<p>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.</p>

Germany

Olaf Kaczmarek

Frithjof Karsch

United States

Peter Petreczky

Christian Schmidt

Sipaz Sharma

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

<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>

Dibyendu Bala

India

Sayantan Sharma

Swagatam Tah

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

We calculate the temperature dependence of bottomonium correlators in (2+1)-flavor lattice QCD with the aim to constrain in-medium properties of bottomonia at high temperature. The lattice calculations are performed using HISQ action with physical strange quark mass and light quark masses twenty times smaller than the strange quark mass at two lattice spacings $\textit{a}$ = 0$\textit{.}$0493 fm and 0$\textit{.}$0602 fm, and temporal extents $\textit{N}$ = 16 − 30, corresponding to the temperatures $\textit{T}$ = 133 − 250 MeV. We use a tadpole-improved NRQCD action including spin-dependent $\textit{v}$ corrections for the heavy quarks and extended meson operators in order to be sensitive to in-medium properties of the bottomonium states of interest. We find that within estimated errors the bottomonium masses do not change compared to their vacuum values for all temperatures under our consideration; however, we find different nonzero widths for the various bottomonium states.

China

Heng-Tong Ding

Wei-Ping Huang

Rasmus Larsen

Stefan Meinel

Swagato Mukherjee

Zhanduo Tang

In-medium bottomonium properties from lattice NRQCD calculations with extended meson operators

In this work, we report a lattice calculation of -dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer − . The calculations are based on an = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer − .

Xiang Gao

Qi Shi

Sergey Syritsyn

Yong Zhao

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), $$ \overset{\sim }{H}\left(x,\xi, t\right) $$ , at zero skewness, , with multiple values of the momentum transfer, . Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on an = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of = 0 093 fm, and a pion mass of = 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of $$ \overset{\sim }{H} $$ up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space.

Shohini Bhattacharya

Poland

Krzysztof Cichy

Martha Constantinou

Andreas Metz

Joshua Miller

Fernanda Steffens

Moments of axial-vector GPD from lattice QCD: quark helicity, orbital angular momentum, and spin-orbit correlation

We present a lattice quantum chromodynamics (QCD) calculation of the <math><mi>x</mi></math>-dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of <math><mi>a</mi><mo>=</mo><mn>0.076</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> at physical pion mass, with the pion boosted to 1.8 GeV and kaon boosted to 2.3 GeV. We renormalize the matrix elements in the hybrid scheme and match to <math><mover><mi>MS</mi><mo>¯</mo></mover></math> with a subtraction of the leading renormalon in the Wilson-line mass. The perturbative matching is improved by resumming the large logarithms related to the small quark and gluon momenta in the soft-gluon limit. After resummation, we demonstrate that we are able to calculate a range of <math><mi>x</mi><mo>∈</mo><mo>[</mo><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><mn>1</mn><mo>−</mo><msub><mi>x</mi><mn>0</mn></msub><mo>]</mo></math> with <math><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><mn>0.25</mn></math> for pion and <math><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><mn>0.2</mn></math> for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the <math><mi>x</mi></math>-dependence cannot be direct calculated beyond these ranges, we estimate higher moments of the pion and kaon DAs by complementing our calculation with short-distance factorization.

Ian Cloët

Nikhil Karthik

Rui Zhang

Lattice QCD calculation of <math><mi>x</mi></math>-dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation

We report the first lattice QCD computation of pion and kaon electromagnetic form factors, <math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math>, at large momentum transfer up to 10 and <math><mn>28</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, respectively. Utilizing physical masses and two fine lattices, we achieve good agreement with JLab experimental results at <math><msup><mi>Q</mi><mn>2</mn></msup><mo>≲</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>. For <math><msup><mi>Q</mi><mn>2</mn></msup><mo>≳</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, our results provide ab initio QCD benchmarks for the forthcoming experiments at JLab 12 GeV and future electron-ion colliders. We also test the QCD collinear factorization framework utilizing our high-<math><msup><mi>Q</mi><mn>2</mn></msup></math> form factors at next-to-next-to-leading order in perturbation theory, which relates the form factors to the leading Fock-state meson distribution amplitudes. Comparisons with independent lattice QCD calculations using the same framework demonstrate, within estimated uncertainties, the universality of these nonperturbative quantities.

Andrew D. Hanlon

QCD Predictions for Meson Electromagnetic Form Factors at High Momenta: Testing Factorization in Exclusive Processes

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to   <math> <mover> <mi>MS</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\textrm{MS}} $$  with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum P  z  ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

Ethan Baker

Dennis Bollweg

Peter Boyle

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

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

We study the correlator of temporal Wilson lines at nonzero temperature in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor lattice QCD with the aim to define the heavy quark-antiquark potential at nonzero temperature. For temperatures <math><mn>153</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>352</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> the spectral representation of this correlator is consistent with a broadened peak in the spectral function, position, or width of which then defines the real or imaginary parts of the heavy quark-antiquark potential at nonzero temperature, respectively. We find that the potential’s real part is not screened contrary to the widely held expectations. We comment on how this fact may modify the picture of quarkonium melting in the quark-gluon plasma.