Model Of Baryons Research Articles

Quark core-gluon model for heavy hybrid baryons

Besides the ordinary hadrons, quantum chromodynamics (QCD) allows the existence of states in which excitations of the gluonic field can play the role of valence particles, either alone in a glueball, or coupled to quarks in a hybrid. So, hybrid baryons, made of three quarks and a gluon, can exist. Till now, there is no experimental evidence for such exotic hadrons but experimental efforts are being made to search for them at CEBAF Large Acceptance Spectrometer. In this work, a hybrid baryon is considered as a two-body system composed of a color octet three-quark core and a gluon, interacting via a QCD-inspired interaction. A semirelativistic potential model is built in which the dominant interaction is a potential simulating the flux tube confinement, and the Casimir scaling is assumed to link interactions between triplet and octet color sources. This picture is similar to the quark-diquark description for baryons. It is chosen in order to take properly into account the helicity of the gluon. Only cccg and bbbg states are considered because the strong mass asymmetry between the quark core and the gluon is expected to favor the formation of the core. As the results for heavy hybrid baryons seem relevant, we consider this paper as a proof of concept which can be extended for the study of light hybrid baryons. Published by the American Physical Society 2024

Intrinsic Mass–Richness Relation of Clusters from THE THREE HUNDRED Hydrodynamic Simulations

The main systematics in cluster cosmology is the uncertainty in the mass–observable relation. In this paper, we focus on the most direct cluster observable in optical surveys, i.e., richness, and constrain the intrinsic mass–richness (MR) relation of clusters in THE THREE HUNDRED hydrodynamic simulations with two runs: GIZMO-SIMBA and GADGET-X. We find that modeling the richness at a fixed halo mass with a skewed Gaussian distribution yields a simpler and smaller scatter compared to the commonly used lognormal distribution. Additionally, we observe that baryon models have a significant impact on the scatter while exhibiting no influence on the mass dependence and a slight effect on the amplitude in the MR relation. We select member galaxies based on both stellar mass M ⋆ and absolute magnitude M . We demonstrate that the MR relations obtained from these two selections can be converted to each other by using the M⋆–M relation. Finally, we provide a seven-parameter fitting result comprehensively capturing the dependence of the MR relation on both stellar mass cutoff and redshift.

Mass spectrum of hexaquarks in the Gürsey-Radicati mass formula

It is conventionally claimed that hexaquarks are exotic particles, most of which we know have not yet been experimentally detected. In this work, we attempt to extend a simple phenomenological model based on the Gürsey-Radicati mass model for hadrons, including charm and bottom baryons, and predict the mass of dibaryon states. To illustrate our goal, we perform a numerical tuning of this model, which consists of five sets, each containing six or seven free parameters for baryons and dibaryons. In the long run, other predicted values for the mass of the extra hexaquarks may turn out to be consistent with the forthcoming experimental results. As we have claimed, the results of this work give us a deeper insight into the structural properties of six-quark particles. Finally, we have also included other available data from other works and compared them with ours.

The Three Hundred: Msub–Vcirc relation

ABSTRACT In this study, we investigate a recent finding based on strong lensing observations, which suggests that the sub-haloes observed in clusters exhibit greater compactness compared to those predicted by ΛCDM simulations. To address this discrepancy, we compare the cumulative sub-halo mass function and the Msub–Vcirc relation between observed clusters and 324 simulated clusters from $\rm \small {The\,Three\,\,Hundred}$ project, focusing on the hydrodynamic resimulations using $\rm \small {Gadget-X}$ and $\rm \small {Gizmo-Simba}$ baryonic models. The cumulative sub-halo mass function of $\rm \small {Gizmo-Simba}$ simulated clusters aligns with observations, while $\rm \small {Gadget-X}$ simulations exhibit discrepancies in the lower sub-halo mass range, possibly due to its strong supernova feedback. Both $\rm \small {Gadget-X}$ and $\rm \small {Gizmo-Simba}$ simulations demonstrate a redshift evolution of the sub-halo mass function and the Vcirc function, with slightly fewer sub-haloes observed at lower redshifts. Neither the $\rm \small {Gadget-X}$ nor $\rm \small {Gizmo-Simba}$ (albeit a little closer) simulated clusters’ predictions for the Msub–Vcirc relation align with the observational result. Further investigations on the correlation between sub-halo/halo properties and the discrepancy in the Msub–Vcirc relation reveal that the sub-halo’s half mass radius and galaxy stellar age, the baryon fraction, and sub-halo distance from the cluster’s centre, as well as the halo relaxation state, play important roles on reproducing this relation. Nonetheless, challenges persist in accurately reproducing the observed Msub–Vcirc relationship within our current hydrodynamic cluster simulation that adheres to the standard ΛCDM cosmology. These challenges may stem from shortcomings in our baryon modelling, numerical intricacies within the simulation, or even potential limitations of the ΛCDM framework.

