arXiv subjects

Zoltán Fodor

Publications and source records attributed to Zoltán Fodor.

16 recordsLinked to original sources

arXiv2026

Electric charge fluctuations from lattice QCD in the continuum limit

Electric charge fluctuations $χ_n^Q$ allow comparisons between theory and experiment, but are elusive on the lattice due to severe cutoff effects. We use a 4HEX action to obtain $χ_2^Q$ and, for the first time ever, $χ_4^Q$ in the continuum limit. We find disagreement with the hadron resonance gas (HRG) model, which we cannot explain with finite volume effects. We include light meson interactions in the HRG model via the S-matrix, reducing the tension for $χ_4^Q$, but worsening the agreement for $χ_2^Q$. We propose measuring the ratio $χ_4^Q/χ_2^Q$ at the LHC to investigate this tension.

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arXiv2026

Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($μ_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $μ_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $μ_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $μ_B\approx500$~MeV.

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arXiv2025

Finite density lattice QCD without extrapolations

Finite density lattice QCD usually relies on extrapolations in baryon chemical potential ($μ_B$), be it Taylor expansion, T' expansion (\cite{Borsanyi:2021sxv}) or analytical continuation. However, their range of validity is difficult to control. In the canonical formulation, the baryon density is the parameter of the system, not $μ_B$. Here we demonstrate that we can access finite density QCD in the canonical formulation with physical quark masses. We present first results with both the strangeness ($n_S$) and baryon ($n_B$) densities as parameters. Specifically, we compute the QCD pressure and chemical potentials as functions of $n_B$ and $n_S$. Our computations rely on high-statistics simulations with 2+1 4HEX-staggered fermions.

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arXiv2025

Finite density QCD phase structure from strangeness fluctuations

Charting the phase diagram of Quantum Chromodynamics (QCD) at large density is a challenging task due to the complex action problem in lattice simulations. Through simulations at imaginary baryon chemical potential $μ_B$ we observe that, if the strangeness neutrality condition is imposed, both the strangeness chemical potential $μ_S/μ_B$ and the strangeness susceptibility $χ_2^S$ take on constant values at the chiral transition for varying $μ_B$. We present new lattice data to extrapolate contours of constant $μ_S/μ_B$ or $χ_2^S$ to finite baryon chemical potential. We argue that they are good proxies for the QCD crossover because, as we show, they are only mildly influenced by criticality and by finite volume effects. We obtain continuum limits for these proxies up to $μ_B = 400$ MeV, through a next-to-next-to-leading order (N$^2$LO) Taylor expansion based on large-statistics data on $16^3 \times 8$, $20^3 \times 10$ and $24^3 \times 12$ lattices with our 4HEX improved staggered action. We show that these are in excellent agreement with existing results for the chiral transition and, strikingly, also with analogous contours obtained with the hadron resonance gas (HRG) model. On the $16^3 \times 8$ lattice, we carry out the expansion up to next-to-next-to-next-to-next-to-leading order (N$^4$LO), and extend the extrapolation beyond $μ_B=500$ MeV, again finding perfect agreement with the HRG model. This suggests that the crossover line constructed from this proxy starts deviating from the chemical freeze-out line near $μ_B\approx500$ MeV, as expected but not yet observed.

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arXiv2025

A new 4D lattice QCD equation of state: extended density coverage from a generalized $T^\prime$-expansion

We present a new equation of state for QCD in which the temperature $T$ and the three chemical potentials for baryon number $μ_B$, electric charge $μ_Q$ and strangeness $μ_S$ can be varied independently. This result is based on a generalization of the $T'$-expansion scheme, thanks to which the diagonal $μ_B$ extrapolation was pushed up to a baryo-chemical potential $μ_B/T \sim 3.5$ for the first time. This considerably extended the coverage of the Taylor expansion, limited to $μ_B/T < 2.5-3$. As a consequence, we are able to offer a substantially larger coverage of the four-dimensional QCD phase diagram as well, compared to previously available Taylor expansion results. Our results are based on new continuum estimated lattice results on the full set of second and fourth order fluctuations.

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arXiv2025

Search for a Lee-Yang edge singularity in high-statistics Wuppertal-Budapest data

Near a critical endpoint the Lee-Yang edge singularity approaches the real axis in the complex chemical potential plane. In the vicinity of the critical point the functional form of this approach depends on the universality class. Assuming a three dimensional Ising critical point in the QCD phase diagram the location of the critical endpoint can be extrapolated provided that the position of the Lee-Yang edge singularity is known at multiple temperatures. A popular method to estimate the position of a singularity is to model the free energy as a rational function of the baryon chemical potential $μ_\text{B}$. The parameters of this model can be constrained by the cumulants of the net baryon density taken at $μ_\text{B}^2\leq0$ . Using high-statistics simulations on a lattice $16^3\times8$ by the Wuppertal-Budapest Collaboration we estimate the location of the closest singularity in the QCD phase diagram. We also compare various models for the functional form of the free energy and discuss the predictive power of this approach.

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arXiv2024

Finite volume effects near the chiral crossover

The effect of a finite volume presents itself both in heavy ion experiments as well as in recent model calculations. The magnitude is sensitive to the proximity of a nearby critical point. We calculate the finite volume effects at finite temperature in continuum QCD using lattice simulations and set the focus on the vicinity of the chiral crossover. We investigate the impact of finite volumes at zero and small chemical potentials on the QCD transition through the chiral observables.

