arXiv subjects

Heng-Tong Ding

Publications and source records attributed to Heng-Tong Ding.

At least 19 recordsLinked to original sources

arXiv2026

Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules

We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $η_c$ and $J/ψ$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

hep-lat↗

arXiv2026

QCD Chiral Crossover Line from Lee-Yang Edge Singularities

We propose a universality-based reconstruction of the QCD chiral crossover line from Lee-Yang edge singularities in the complex baryon chemical potential plane. The framework maps lattice-extracted complex Lee-Yang-zero estimates, treated as proxies for edge singularities, to the universal chiral Lee-Yang edge and thereby determines the $μ_B$ dependence of both the chiral critical line in the light-quark chiral limit and the pseudo-critical crossover line at physical quark masses. As an illustration, we apply the framework to Lee-Yang-zero estimates recently obtained by the Wuppertal-Budapest collaboration from high-statistics lattice QCD simulations. Without imposing the previously determined small-$μ_B$ expansion of the crossover line as input, the reconstructed curvature is consistent with existing continuum lattice-QCD results at small $μ_B$. The fitted chiral-limit transition temperature is also compatible with existing chiral-scaling analyses. These results demonstrate that lattice information on Lee-Yang singularities, combined with universal chiral scaling, provides a quantitatively consistent constraint on the QCD crossover line within the present temperature window and establishes a framework that can be systematically improved with future Lee-Yang-zero determinations.

hep-lat↗

arXiv2026

Static Quark-Antiquark Interactions Under Rotation

We study static quark--antiquark interactions in rotating SU(3) gluodynamics using quenched lattice simulations at imaginary angular velocity. At zero temperature, we extract the static potential from Wilson loops for quark--antiquark pairs aligned with the rotation axis, for transverse pairs with one source on the rotation axis, and for symmetric transverse pairs across the rotation axis. Within the present accuracy, no significant rotation dependence or anisotropy is observed in the zero-temperature potential. At finite temperature, imaginary rotation suppresses the color-averaged free energies obtained from Polyakov-loop correlators in both longitudinal and transverse geometries. Axial-diagonal comparisons are used to identify a bulk region where open-boundary artifacts are reduced. In this region, the large-distance longitudinal free-energy shift is well described by $ΔF_z(R_{xy})=A R_{xy}^2+B$. The transverse channels exhibit the same qualitative suppression, while their distance dependence additionally reflects the radial arrangement of the static sources and is compatible with a radial single-source free-energy shift in the bulk region. For the finite-temperature observables studied above $T_c$, the response weakens as the temperature is increased. These results provide lattice evidence for a position- and geometry-dependent response of bare static-source free energies to imaginary rotation in a gluonic medium.

hep-lat↗

arXiv2026

Chiral and $U(1)_A$ symmetries in background magnetic fields from lattice QCD

We study chiral symmetry and singlet $U(1)_A$ symmetry in QCD in a background magnetic field using lattice QCD. We first clarify the neutral-sector symmetry structure in a pure magnetic background, where the unequal electric charges of the light quarks explicitly reduce the non-singlet flavor symmetry. We identify the neutral-pion--sigma susceptibility difference, $χ_{π^0}-χ_σ$, as the chiral-partner splitting associated with the surviving neutral non-singlet axial symmetry, and the neutral-pion--delta susceptibility difference, $χ_{π^0}-χ_{δ^0}$, as the singlet $U(1)_A$ partner splitting. We also discuss the disconnected contribution to the neutral-pion susceptibility and its continuum constraint. Numerical results are obtained on fixed-scale $(2+1)$-flavor HISQ ensembles with $m_l=m_s^{\rm phys}/10$, corresponding to a pion mass of about $220~{\rm MeV}$ at vanishing magnetic field. We find that the neutral chiral-partner splitting increases with the magnetic field strength $eB$ at low temperature and decreases at sufficiently large $eB$ near the crossover, providing susceptibility-splitting counterparts of magnetic catalysis and inverse magnetic catalysis, respectively. The singlet $U(1)_A$ partner splitting shows an analogous low-temperature enhancement and large-field suppression near the crossover, with the suppression setting in at larger $eB$ and remaining milder than in the chiral channel. These results provide a first lattice-QCD study of neutral-sector probes of chiral and singlet $U(1)_A$ partner susceptibility splittings in background magnetic fields.

hep-lat↗

arXiv2026

Isospin-Driven Splitting of Chemical Potentials in Isobar Collisions from Lattice QCD