Thermal effects on the baryon–quark phase transition in hot hybrid neutron stars: a statistical mean-field baryonic model with the standard NJL model for deconfined quarks

Thermal effects on the baryon–quark phase transition in hot hybrid neutron stars: a statistical mean-field baryonic model with the standard NJL model for deconfined quarks

Painting baryons on to N-body simulations of galaxy clusters with image-to-image deep learning

ABSTRACT Galaxy cluster mass functions are a function of cosmology, but mass is not a direct observable, and systematic errors abound in all its observable proxies. Mass-free inference can bypass this challenge, but it requires large suites of simulations spanning a range of cosmologies and models for directly observable quantities. In this work, we devise a U-net – an image-to-image machine learning algorithm – to ‘paint’ the illustristng model of baryons on to dark matter-only (DMO) simulations of galaxy clusters. Using 761 galaxy clusters with M200c ≳ 1014 M⊙ from the TNG300 simulation at z < 1, we train the algorithm to read in maps of projected dark matter mass and output maps of projected gas density, temperature, and X-ray flux. Despite being trained on individual images, the model reproduces the true scaling relation and scatter for the MDM–LX, as well as the distribution functions of the cluster X-ray luminosity and gas mass. For just one decade in cluster mass, the model reproduces three orders of magnitude in LX. The model is biased slightly high when using dark matter maps from the DMO simulation. The model performs well on inputs from TNG300-2, whose mass resolution is eight times coarser; further degrading the resolution biases the predicted luminosity function high. We conclude that U-net-based baryon painting is a promising technique to build large simulated cluster catalogues, which can be used to improve cluster cosmology by combining existing full-physics and large N-body simulations.

Baryonic models of ultra-low-mass compact stars for the central compact object in HESS J1731-347

The recent attempt on mass and radius inference of the central compact object within the supernova remnant HESS J1731-347 suggests for this object an unusually low mass of M=0.77−0.17+0.20M⊙ and a small radius of R=10.4−0.78+0.86km. We explore the ways such a result can be accommodated within models of dense matter with heavy baryonic degrees of freedom which are constrained by the multi-messenger observations. We find that to do so using only purely nucleonic models, one needs to assume a rather small value of the slope of symmetry energy Lsym. Once heavy baryons are included higher values of the slope Lsym become acceptable at the cost of a slightly reduced maximum mass of static configuration. These two scenarios are distinguished by the particle composition and will undergo different cooling scenarios. In addition, we show that the universalities of the I-Love-Q relations for static configurations can be extended to very low masses without loss in their accuracy.

Production and enhancement of (multi-) strange hadrons in Au+Au collisions at sNN=200 GeV RHIC energy and Pb+Pb collisions at sNN=2.76 TeV LHC energy

