arXiv subjects

Frithjof Karsch

Publications and source records attributed to Frithjof Karsch.

At least 19 recordsLinked to original sources

arXiv2026

Testing machine-learned distributions against Monte Carlo data for the QCD chiral phase transition

We demonstrate that conditional Masked Autoregressive Flows constitute a flexible interpolation tool for lattice QCD observables, conditioned on bare lattice parameters. As a benchmark, we use the chiral phase structure of QCD with five degenerate light quark flavours, which on coarse lattices exhibits a region of first-order chiral transitions terminating in a critical quark mass. The method successfully reproduces standard reweighting in the gauge coupling, and naturally extends to interpolation in quark mass and spatial volume, for which reweighting is computationally prohibitive or inapplicable, respectively. Once trained, the model generates samples across the full parameter space in minutes, which can be used to obtain consistent first estimates of the critical quark mass without simulating all intermediate parameter values. This offers a concrete reduction in the number of lattice ensembles required. Precision on the critical mass from learned distributions is so far prohibited by the mode-covering effect inherent to maximum-likelihood-based training, which introduces a systematic bias near first-order transitions. At the current stage, the method is well-suited for a range of practical applications: localising phase boundaries, identifying the universal scaling axes at a critical point, and accelerating informed determinations of parameter values ahead of high-precision Monte Carlo campaigns.

hep-lat↗

arXiv2026

Universal and non-universal finite-volume effects in the vicinity of chiral phase transition in (2+1)-flavor QCD

In this proceeding, we discuss the finite-size scaling analysis of the order parameter related to the chiral phase transition in QCD with two massless quarks. We use data obtained in lattice QCD calculations performed with highly improved staggered quarks (HISQ) for a range of light quark masses, $1/240 \leq m_\ell/m_s \leq 1/27$ for different spatial volumes ($N_\sigma$) on Euclidean lattices with temporal extent $N_\tau=8$, satisfying $3\,N_\tau \leq N_\sigma \leq 10\,N_\tau$. We observe that infinite volume extrapolated data for the order parameter agree reasonably well with the expected $O(2)$ scaling behavior even for physical ratios of the light-to-strange quark mass ratio. We quantify deviations from asymptotic scaling and perform a detailed analysis of the influence of finite-size effects in terms of temperature and quark masses at a fixed lattice cutoff. This is crucial for improving the reliability of the infinite-volume extrapolated estimate of the chiral order parameter and for a more precise determination of chiral phase transition temperature from direct Lattice QCD simulations.

hep-lat↗

arXiv2025

Higher order net-baryon number cumulants and baryon-strangeness correlations: Comparing QCD results on thepseudo-critical line with RHIC-BES II results on the freeze-out line

We present lattice QCD results for ratios of net-baryon number cumulants along the pseudo-critical line and compare them with STAR measurements from the RHIC BES-II program. The ratio of first and second order cumulants, $R_{12}^B$, agrees well with corresponding net-proton number cumulants down to $\sqrt{s_{NN}}=11.5$ GeV or baryon chemical potentials $\mu_B/T \le 2$. Likewise higher-order cumulant ratios, $R_{31}^B$ and $R_{42}^B$, show no sign for the existence of a critical point in the parameter range explored with these cumulant ratios. A QCD critical point is unlikely to occur within the BES-II range in collider mode. Moreover, the results demonstrate that a non-interacting HRG description breaks down for $\mu_B/T > 1$. We further analyze baryon-strangeness correlations normalized by strangeness fluctuations, finding consistency with STAR data at large beam energies but deviations at lower energies. Comparisons of electric-charge and strangeness correlations with STAR and ALICE data also show agreement at high energies, while the deviations at lower energies emphasize the role of unobserved strange resonances and the need for controlled feed-down corrections in baryon-strangeness correlations.

hep-lat↗

arXiv2025

Finite-volume analysis and universal scaling signatures near the chiral phase transition in (2+1)-flavor QCD