Strong magnetic fields produced in relativistic heavy-ion collisions can modify fluctuations of conserved charges and, consequently, their associated chemical potentials. We present first-principles $(2+1)$-flavor lattice-QCD results for isospin-driven splittings of conserved-charge chemical potentials between the isobar systems $^{96}_{44}\mathrm{Ru}+^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+^{96}_{40}\mathrm{Zr}$ in the QCD crossover region, both at vanishing and nonzero magnetic fields along the pseudo-critical line $T_{pc}(eB)$. We outline a framework that, under strangeness neutrality and charge-to-baryon ratio $r\equiv n_{\rm Q}/n_{\rm B}$, maps the isospin difference between two nuclei, as encoded in $r_{\rm Zr}$ and $r_{\rm Ru}$, onto splitting ratios $Δμ_{\rm Q}/Δμ_{\rm B}$, $Δμ_{\rm S}/Δμ_{\rm B}$, and $Δμ_{\rm S}/Δμ_{\rm Q}$ as functions of $μ_{\rm B}(r_{\rm Ru})/Δμ_{\rm B}$. Using continuum-estimated lattice results for the leading-order coefficients $q_1\equiv(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ and $s_1\equiv(μ_{\rm S}/μ_{\rm B})_{\rm LO}$, we find that, at vanishing magnetic field, the splitting ratios are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield $Δμ_{\rm Q}<0$ and $Δμ_{\rm S}>0$, with the electric-charge sector dominating. At nonzero magnetic fields, the splitting ratios show only moderate $eB$ dependence. We therefore further examine Ru--Zr differences in the normalized magnetic-field response of chemical-potential ratios, particularly those involving $μ_{\rm Q}/μ_{\rm B}$, which display a pronounced enhancement in lattice QCD. We also present hadron resonance gas (HRG) results and experimentally motivated proxy observables with kinematic cuts to facilitate contact with experiment.

hep-lat↗

arXiv2026

Hyperon-Nucleon Spectrometer

Chirality lies at the heart of low-energy QCD, governing the symmetry structure that shapes hadron masses and strong interaction dynamics. Among the most compelling open questions tied to chiral dynamics and spontaneous chiral symmetry breaking is the longstanding $Λ$ polarization puzzle, in which $Λ$ hyperons produced in unpolarized hadronic collisions exhibit a surprisingly large transverse polarization that remains theoretically unexplained. This whitepaper presents the proposal for the Hyperon-Nucleon Spectrometer (H-NS) at the High-Intensity heavy-ion Accelerator Facility (HIAF). Leveraging the high energy and high intensity of HIAF's proton and heavy-ion beams, the H-NS experiment will perform systematic studies of hyperon polarization phenomena and their underlying mechanisms in proton-proton ($pp$), proton-nucleus ($pA$), and nucleus-nucleus ($AA$) collisions in the fixed target mode. A wide-range beam energy scan, including proton beams from 3 GeV up to 9.3 GeV (HIAF) and up to 32 GeV (upgraded HIAF), will be conducted to examine the dependence of polarization on collision energy. The spectrometer is designed with specialized detectors capable of high-precision reconstruction of final-state baryon polarizations. Among its many interesting and important measurements, H-NS will simultaneously measure hyperon and proton spin observables to explore the polarization mechanism in hadronic interactions and the spin structure of baryons. Furthermore, the use of $pA$ and $AA$ collisions will enable detailed investigations of cold and hot nuclear matter effects on spin polarization. Its physics program and detector development will significantly benefit the future Electron-ion Collider in China.

physics.ins-det↗

arXiv2026

Chiral Properties of $(2\!+\!1)$-Flavor QCD in Magnetic Fields at Zero Temperature

We present a lattice QCD study of the chiral properties of $(2\!+\!1)$-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation. We compute the renormalized chiral condensates together with pseudoscalar meson masses and decay constants for pions, kaons, and the fictitious $η^0_{s\bar{s}}$ pseudoscalar as functions of the magnetic-field strength $eB$ up to $eB\simeq1.2$ $\mathrm{GeV}^2$. The chiral condensates exhibit clear magnetic catalysis, increasing monotonically with the field strength. In the meson sector, neutral pseudoscalar masses decrease steadily with $eB$, whereas charged pseudoscalar masses display a nonmonotonic response: They rise at small fields, consistent with the lowest-Landau-level expectation, but then saturate and slightly decrease at larger fields, signaling sizable internal-structure effects. At the same time, neutral pseudoscalar decay constants are strongly enhanced by the magnetic field. To quantify deviations from chiral symmetry relations, we isolate the magnetic-field-induced shift in the Gell-Mann--Oakes--Renner corrections and find it to remain small for the neutral pion but to become sizable for the neutral kaon. To elucidate the origin of the magnetic response, we separately analyze the sea- and valence-quark contributions to both neutral and charged meson masses, finding that valence effects dominate at zero temperature. These results provide new insights into the interplay between QCD chiral symmetry breaking and strong magnetic fields.