In this article, we investigate $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Pb}+\mathrm{Pb}$ collision systems to understand the (multi-) strange hadron production at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies using the Monte Carlo $\mathrm{HYDJET}++$ model. We study the ${p}_{T}$ spectra, particle ratios, and strangeness enhancement factor for (multi-) strange hadrons. The ${p}_{T}$ spectra of ${K}^{+}({K}^{\ensuremath{-}})$, ${K}_{s}^{0}$, $\mathrm{\ensuremath{\Lambda}}(\overline{\mathrm{\ensuremath{\Lambda}}})$, ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}({\overline{\mathrm{\ensuremath{\Xi}}}}^{+})$, and ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}({\overline{\mathrm{\ensuremath{\Omega}}}}^{+})$ are shown for both $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Pb}+\mathrm{Pb}$ collision systems in various centrality intervals. We find that the strange quark thermalization might not be achieved by the model for multistrange baryons toward peripheral collisions. The ${p}_{T}$-differential particle ratios, focused on strange hadron-to-meson ratios, are reported for 0--5% and 40--60% centrality intervals for both the collision systems. We observe an enhancement in the particle ratios at intermediate ${p}_{T}$ region. ${p}_{T}$ integrated strange-to-nonstrange ratios suggest that chemical equilibrium might not be achieved for multistrange hadrons. We report the strangeness enhancement factor for $\mathrm{\ensuremath{\Lambda}}(\overline{\mathrm{\ensuremath{\Lambda}}})$, ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}({\overline{\mathrm{\ensuremath{\Xi}}}}^{+})$, and ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}+{\overline{\mathrm{\ensuremath{\Omega}}}}^{+}$ at both RHIC and LHC energies. An increase in the enhancement factor is observed with the increase in strangeness content of the baryons. We also observe that enhancement is higher in $\mathrm{Au}+\mathrm{Au}$ collisions than in $\mathrm{Pb}+\mathrm{Pb}$ collisions. Further, we compare the $\mathrm{HYDJET}++$ results with the experimental data and various other simulation models, wherever possible.

Constraining the baryonic feedback with cosmic shear using the DES Year-3 small-scale measurements

ABSTRACT We use the small scales of the Dark Energy Survey (DES) Year-3 cosmic shear measurements, which are excluded from the DES Year-3 cosmological analysis, to constrain the baryonic feedback. To model the baryonic feedback, we adopt a baryonic correction model and use the numerical package baccoemu to accelerate the evaluation of the baryonic non-linear matter power spectrum. We design our analysis pipeline to focus on the constraints of the baryonic suppression effects, utilizing the implication given by a principal component analysis on the Fisher forecasts. Our constraint on the baryonic effects can then be used to better model and ameliorate the effects of baryons in producing cosmological constraints from the next-generation large-scale structure surveys. We detect the baryonic suppression on the cosmic shear measurements with a ∼2σ significance. The characteristic halo mass for which half of the gas is ejected by baryonic feedback is constrained to be $M_c \gt 10^{13.2} \, h^{-1} \, \mathrm{M}_{\odot }$ (95 per cent C.L.). The best-fitting baryonic suppression is $\sim 5{{\ \rm per\ cent}}$ at $k=1.0 \, {\rm Mpc}\ h^{-1}$ and $\sim 15{{\ \rm per\ cent}}$ at $k=5.0 \, {\rm Mpc} \ h^{-1}$. Our findings are robust with respect to the assumptions about the cosmological parameters, specifics of the baryonic model, and intrinsic alignments.

Self-interacting dark baryons

Using results from lattice QCD, it is possible to quantitatively design models of dark baryons leading to velocity-dependent self-interaction cross sections that match the values needed for solving small-scale structure problems of standard cold dark matter. However it is not obvious that the main dark matter component in such models will be nucleons rather than large nuclei, or dark pions or atoms, whose scattering properties would be different. We first identify the parameters of a dark SU(3) sector analogous to QCD---the confinement scale $\mathrm{\ensuremath{\Lambda}}$ and pion mass ${m}_{\ensuremath{\pi}}$---needed to reproduce desired self-interaction cross sections. Then we show that these values can generically be compatible with the absence of a sufficiently stable deuteron bound state, and hence leading to no heavier nuclei, thus establishing the consistency of the scenario for self-interacting dark nucleons. The range of dark photon masses needed to avoid dominant pion or atomic dark matter is determined, as well as allowed values for the kinetic mixing parameter. The dark proton might be detected directly in future searches, by dark photon exchange.