For quantifying the universal properties of the chiral phase transition in QCD through numerical calculations on a discrete space-time lattice, one needs to perform controlled extrapolations to the continuum and infinite-volume limits followed by an extrapolation to the limit of massless light quarks. We discuss here, the results on the latter two limits at still finite lattice spacings. We use here for chiral symmetry breaking, an improved order parameter free of additive and multiplicative divergences and we analyse its volume and quark mass dependence. Comparing to the expected universal behavior in the chiral limit, we quantify deviations from the universal finite-size scaling behavior as function of the light to strange quark mass ratio.

hep-lat↗

arXiv2025

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

We study the generalized charm susceptibilities in 2+1 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 non-zero above the chiral crossover.

hep-lat↗

arXiv2025

Towards a parameter-free analysis of the QCD chiral phase transition and its universal critical behavior

To quantify the universal properties of chiral phase transition in (2+1)-flavor QCD, we use an improved, renormalized order parameter for the chiral symmetry breaking. We construct ratios of this divergence-free order parameter from its values for different pairs of light quark masses. From this, we determine in a parameter-independent manner, the chiral phase transition temperature $T_c$ and the associated critical exponent $\delta$ of the universality class. We present first numerical results of these calculations on $N_\tau=8$ lattices, with staggered fermions.

hep-lat↗

arXiv2025

Thermodynamics of charmed hadrons across chiral crossover from lattice QCD

We use up to fourth-order charm fluctuations and their correlations with net baryon number, electric charge, and strangeness fluctuations, calculated within the framework of lattice QCD, to study the continuum partial pressure contributions of charmed baryons and mesons. We show that, at and below the chiral crossover temperature, these partial pressures receive enhanced contributions from experimentally unobserved charmed hadrons predicted by the Quark Model. Additionally, we demonstrate that at the chiral crossover, the Hadron Resonance Gas description breaks down, signaling the modification of open charm hadrons and thereby implying the onset of charm deconfinement. We present evidence for the survival of low-lying non-radial $1S$ and $1P$ hadron-like excitations above the chiral crossover, which hints at the sequential melting of charmed hadrons. Finally, we investigate the continuum partial pressure contribution of charm quark-like excitation that emerges at the chiral crossover and calculate its temperature-dependent in-medium mass.

hep-lat↗

arXiv2024

Towards a parameter-free determination of critical exponents and chiral phase transition temperature in QCD

In order to quantify the universal properties of the chiral phase transition in (2+1)-flavor QCD, we make use of an improved, renormalized order parameter for chiral symmetry breaking which is obtained as a suitable difference of the $2$-flavor light quark chiral condensate and its corresponding light quark susceptibility. Having no additive ultraviolet as well as multiplicative logarithmic divergences, we use ratios of this order parameter constructed from its values for two different light quark masses. We show that this facilitates determining in a parameter-independent manner, the chiral phase transition temperature $T_c$ and the associated critical exponent $\delta$ which, for sufficiently small values of the light quark masses, controls the quark mass dependence of the order parameter at $T_c$. We present first results of these calculations from our numerical analysis performed with staggered fermions on $N_\tau=8$ lattices.

hep-lat↗

arXiv2024

Aspects of the chiral crossover transition in (2+1)-flavor QCD with M\"{o}bius domain-wall fermions

The non-singlet part of the chiral symmetry in QCD with two light flavors is known to be restored through a crossover transition at a pseudo-critical 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 (2+1)-flavor QCD configurations generated using the M\"{o}bius domain-wall discretization on an $N_\tau=8$ lattice, we construct suitable observables where the singlet and non-singlet 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 pseudo-critical temperature $T_{pc}=158.7{}_{{}-2.3}^{{}+2.6}$ MeV where the non-singlet part of the chiral symmetry is effectively restored. From a calculation of the topological susceptibility and its temperature dependence we find that the singlet $U_A(1)$ part of the chiral symmetry is not effectively restored at $T<186$ MeV.

hep-lat↗

arXiv2023

Lee-Yang and Langer edge singularities from analytic continuation of scaling functions

