We present a lattice determination of the heavy-quark diffusion coefficient in (2+1)-flavor QCD with almost physical quark masses. The momentum and spatial diffusion coefficients are extracted for a wide temperature range, from $\textit{T}$ = 163 MeV to 10 GeV. The results are in agreement with previous works from the HotQCD collaboration, and show fast thermalization of the heavy quark inside the QGP. Near the chiral crossover temperature $\textit{T}$ ≃ 150 MeV, our results are close to the AdS/CFT estimation computed at strong coupling.

United States

Dennis Bollweg

Jorge Golán

Germany

Olaf Kaczmarek

Rasmus Larsen

Guy Moore

Swagato Mukherjee

Peter Petreczky

China

Hai-Tao Shu

Simon Stendebach

Johannes Weber

Temperature dependence of heavy quark diffusion from (2+1)-flavor lattice QCD

Quarkonia, which are bound states of a heavy quark and antiquark, play a key role in probing the quark-gluon plasma (QGP). The dynamics of quarkonia in the QGP are encoded in their finite-temperature spectral functions. In this work, we estimate the quarkonium spectral functions in the pseudoscalar channel using (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD with a pion mass of 320 MeV, at temperatures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>220</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.2</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>251</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.4</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>293</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">(</mo><mn>1.6</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></math>. Reconstructing the spectral function from the Euclidean lattice correlator is a well-known ill-posed problem, requiring additional physics-motivated input. We address this by smoothly matching contributions from different frequency regions of the spectral function, using appropriate physics valid for each region. The spectral function around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>∼</mo><mn>2</mn><msub><mi>M</mi><mi>q</mi></msub></math> is obtained using a nonperturbative complex potential, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>≫</mo><mn>2</mn><msub><mi>M</mi><mi>q</mi></msub></math> it is modeled using results from vacuum perturbation theory. Since the pseudoscalar channel does not receive a transport contribution near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>∼</mo><mn>0</mn></math>, we find that the combination of these two regions already provides a good description of the relativistic lattice pseudoscalar correlator. We observe a substantial thermal width in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> state, indicating that pseudoscalar charmonium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>) is nearing dissolution at the studied temperatures. In comparison, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub></math> ground state exhibits little change and remains well defined.

Pakistan

Sajid Ali

Dibyendu Bala

 Pavan

Thermal static potential and pseudoscalar quarkonium spectral functions from (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD

We study the generalized charm susceptibilities 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 on the lattice at several lattice spacings. We show that, below the chiral crossover, these susceptibilities are well described by the hadron resonance gas (HRG) model if charmed hadrons not listed in tables of the Particle Data Group are included. However, the HRG description abruptly breaks down just above the chiral crossover. To understand this, we use a model for the charm pressure in which it is expressed as the sum of partial pressures from charmed baryons, charmed mesons, and charm quarks. We present continuum estimates of these partial pressures and find that, while the partial pressures of charmed mesons and baryons drop below their respective HRG predictions, the charm quark pressure becomes nonzero above the chiral crossover.

Frithjof Karsch

Christian Schmidt

Sipaz Sharma

Generalized susceptibilities and the properties of charm degrees of freedom across the QCD crossover temperature

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.

India

Sayantan Sharma

Swagatam Tah

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

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>.

Rajiv V. Gavai

Mischa E. Jaensch

Taiwan

Mugdha Sarkar

Ravi Shanker

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

Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at <math><mi>T</mi><mo>=</mo><mn>470</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> (<math><mo>∼</mo><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math>), as well as in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor QCD at <math><mi>T</mi><mo>=</mo><mn>220</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> (<math><mo>∼</mo><mn>1.2</mn><msub><mi>T</mi><mrow><mi>p</mi><mi>c</mi></mrow></msub></math>) with <math><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>320</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. In order to quantify the nonperturbative effects, the lattice correlator is compared with the corresponding <math><mi>NLO</mi><mo>+</mo><msup><mi>LPM</mi><mi>LO</mi></msup></math> estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian process regression. We find that the resulting photon rates agree within errors.

Anthony Francis

France

Greg Jackson

Jonas Turnwald

Nicolas Wink

Lattice QCD estimates of thermal photon production from the QGP

We analyze the color-magnetic (or “<math><mi>B</mi></math>”) field two-point function that encodes the finite-mass correction to the heavy-quark momentum-diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at <math><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math>, using a range of gradient flow times for noise suppression and operator renormalization. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations to next-to-leading order of this correlation function, matching gradient-flowed correlators to <math><mover><mi>MS</mi><mo>¯</mo></mover></math>, are used to resolve nontrivial renormalization issues. We perform a spectral reconstruction based on perturbative model fits to estimate the coefficient <math><msub><mi>κ</mi><mi>B</mi></msub></math> of the finite-mass correction to the heavy-quark momentum-diffusion coefficient. The approach we present here yields high-precision data for the correlator with all renormalization issues incorporated at next-to-leading order and is also applicable for actions with dynamical fermions.

Luis Altenkort

David de la Cruz

Guy D. Moore

Lattice <math><mrow><mi>B</mi></mrow></math>-field correlators for heavy quarks

Determining the type of excitations that can exist in a thermal medium is key to understanding how hadronic matter behaves at extreme temperatures. In this work we study this question for pseudo-scalar mesons comprised of light-strange and strange-strange quarks, analysing how their low-energy spectral properties are modified as one passes through the high-temperature chiral crossover region between T = 145.6 MeV and 172.3 MeV. We utilise the non-perturbative constraints satisfied by correlation functions at finite temperature in order to extract the low-energy meson spectral function contributions from spatial correlator lattice data in N  f  = 2 + 1 flavour QCD. The robustness of these contributions are tested by comparing their predictions with data for the corresponding temporal correlator at different momentum values. We find that around the pseudo-critical temperature T pc the data in both the light-strange and strange-strange channels is consistent with the presence of a distinct stable particle-like ground state component, a so-called thermoparticle excitation. As the temperature increases this excitation undergoes collisional broadening, and this is qualitatively the same in both channels. These findings suggest that pseudo-scalar mesons in QCD have a bound-state-like structure at low energies within the chiral crossover region which is still strongly influenced by the vacuum states of the theory.

Peter Lowdon

Owe Philipsen

Pseudo-scalar meson spectral properties in the chiral crossover region of QCD

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range <math><mrow><mn>195</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>&lt;</mo><mi>T</mi><mo>&lt;</mo><mn>293</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, the spatial diffusion coefficients of the charm and bottom quarks are smaller than those obtained in phenomenological models that describe the <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra and elliptic flow of open heavy flavor hadrons.

Norway

Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice 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