The THREEHUNDRED project: The effect of baryon processes at galaxy cluster scale

The role of baryon models in hydrodynamic simulations is still unclear. Future surveys that use cluster statistics to precisely constrain cosmological models require a better understanding of the baryonic effects. Using the hydro-simulated galaxy clusters from different baryon models (Gadget-MUSIC, Gadget-X and Gizmo-SIMBA) from the THREEHUNDRED project, we can address this question into more details. We find that the galaxy cluster mass change due to different baryon models is at a few per cent level. However, the mass changes can be positive or negative depending on the baryon models. Such a small mass change leaves a weak influence (slightly larger compared to the mass changes) on both the cumulative halo numbers and the differential halo mass function (HMF) above the mass completeness. Similarly to to the halo mass change, the halo mass or the HMF can be increased or decreased with respect to the dark-matter-only (DMO) run depending on the baryon models.

Magnetic particles and strings in iron langasite

Magnetic topological defects can store and carry information. Replacement of extended defects, such as domain walls and Skyrmion tubes, by compact magnetic particles that can propagate in all three spatial directions may open an extra dimension in the design of magnetic memory and data processing devices. We show that such objects can be found in iron langasite, which exhibits a hierarchy of non-collinear antiferromagnetic spin structures at very different length scales. We derive an effective model describing long-distance magnetic modulations in this chiral magnet and find unusual two- and three-dimensional topological defects. The order parameter space of our model is similar to that of superfluid 3He-A, and the particle-like magnetic defect is closely related to the Shankar monopole and hedgehog soliton in the Skyrme model of baryons. Mobile magnetic particles stabilized in non-collinear antiferromagnets can play an important role in antiferromagnetic spintronics.

Weighing the Galactic disk using phase-space spirals

Using the method that was developed in the first paper of this series, we measured the vertical gravitational potential of the Galactic disk from the time-varying structure of the phase-space spiral, using data fromGaiaas well as supplementary radial velocity information from legacy spectroscopic surveys. For eleven independent data samples, we inferred gravitational potentials that were in good agreement, despite the data samples’ varied and substantial selection effects. Using a model for the baryonic matter densities, we inferred a local halo dark matter density of 0.0085 ± 0.0039 M⊙ pc−3 = 0.32 ± 0.15 GeV cm−3. We were also able to place the most stringent constraint on the surface density of a thin dark disk with a scale height ≤50 pc, corresponding to an upper 95% confidence limit of roughly 5 M⊙ pc−2(compared to the previous limit of roughly 10 M⊙ pc−2, given the same scale height). For the inferred halo dark matter density and thin dark disk surface density, the statistical uncertainties are dominated by the baryonic model, which potentially could also suffer from a significant systematic error. With this level of precision, our method is highly competitive with traditional methods that rely on the assumption of a steady state. In a general sense, this illustrates that time-varying dynamical structures are not solely obstacles to dynamical mass measurements, but they can also be regarded as assets containing useful information.

Calibrating galaxy formation effects in galactic tests of fundamental physics

Galactic scale tests have proven to be powerful tools in constraining fundamental physics in previously under-explored regions of parameter space. The astrophysical regime which they probe is inherently complicated, and the inference methods used to make these constraints should be robust to baryonic effects. Previous analyses have assumed simple empirical models for astrophysical noise without detailed calibration or justification. We outline a framework for assessing the reliability of such methods by constructing and testing more advanced baryonic models using cosmological hydrodynamical simulations. As a case study, we use the Horizon-AGN simulation to investigate warping of stellar disks and offsets between gas and stars within galaxies, which are powerful probes of screened fifth forces. We show that the degree of `U'-shaped warping of galaxies is well modelled by Gaussian random noise, but that the magnitude of the gas-star offset is correlated with the virial radius of the host halo. By incorporating this correlation we confirm recent results ruling out astrophysically relevant Hu-Sawicki $f(R)$ gravity, and identify a $\sim 30\%$ systematic uncertainty due to baryonic physics. Such an analysis must be performed case-by-case for future galactic tests of fundamental physics.