hep-lat↗

arXiv2026

Lattice QCD at finite temperature and density

I review recent lattice results on strongly interacting matter under extreme conditions, with emphasis on the finite-temperature QCD transition at $μ_B=0$, its approach toward the chiral limit and the fate of the $U_A(1)$ anomaly, as well as recent constraints on the QCD phase boundary and the possible critical endpoint at $μ_B>0$. I also discuss selected advances in lattice methods and in QCD thermodynamics under external conditions, in particular strong magnetic fields, isospin chemical potential, rotation, acceleration, and quark spin polarization.

hep-lat↗

arXiv2026

Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD

We investigate the temperature dependence of the shear viscosity ($η$) and bulk viscosity ($ζ$) of the gluon plasma using lattice QCD over the range 0.76--2.25$\,T_c$, extending from below the transition temperature $T_c$ across the transition region and into the deconfined phase. At each temperature, we employ three large, fine lattices, which enables controlled continuum extrapolations of the energy-momentum tensor correlators. Using gradient flow together with a recently developed blocking technique, we achieve percent-level precision for these correlators, providing strong constraints for a model-based spectral analysis. Since the inversion to real-time information is intrinsically ill posed, we extract viscosities by fitting spectral functions whose ultraviolet behavior is matched to the best available perturbative result, while the infrared region is described by a Lorentzian transport peak. The dominant modeling uncertainty associated with the transport peak width is bracketed by varying it over a physically motivated range set by thermal scales. We find that the shear-viscosity-to-entropy-density ratio, $η/s$, exhibits a minimum near the transition temperature $T_c$ and increases for $T>T_c$, whereas the bulk-viscosity-to-entropy-density ratio, $ζ/s$, decreases monotonically over the entire temperature range studied.

hep-lat↗

arXiv2026

QCD in strong magnetic fields: fluctuations of conserved charges and equation of state

We present continuum-estimated (2+1)-flavor lattice QCD results for second-order fluctuations of conserved charges and the leading-order equation of state in the presence of strong magnetic fields at nonzero baryon chemical potential, using the HISQ action at the physical pion mass. The baryon-electric charge correlation $χ^{\rm BQ}_{11}$ exhibits striking sensitivity to the magnetic field: $R_{cp}$-like double ratios $χ^{\rm BQ}_{11}/χ^{\rm Q}_{2}$ and $χ^{\rm BQ}_{11}/χ^{\rm QS}_{11}$ reach enhancements of $\sim2$ and $\sim2.25$ at $eB \simeq 8M_π^2$ along the transition line, establishing $χ^{\rm BQ}_{11}$ as a magnetometer of QCD. To bridge theoretical predictions and experimental observations, we construct HRG-based proxy observables and apply systematic kinematic cuts emulating STAR and ALICE detector acceptances, which retain $\sim80\%$ of the lattice QCD magnetic sensitivity. Extending to the QCD equation of state under strangeness neutrality and isospin asymmetry, we determine the chemical potential ratio $q_1\equiv(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ and the pressure coefficient $P_2$ for magnetic field strengths up to $eB \simeq 0.8~{\rm GeV}^2 \sim 45 M_π^2$. The results reveal temperature-band crossings, hierarchy reversals, and non-monotonic structures driven by the nontrivial interplay between thermal and magnetic effects.

hep-lat↗

arXiv2025

QCD in strong magnetic fields: fluctuations of conserved charges and EoS

Strong magnetic fields can profoundly affect the equilibrium properties, characterized by the equation of state and bulk thermodynamics of strongly interacting matter. Although such fields are expected in off-central heavy-ion collisions, directly measuring their experimental imprints remains extremely challenging. To address this, we propose the baryon-electric charge correlations $χ^{\rm BQ}_{11}$ and the chemical potential ratio $μ_{\rm Q}/μ_{\rm B}$ as magnetic-field-sensitive probes, based on (2+1)-flavor QCD lattice simulations at physical pion masses. Along the transition line, $χ^{\rm BQ}_{11}$ and $(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ in Pb-Pb collisions increase by factors of 2.1 and 2.4 at $eB \simeq 8M_π^2$, respectively. To bridge theoretical predictions and experimental observations, we construct HRG-based proxies and apply systematic kinematic cuts to emulate STAR and ALICE detector acceptances. Furthermore, we extend this investigation to the QCD equation of state, and examine the leading-order thermodynamic coefficients for strangeness-neutral scenarios up to $eB \simeq 0.8 {\rm GeV}^2 \sim 45 m_π^2$, revealing intriguing non-monotonic structures.