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arXiv2023

Continuum extrapolated high order baryon fluctuations

Fluctuations play a key role in the study of QCD phases. Lattice QCD is a valuable tool to calculate them, but going to high orders is challenging. Up to the fourth order, continuum results are available since 2015. We present the first continuum results for sixth order baryon fluctuations for temperatures between $T=130 - 200$ MeV, and eighth order at $T=145$ MeV in a fixed volume. We show that for $T \leq 145$ MeV, relevant for criticality search, finite volume effects are under control. Our results are in sharp contrast with well known results in the literature obtained at finite lattice spacing.

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arXiv2022

From ten-flavor tests of the $β$-function to $α_s$ at the Z-pole

New tests are applied to two $β$-functions of the much-discussed BSM model with ten massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The renormalization scheme of the two $β$-functions is defined on the gauge field gradient flow in respective finite or infinite physical volumes at zero lattice spacing. Recently published results in the ten-flavor theory led to indicators of an infrared fixed point (IRFP) in the finite-volume step $β$-function in the strong coupling regime of the theory arXiv:2004.00754. We analyze our substantially extended set of ten-flavor lattice ensembles at strong renormalized gauge couplings and find no evidence or hint for IRFP in the finite-volume step $β$-function within controlled lattice reach. We also discuss new ten-flavor tests of the recently introduced lattice definition and algorithmic implementation of the $β$-function defined on the gradient flow of the gauge field over infinite Euclidean space-time in the continuum. Originally we introduced this new algorithm to match finite-volume step $β$-functions in massless near-conformal gauge theories with the infinite-volume $β$-function reached in the chiral limit from small fermion mass deformations of spontaneous chiral symmetry breaking. Results from the lattice analysis of the ten-flavor infinite-volume $β$-function are consistent with the absence of IRFP from our step $β$-function based analysis. We make important contact at weak coupling in infinite volume with gradient flow based three-loop perturbation theory, serving as a first pilot study toward the long-term goal of developing alternate approach to the determination of the strong coupling $α_s$ at the Z-boson pole in QCD.

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arXiv2021

Quantifying corrections to the hadron resonance gas with lattice QCD

The hadron resonance gas (HRG) model and its extensions are often used to describe the hadronic phase of strongly interacting matter. In our work we use lattice-QCD simulations with temporal extents of $N_τ=8,10$ and $12$ to quantify corrections to the ideal HRG. Firstly, we determine a number of subleading fugacity expansion coefficients of the QCD free energy via a two-dimensional scan on the imaginary baryon number chemical potential ($μ_B$) - strangeness chemical potential ($μ_S$) plane. Using the aforementioned coefficients, we also extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials via a truncated fugacity expansion. Our results extrapolated along the crossover line $T_\mathrm{c}(μ_B)$ at strangeness neutrality are able to reproduce trends of experimental net-proton fluctuations measured by the STAR Collaboration.

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arXiv2017

Leptonic decay-constant ratio $f_K/f_π$ from lattice QCD using 2+1 clover-improved fermion flavors with 2-HEX smearing

We present a calculation of the leptonic decay-constant ratio $f_K/f_π$ in 2+1 flavor QCD. Our data set includes five lattice spacings and pion masses reaching down below the physical one. Special emphasis is placed on a careful study of all systematic uncertainties, especially the continuum extrapolation. Our result is perfectly compatible with the first-row unitarity constraint of the Standard Model.

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arXiv2015

Static $\bar{Q}Q$ pair free energy and screening masses from correlators of Polyakov loops: continuum extrapolated lattice results at the QCD physical point

We study the correlators of Polyakov loops, and the corresponding gauge invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at finite temperature. Our simulations were carried out on $N_t$ = 6, 8, 10, 12, 16 lattices using Symanzik improved gauge action and a stout improved staggered action with physical quark masses. The free energies calculated from the Polyakov loop correlators are extrapolated to the continuum limit. For the free energies we use a two step renormalization procedure that only uses data at finite temperature. We also measure correlators with definite Euclidean time reversal and charge conjugation symmetry to extract two different screening masses, one in the magnetic, and one in the electric sector, to distinguish two different correlation lengths in the full Polyakov loop correlator.

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arXiv2014

Spectral functions of charmonium with 2+1 flavours of dynamical quarks

Finite temperature charmonium spectral functions in the pseudoscalar(PS) and vector(V) channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057fm), with a non-physical pion mass of 545MeV. The highest temperature studied is approximately 1.4Tc. Up to this temperature no significant variation of the spectral function is seen in the PS channel. The V channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at omega > 0. These results are in accord with previous calculations using the quenched approximation.

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arXiv2012

Can the nearly conformal sextet gauge model hide the Higgs impostor?

New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β-function (DeGrand:2012yq). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β-function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

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arXiv2012

Systematic errors in partially-quenched QCD plus QED lattice simulations

At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $\mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations from the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors.

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arXiv2007

Curvature of the phase transition line in the mu-T plane

We determined the curvature of the phase transition line in the mu-T plane using a Taylor expansion in mu. The Polyakov loop and the strange quark number susceptibility were measured to locate the pseudocritical line. The analysis was carried out on Nt=4,6,8,10 lattices generated with a Symanzik improved gauge and stout-link improved (2+1) flavour staggered fermion action using physical quark masses.

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