropriately describe the dynamics of soft-modes for a wide range of temperatures and under non-equilibrium conditions. The non-equilibrium state has been realized starting from an over-occupied initial condition for low momentum soft gluons whereas the thermal state comprises of strongly interacting soft gluons at temperatures where these are well separated from the hard momentum modes. Spectra of positive Lyapunov exponents is observed in both these states, similar to a chaotic dynamical system. From the Kolmogorov-Sinai entropy rate measured in terms of this spectrum, we estimate a typical time-scale of <math altimg='si2.svg'><mo>&#8764;</mo><mn>0.50</mn><mo stretchy='false'>(</mo><mn>3</mn><mo stretchy='false'>)</mo></math> fm/c to achieve thermalization at <math altimg='si3.svg'><mi>T</mi><mo>&#8764;</mo><mn>600</mn></math> MeV starting from the non-thermal state. We also measure, for the first time, the <math altimg='si1.svg'><msub><mrow><mi>&#955;</mi></mrow><mrow><mi>L</mi></mrow></msub></math> for long wavelength critical modes of SU(2) using the out-of-time-ordered correlator of a classical <math altimg='si4.svg'><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> scalar field theory, which shares the same universal behavior with SU(2), near the deconfinement phase transition. The <math altimg='si1.svg'><msub><mrow><mi>&#955;</mi></mrow><mrow><mi>L</mi></mrow></msub></math> is observed to maximize at the transition temperature.

Sayak Guin

Understanding thermalization in a non-Abelian gauge theory in terms of its soft modes

<p>The nonsinglet part of the chiral symmetry in quantum chromodynamics (QCD) with two light flavors is known to be restored through a crossover transition at a pseudocritical temperature. However, the temperature dependence of the singlet part of the chiral symmetry and whether it is effectively restored at the same temperature is not well understood. Using (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD configurations generated using the Möbius domain-wall discretization on an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math> lattice, we construct suitable observables where the singlet and nonsinglet chiral symmetries are disentangled in order to study their temperature dependence across the crossover transition. From the peak of the disconnected part of the chiral susceptibility, we obtain a pseudocritical temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>=</mo><msubsup><mrow><mn>158.7</mn></mrow><mrow><mo>−</mo><mn>2.3</mn></mrow><mrow><mo>+</mo><mn>2.6</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> where the nonsinglet part of the chiral symmetry is effectively restored. From a calculation of the topological susceptibility and its temperature dependence we find that the singlet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">U</mi><mi>A</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> part of the chiral symmetry is not effectively restored at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>≲</mo><mn>186</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.</p>

Rajiv V. Gavai

Mischa E. Jaensch

Frithjof Karsch

Taiwan

Mugdha Sarkar

Sipaz Sharma

Tristan Ueding

Aspects of the chiral crossover transition in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD with Möbius domain-wall fermions

We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting nonperturbative features as a function of time due to correlated momentum kicks it receives from the medium, eventually going over to a diffusive regime. We extract the momentum diffusion coefficient for a mass range describing charm and bottom quarks and find sizable discrepancies from the heavy-quark limit.

Sören Schlichting

Heavy-Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium

We study the QCD equation of state and the chiral condensate using the hadron resonance gas model with repulsive mean-field interactions. We find that the repulsive interactions improve the agreement with the lattice results on the derivatives of the pressure with respect to the baryon chemical potential up to eighth order. From the temperature dependence of the chiral condensate we estimate the crossover temperature as a function of baryon chemical potential, <math><mrow><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>)</mo></mrow></mrow></math>. We find that the chiral crossover line starts to deviate significantly from the chemical freeze-out line already for <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>&gt;</mo><mn>400</mn><mspace width="4pt"></mspace><mi>MeV</mi></mrow></math>. Furthermore, we find that the chiral pseudocritical line can be parametrized as <math><mrow><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>)</mo></mrow><mo>/</mo><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>−</mo><msub><mi>κ</mi><mn>2</mn></msub><msup><mrow><mo>[</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>]</mo></mrow><mn>2</mn></msup><mo>−</mo><msub><mi>κ</mi><mn>4</mn></msub><msup><mrow><mo>[</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>]</mo></mrow><mn>4</mn></msup></mrow></math> with <math><mrow><msub><mi>κ</mi><mn>2</mn></msub><mo>=</mo><mn>0.0150</mn><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math> and <math><mrow><msub><mi>κ</mi><mn>4</mn></msub><mo>=</mo><mn>3.1</mn><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math>, which are in agreement with lattice QCD results for small values of <math><msub><mi>μ</mi><mi>B</mi></msub></math>. For the first time we find a tiny but nonzero value of <math><msub><mi>κ</mi><mn>4</mn></msub></math> in our study.