hep-lat↗

arXiv2025

Baryon Electric Charge Correlation as QCD Magnetometer

The detection of strong magnetic fields in peripheral heavy-ion collisions is crucial for observing effects such as the chiral magnetic effect but has proven exceptionally difficult. To address this, we propose the baryon electric charge correlation $χ^{\rm BQ}_{11}$ and the chemical potential ratio $μ_{\rm Q}/μ_{\rm B}$ as sensitive probes of magnetic fields, based on (2+1)-flavor lattice QCD simulations at the physical pion mass. Along the transition line, $χ^{\rm BQ}_{11}$ and $(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ in Pb-Pb collisions increase by factors of 2.1 and 2.4 at $eB \simeq 8M_π^2$, respectively. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas model. This allows us to construct experimentally relevant proxy observables. Furthermore, we demonstrate that $(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ is also sensitive to the collision system, showing a $1.5$-fold increase from Zr-Zr to Ru-Ru isobar collisions. Our findings offer new insights into thermo-magnetic effects and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.

hep-lat↗

arXiv2025

Leading-Order QCD Equation of State in Strong Magnetic Fields at Nonzero Baryon Chemical Potential

We present continuum-estimated $(2+1)$-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark (HISQ) action with physical pion masses on lattices of temporal extent $N_τ= 8,\,12$, covering $145 \lesssim T \lesssim 165~\mathrm{MeV}$ and $eB \lesssim 0.8~\mathrm{GeV}^2$, imposing strangeness neutrality with baseline results at electric charge to baryon number ratio $r = 0.4$. We determine the $T$--$eB$ dependence of $q_1$ and $s_1$ (electric charge and strangeness chemical potential ratios), pressure coefficient $P_2$, baryon number density coefficient $N_1^{\rm B}$, and energy-like coefficients $Θ_2$ (trace anomaly), $ε_2$ (energy density), and $σ_2$ (entropy density). Magnetic fields induce temperature-band crossings for $q_1$ and $P_2$ and non-monotonic structures in the energy-like coefficients, with $Θ_2$ at strong fields possibly vanishing or turning negative at higher $T$, indicating dominance of the pressure term over the energy contribution. We also examine the $r$-dependence, finding that $r=0$ (charge-neutral matter) shows the most muted magnetic-field enhancement of $P_2$ despite larger $|q_1|$, providing a useful reference for neutron-star-like conditions. Comparisons with the hadron resonance gas (HRG) model show qualitative agreement at low $T$ and weak $eB$, with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.

hep-lat↗

arXiv2025

Second order fluctuations of conserved charges in external magnetic fields

We present a first-principles lattice QCD investigation of second-order fluctuations of and correlations among conserved charges -- baryon number (B), electric charge (Q), and strangeness (S) -- in the presence of external magnetic fields. Our study employs lattice simulations of (2+1)-flavor QCD with physical pion masses using highly improved staggered fermions (HISQ) on $48^3 \times 12$ and $32^3 \times 8$ lattices, covering a wide range of magnetic field strengths up to $eB \simeq 0.8$ GeV$ ^2$. We identify clear signals of magnetic field-induced modifications to these fluctuations and correlations, with the baryon-electric charge correlation, $χ^{\rm BQ}_{11}$, exhibiting particularly strong sensitivity to the magnetic field. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas (HRG) model and construct proxy observables for fluctuations measurable in heavy-ion collision experiments. Our findings highlight $χ^{\rm BQ}_{11}$ as a promising ``magnetometer" for probing the presence of magnetic fields in QCD matter. Furthermore, we explore experimentally relevant ratios involving $χ^{\rm BQ}_{11}$, demonstrating their potential in mitigating volume effects and enhancing sensitivity to magnetic fields in collision environments. Additionally, we assess the limitations of the HRG model at strong magnetic fields, revealing deviations that indicate nontrivial modifications to hadronic degrees of freedom. These results offer new insights into the interplay between thermal and magnetic effects in the QCD phase diagram and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.