A general framework to test gravity using galaxy clusters III: observable-mass scaling relations in f(R) gravity

ABSTRACT We test two methods, including one that is newly proposed in this work, for correcting for the effects of chameleon f(R) gravity on the scaling relations between the galaxy cluster mass and four observable proxies. Using the first suite of cosmological simulations that simultaneously incorporate both full physics of galaxy formation and Hu-Sawicki f(R) gravity, we find that these rescaling methods work with a very high accuracy for the gas temperature, the Compton Y-parameter of the Sunyaev–Zel’dovich (SZ) effect and the X-ray analogue of the Y-parameter. This allows the scaling relations in f(R) gravity to be mapped to their Λ cold dark matter counterparts to within a few per cent. We confirm that a simple analytical tanh formula for the ratio between the dynamical and true masses of haloes in chameleon f(R) gravity, proposed and calibrated using dark-matter-only simulations in a previous work, works equally well for haloes identified in simulations with two very different – full-physics and non-radiative – baryonic models. The mappings of scaling relations can be computed using this tanh formula, which depends on the halo mass, redshift, and size of the background scalar field, also at a very good accuracy. Our results can be used for accurate determination of the cluster mass using SZ and X-ray observables, and will form part of a general framework for unbiased and self-consistent tests of gravity using data from present and upcoming galaxy cluster surveys. We also propose an alternative test of gravity, using the YX–temperature relation, which does not involve mass calibration.

Weighing the Galactic disk in sub-regions of the solar neighbourhood using Gaia DR2

Aims. We infer the gravitational potential of the Galactic disk by analysing the phase-space densities of 120 stellar samples in 40 spatially separate sub-regions of the solar neighbourhood, using Gaia’s second data release (DR2), in order to quantify spatially dependent systematic effects that bias this type of measurement. Methods. The gravitational potential was inferred under the assumption of a steady state in the framework of a Bayesian hierarchical model. We performed a joint fit of our stellar tracers’ three-dimensional velocity distribution, while fully accounting for the astrometric uncertainties of all stars as well as dust extinction, and we also masked angular areas of known open clusters. The inferred gravitational potential is compared, post-inference, to a model for the baryonic matter and halo dark matter components. Results. We see an unexpected but clear trend for all 40 spatially separate sub-regions: Compared to the potential derived from the baryonic model, the inferred gravitational potential is significantly steeper close to the Galactic mid-plane (≲60 pc), but flattens such that the two agree well at greater distances (∼400 pc). The inferred potential implies a total matter density distribution that is highly concentrated to the Galactic mid-plane and decays quickly with height. We see a dependence on the Galactic radius that is consistent with a disk scale length of a few kiloparsecs. Apart from this, there are discrepancies between stellar samples, implying spatially dependent systematic effects which are, at least in part, explained by substructures in the phase-space distributions. Conclusions. In terms of the inferred matter density distribution, the very low matter density that is inferred at greater heights (≳300 pc) is inconsistent with the observed scale height and matter distribution of the stellar disk, which cannot be explained by a misunderstood density of cold gas or other hidden mass. Our interpretation is that these results must be biased by a time-varying phase-space structure, possibly a breathing mode, that is large enough to affect all stellar samples in the same manner.

Hmcode-2020: improved modelling of non-linear cosmological power spectra with baryonic feedback

ABSTRACT We present an updated version of the hmcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of baryon-acoustic oscillation (BAO) damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an root mean square (RMS) error of 2.5 per cent across a range of cosmologies, scales $k \lt 10\, h\, \mathrm{Mpc}^{-1}$, and redshifts z < 2. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at z ≃ 2, or for cosmologies with unusual dark energy equations of state. This represents a significant improvement over previous versions of hmcode, and over other popular fitting functions, particularly for massive-neutrino cosmologies with high neutrino mass. We also present a simple halo model that can be used to model the impact of baryonic feedback on the power spectrum. This six-parameter physical model includes gas expulsion by active galactic nuclei (AGN) feedback and encapsulates star formation. By comparing this model to data from hydrodynamical simulations, we demonstrate that the power spectrum response to feedback is matched at the <1 per cent level for z < 1 and $k\lt 20\, h\, \mathrm{Mpc}^{-1}$. We also present a single-parameter variant of this model, parametrized in terms of feedback strength, which is only slightly less accurate. We make code available for our non-linear and baryon models at https://github.com/alexander-mead/HMcode and it is also available within camb and soon within class.