Deeptak Biswas

Chiral condensate and the equation of state at nonzero baryon density from the hadron resonance gas model with a repulsive mean field

Mean-field model quantum field theories of hadrons were traditionally developed to describe cold and dense nuclear matter and are by now very well constrained from the recent neutron star merger observations. We show that when augmented with additional known hadrons and resonances but not included earlier, these mean-field models can be extended beyond its regime of applicability. Calculating some specific ratios of baryon number susceptibilities for finite temperature and moderate values of baryon densities within mean-field approximation, we show that these match consistently with the lattice QCD data available at lower densities, unlike the results obtained from a noninteracting hadron resonance gas model. We also estimate the curvature of the line of constant energy density, fixed at its corresponding value at the chiral crossover transition in QCD, in the temperature-density plane. The number density at low temperatures and high density is found to be about twice the nuclear saturation density. Moreover from this line we can indirectly constrain the critical endpoint of QCD to be beyond <math><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>596</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> for temperature <math><mo>∼</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

Aman Abhishek

Toward a universal description of hadronic phase of QCD

We calculate the eigenmodes of the highly improved staggered quark matrix near the chiral crossover transition in QCD with <math><mn>2</mn><mo>+</mo><mn>1</mn></math> flavors with the aim to gain more insights into its temperature dependence. On performing the continuum extrapolation, we do not observe any gap opening up in the infrared part of the eigenvalue density of the QCD Dirac operator; instead we observe a peak. The existence of the peak and oscillations of the infrared eigenmodes can be understood in terms of an interacting ensemble of instantons. From the properties of the continuum extrapolated eigenspectrum we further show that the anomalous <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> part of the chiral symmetry is not effectively restored simultaneously along with its nonsinglet counterpart. We provide an explanation for this observation, further showing interesting connections between the anomalous <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> restoration and the change in the infrared part of the eigenvalue distribution.

Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit

We present a microscopic study of chiral plasma instabilities and axial charge transfer in non-Abelian plasmas with a strong gauge-matter coupling <math><mrow><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>64</mn></mrow></math>, by performing <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn><mi>D</mi></mrow></math> real-time classical-statistical lattice simulation with dynamical fermions. We explicitly demonstrate for the first time that—unlike in an Abelian plasma—the transfer of chirality from the matter sector to the gauge fields occurs predominantly due to topological sphaleron transitions. We elaborate on the similiarities and differences of the axial charge dynamics in cold Abelian U(1) and non-Abelian SU(2) plasmas, and comment on the implications of our findings for the study of anomalous transport phenomena, such as the chiral magnetic effect in QCD matter.

Chiral Instabilities and the Fate of Chirality Imbalance in Non-Abelian Plasmas

In this work we address the question of how well the chiral crossover transition can be understood in terms of a noninteracting hadron resonance gas model. Using the latest results on the variation of hadron masses as a function of the pion mass from lattice quantum chromodynamics, we study the temperature dependence of the renormalized chiral condensate in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor QCD. Furthermore, we suggest a better criterion to estimate of the pseudocritical temperature, which gives <math><mrow><msub><mi>T</mi><mi>c</mi></msub><mo>=</mo><mn>161.2</mn><mo>±</mo><mn>1.7</mn></mrow></math> MeV, which is much improved compared to all the earlier results within the hadron resonance gas model or chiral perturbation theory. For the curvature of the pseudocritical line we find <math><mrow><msub><mi>κ</mi><mn>2</mn></msub><mo>=</mo><mn>0.0203</mn><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>, which is in very good agreement with continuum extrapolated lattice results.