We discuss the analytic continuation of scaling function in the 3-dimensional Z(2),O(2) andO(4) universality classes using the Schofield representation of the magnetic equation of state. We show that a determination of the location of Lee-Yang edge singularities and, in the case of Z(2), also the Langer edge singularity yields stable results. Results for the former are in good agreement with Functional Renormalization Group calculations. We also present results for the location of the Langer edge singularity in the 3-d,Z(2) universality class. We find that in terms of the complex scaling variable z the distance of the Langer edge singularity to the critical point agrees within errors with that of the Lee-Yang edge singularity. Furthermore the magnitude of the discontinuity along the Langer branch cut is an order of magnitude smaller than that along the Lee-Yang branch cut.

hep-lat↗

arXiv2023

Scaling functions of the three-dimensional $Z(2)$, $O(2)$ and $O(4)$ models and their finite size dependence in an external field

We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$ universality classes and their finite size dependence using Monte Carlo simulations of improved $ϕ^4$ models. Results for the scaling functions are fitted to the Widom-Griffiths form, using a parametrization also used in analytic calculations. We find good agreement on the level of scaling functions and the location of maxima in the universal part of susceptibilities. We also find that an earlier parametrization of the $O(4)$ scaling function, using 14 parameters, is well reproduced when using the Widom-Griffiths form with only three parameters. We furthermore show that finite size corrections to the scaling functions are distinctively different in the $Z(2)$ and $O(N)$ universality classes and determine the volume dependence of the peak locations in order parameter and mixed susceptibilities.

hep-lat↗

arXiv2023

Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

hep-lat↗

arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

hep-ph↗

arXiv2022

The International Lattice Data Grid -- towards FAIR Data

The International Lattice Data Grid (ILDG) is a community-wide initiative to realize the sharing of primary data from lattice QCD simulations according to the principles of FAIR data. We recall the basic concepts of ILDG as a federation of autonomous regional grids with common standards for (meta-)data and services, and report on current activities, progress, and plans to restore and extend the usability of ILDG.

hep-lat↗

arXiv2022

Lattice QCD at non-zero temperature and density

Soon after the formulation of Quantum Chromodynamics in 1972 its regularization on Euclidean space-time lattices had been introduced by Kenneth Wilson. This paved ground for numerical studies of non-perturbative aspects of QCD, first shown by Michael Creutz. Ever since these first lattice QCD calculations the exploration of the QCD phase diagram and the thermodynamics of strong-interaction matter at non-zero temperature and density was pursued vigorously. In this brief review I try to highlight some of the results on QCD thermodynamics obtain during the last 42 years through lattice QCD calculations.

hep-lat↗

arXiv2022

A machine learning approach to the classification of phase transitions in many flavor QCD

Normalizing flows are generative machine learning models which can efficiently approximate probability distributions, using only given samples of a distribution. This architecture is used to interpolate the chiral condensate obtained from QCD simulations with five degenerate quark flavors in the HISQ action. From this a model for the probability distribution of the chiral condensate as function of lattice volume, quark mass and gauge coupling is obtained. Using the model, first order and crossover regions can be classified and the boundary between these regions can be marked by a critical mass. An extension of this model to studies of phase transitions in QCD with variable number of flavors is expected to be possible.

hep-lat↗

arXiv2022

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

hep-lat↗

arXiv2022

Searching for the QCD critical point along the pseudo-critical/freeze-out line using Padé-resummed Taylor expansions of cumulants of conserved charge fluctuations

Using high-statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we construct estimators for the radius of convergence from an eighth order series expansion of the pressure as well as the number density. We show that the estimator for pressure and number density will be identical in the asymptotic limit. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$~MeV, we find the estimator of the radius of convergence to be $μ_B/T \gtrsim\ 3$ for strangeness-neutral matter. We also present results for the pole structure of the Padé approximants for the pressure at non-zero values of the baryon chemical potential and show that the pole structure of the [4,4] Padé is consistent with not having a critical point at temperatures larger than $135~$MeV and a baryon chemical potential smaller than $μ_B/T \sim \ 2.5$.

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