hep-lat↗

arXiv2025

Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses

We investigate the effects of temperature $T$ and external magnetic fields $eB$ on the chiral condensates and screening masses of neutral pseudoscalar mesons, including $π^0$, $K^0$, and $η_{s\bar{s}}^0$, in (2+1)-flavor lattice QCD with physical quark masses. The chiral condensates are intrinsically connected to the screening masses via Ward-Takahashi identities, with the latter characterizing the inverse of the spatial correlation length in the pseudoscalar channel. Using highly improved staggered quarks, we perform simulations on lattices with temporal extents $N_τ= 8, 12, 16$ and an aspect ratio of 4, covering five temperatures from 145 MeV to 166 MeV. For each temperature, eight magnetic field strengths are simulated, reaching up to $eB \sim 0.8$ GeV$^2$. These simulations allow us to provide continuum estimates for the chiral condensates and screening masses. We observe intricate behavior in the light ($ud$), strange-light ($ds$) and strange ($s$) quark condensates as functions of the magnetic field and temperature, reflecting the competition between magnetic catalysis and inverse magnetic catalysis effects. This complex behavior is also mirrored in the screening masses of the neutral pseudoscalar mesons. Notably, the screening masses of $π^0$ and $K^0$ exhibit a non-monotonic dependence on $eB$, closely following the variations in their corresponding chiral condensates. Meanwhile, the screening mass of $η_{s\bar{s}}^0$ decreases monotonically with increasing $eB$. These findings provide valuable insights for understanding the behavior of QCD in a thermomagnetic medium and can serve as benchmarks for low-energy QCD models and effective theories.

hep-lat↗

arXiv2025

Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions

In this work, we report a lattice calculation of $x$-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer $-t$. The calculations are based on an $N_f=2+1$ 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 $-t$.

hep-lat↗

arXiv2025

Pseudoscalar Screening Mass at Finite Temperature and Magnetic Field from Lattice QCD with Physical Quark Masses

Understanding the screening mass of pseudoscalar mesons at finite temperature and magnetic field is crucial for comprehending the behavior of strongly interacting matter under extreme conditions, such as those found in the early universe or inside neutron stars. Additionally, in heavy ion collisions, strong magnetic fields are generated, which could significantly influence the properties of the quark-gluon plasma. The study of these screening masses provides insight into the modifications of mesonic properties in such environments, which is essential for the theoretical understanding of Quantum Chromodynamics (QCD) phase transitions and the properties of the quark-gluon plasma. Here, we present continuum estimated lattice QCD results on the screening mass of neutral pseudoscalar mesons at finite temperatures and nonzero magnetic fields. The simulations used (2+1)-flavor lattice QCD simulations using physical quark masses employing the HISQ/tree action. The continuum estimation was carried out using lattices having temporal extents $N_τ$ = 8, 12, and 16, all having aspect ratio $N_σ/N_τ$ = 4. The investigated temperature ranges from 145 MeV to 166 MeV, while the magnetic field strength varies from 0 to 1 GeV$^2$. We discuss the dependence of the screening masses of various neutral pseudoscalar mesons on temperature, magnetic field strength, and quark mass.

hep-lat↗

arXiv2025

Baryon-Electric Charge Correlations and Chemical Potentials as Probes of Magnetized QCD

We present the first lattice QCD results of quadratic fluctuations and correlations of conserved charges in (2+1)-flavor lattice QCD in the presence of a background magnetic field. The simulations were performed using the Highly Improved Staggered Quarks with physical pion mass $m_π$ = 135 MeV on $N_τ=8$ and 12 lattices. We find that the correlation between net baryon number and electric charge, denoted as $χ^{\rm BQ}_{11} $, can serve as a magnetometer of QCD. At pseudocritical temperatures ($T_{pc}$) the $χ^{\rm BQ}_{11}$ starts to increase rapidly with magnetic field strength $eB \gtrsim 2M^2_π$ and by a factor 2 at $eB\simeq 8 M^2_π$. By comparing with the hadron resonance gas model, we find that the $eB$ dependence of $χ^{\rm BQ}_{11}$ is mainly due to the doubly charged $Δ$(1232) baryon. Although the doubly charged $Δ$(1232) could not be detected experimentally, its decay products, protons and pions, retain the $eB$ dependence of $Δ$(1232)'s contribution to $χ^{\rm BQ}_{11}$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $μ_{\rm Q}/μ_{\rm B}$, shows significant dependence on the magnetic field strength and varies with the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results provide baselines for effective theory and model studies, and both $χ^{\rm BQ}_{11}$ and $μ_{\rm Q}/μ_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.

hep-lat↗