Modelling the large-scale mass density field of the universe as a function of cosmology and baryonic physics

ABSTRACT We present and test a framework that models the 3D distribution of mass in the universe as a function of cosmological and astrophysical parameters. Our approach combines two different techniques: a rescaling algorithm that modifies the cosmology of gravity-only N-body simulations, and a ‘baryonification’ algorithm that mimics the effects of astrophysical processes induced by baryons, such as star formation and active galactic nuclei (AGN) feedback. We show how this approach can accurately reproduce the effects of baryons on the matter power spectrum of various state-of-the-art hydrodynamical simulations (EAGLE, Illustris, Illustris-TNG, Horizon-AGN, and OWLS, Cosmo-OWLS and BAHAMAS), to better than 1 per cent from very large down to small, highly non-linear, scales ($k\sim 5 \, h\, {\rm Mpc}^{-1}$), and from z = 0 up to z ∼ 2. We highlight that, because of the heavy optimization of our algorithms, we can obtain these predictions for arbitrary baryonic models and cosmology (including massive neutrinos and dynamical dark energy models) with an almost negligible CPU cost. With these tools in hand, we explore the degeneracies between cosmological and astrophysical parameters in the non-linear mass power spectrum. Our findings suggest that after marginalizing over baryonic physics, cosmological constraints inferred from weak gravitational lensing should be moderately degraded.

Effective Spinor Model of Leptons and Baryons

Effective Spinor Model of Leptons and Baryons

Elliptic flow splittings between particles and their antiparticles in relativistic heavy-ion collisions

Relativistic heavy-ion collisions are an important experimental way of studying the new state of matter as well as the phase diagram of the quantum chromodynamics (QCD) under extremely high temperatures and high densities. The elliptic flow is an important experimental observable in relativistic heavy-ion collisions. In recent years, the beam-energy scan program has been carried out on the relativistic heavy-ion collider at Brookhaven National Laboratory in USA, where phenomena different from those in heavy-ion collisions at extremely high energies, such as the elliptic flow splittings between particles and their antiparticles, are observed. Based on an extended multiphase transport model, this phenomenon can be explained through different mean-field potentials for particles and their antiparticles. In the almond-shaped medium produced in these collisions, particles affected by the repulsive potential are more likely to leave the system, while those affected by the attractive potential are more likely to be trapped in the system, enhancing and reducing their respective elliptic flow. The partonic mean-field potentials are extracted from an extended 3-flavor Nambu-Jona-Lasinio (NJL) model. Quarks are affected by more repulsive potentials compared with their antiquarks as a result of the vector-isoscalar coupling, while d quarks are affected by a more repulsive potential compared with u quarks as a result of the vector-isovector coupling, in the baryon-rich and d -quark-rich medium. The hadronic mean-field potentials are also incorporated through the relativistc mean-field model for baryons and antibaryons, and through the chiral effective field theory for kaons and antikaons as well as for π + and π − . In the baryon-rich and neutron-rich medium, antinucleons, antikaons, and π + are affected by more attractive potentials than nucleons, kaons, and π − , respectively. It is found that a strong vector-isoscalar and vector-isovector coupling are needed to reproduce the elliptic flow splittings between nucleons and antinucleons, kaons and antikaons, as well as π + and π − , as observed experimentally by the STAR Collaboration. On the other hand, the NJL model can be used to study the spontaneous chiral symmetry breaking and the phase diagram of the chiral phase transition. In order to describe both the chiral and deconfinement phase transition, one needs to extend the NJL model by incorporating the Polyakov-loop contribution (pNJL). Although the temperature of the crtical point for the chiral phase transition is higher in the pNJL model, it is found that the position or the behavior of the critical point is sensitive to the strength of the vector-isoscalar and the vector-isovector couplings in both the NJL and the pNJL model. In addition, the equation of state of baryon-rich and d -quark-rich quark matter is sensitive to these couplings as well. With these couplings constrainted by the elliptic flow splittings between particles and their antiparticles, information of the quark matter equation of state as well as the QCD phase diagram at finite baryon and isospin chemical potentials can be thus extracted. The study shows that the QCD critical point may be at very low temperatures or does not even exist, while the strong vector-isoscalar and vector-isovector couplings favor a stiff equation of state of quark matter at high net-baryon and isovector densities. In future studies, the transport framework can be further extended to incorporate the Polyakov-loop contribution.