Baryon Chemical Potential Research Articles

Heavy quark mass near the phase transition

Abstract Assuming that the number densities of heavy flavor in hadron gas and in QGP are same at $T_c$, we obtain the effective mass of heavy quark at $T_c$ from the comparison with the hadron resonance gas model which well describes particle yield in heavy-ion collisions. We find that charm quark mass at vanishing baryon chemical potential is around 1.8 GeV which is much heavier than QCD bare mass and close to $D$ meson mass. The mass slightly increases with increasing baryon chemical potential and then decreases.
On the other hand, anticharm quark mass constantly decreases with increasing baryon chemical potential. Bottom quark mass has a similar pattern. Extending the hadron resonance gas model to a bit higher temperature beyond $T_c$, the effective masses of charm and bottom quarks decrease with increasing temperature.

Strangeness-correlations on the pseudocritical line in ( 2+1 )-flavor QCD

We present some lattice QCD results on first (χ1i) and second (χ2i) cumulants of and correlations (χ11ij) among net baryon-number (B), strangeness (S) and electric charge (Q) along the pseudocritical line [Tpc(μB)] in the temperature (T)–baryon chemical potential (μB) phase diagram of (2+1)-flavor QCD. We point out that violations of sum rules among second order cumulants, which hold in the isospin symmetric limit of vanishing electric charge chemical potential, are small along the Tpc(μB) for the entire range of μB covered in the RHIC beam energy scan. For the strangeness neutral matter produced in heavy-ion collisions this leads to a close relation between χ11BS and χ11QS. We compare lattice QCD results for χ11BS/χ2S along the Tpc(μB) line with preliminary experimental measurements of χ11BS/χ2S for collision energies 7.7 GeV≤sNN≤62.4 GeV. While we find good agreements for sNN≥39 GeV, differences are sizeable at smaller values of sNN. Moreover, we compare lattice QCD results for the ratio of the strangeness (μS) to baryon (μB) chemical potentials, which define a strangeness neutral system with fixed electric charge to baryon number density, with experimental results obtained by the STAR collaboration for μS/μB using strange baryon yields on the freeze-out line. Finally, we determine the baryon chemical potential at the freeze-out (μBf) by comparing χ1B/χ2B along the Tpc(μB) with the experimentally measured net-proton cumulants χ1p/χ2p. We find that {μBf,Tpc(μBf)} are consistent with the freeze-out parameters of the statistical-model fits to experimentally measured hadron yields for sNN≥11.5 GeV. Published by the American Physical Society 2024

Hot and dense QCD shear viscosity at (almost) NLO

The next-to-leading order weak-coupling shear viscosity of QCD was computed 6 years ago. However, these results have never been applied at finite baryon chemical potential μ, even though intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here, we extend the next-to-leading order shear viscosity calculations to finite μ, and we show that, while the convergence of the weak-coupling expansion is questionable for achievable plasmas, it is somewhat better at μ > T than at μ = 0.

Electric conductivity of hot and dense nuclear matter

Transport coefficients play an important role in characterising hot and dense nuclear matter, such as that created in ultra-relativistic heavy-ion collisions (URHIC). In the present work we calculate the electric conductivity of hot and dense hadronic matter by extracting it from the electromagnetic spectral function, through its zero energy limit at vanishing 3-momentum. We utilise the vector dominance model (VDM), in which the photon couples to hadronic currents predominantly through the ρ meson. Therefore, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot and dense hadronic matter, by dressing its pion cloud with π-ρ, π-σ, π-K, N-hole, and Δ-hole loops. We then introduce vertex corrections to maintain gauge invariance. Finally, we analyze the low-energy transport peak as a function of temperature and baryon chemical potential, and extract the conductivity along a proposed phase transition line.

Measurements of Chemical Potentials in Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

This Letter presents the most precise measurement to date of the matter-antimatter imbalance at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair sqrt[s_{NN}]=5.02 TeV. Using the Statistical Hadronization framework, it is possible to obtain the value of the electric charge and baryon chemical potentials, μ_{Q}=-0.18±0.90 MeV and μ_{B}=0.71±0.45 MeV, with unprecedented precision. A centrality-differential study of the antiparticle-to-particle yield ratios of charged pions, protons, Ω baryons, and light (hyper)nuclei is performed. These results indicate that the system created in Pb-Pb collisions at the LHC is on average baryon-free and electrically neutral at midrapidity.

Towards a Warm Holographic Equation of State by an Einstein–Maxwell-Dilaton Model

The holographic Einstein–Maxwell-dilaton model is employed to map state-of-the-art lattice QCD thermodynamics data from the temperature (T) axis towards the baryon–chemical potential (μB) axis and aims to gain a warm equation of state (EoS) of deconfined QCD matter which can be supplemented with a cool and confined part suitable for subsequent compact (neutron) star (merger) investigations. The model exhibits a critical end point (CEP) at TCEP=O(100) MeV and μBCEP=500…700 MeV with an emerging first-order phase transition (FOPT) curve which extends to large values of μB without approaching the μB axis. We consider the impact and peculiarities of the related phase structure on the EoS for the employed dilaton potential and dynamical coupling parameterizations. These seem to prevent the design of an overall trustable EoS without recourse to hybrid constructions.

Baryogenesis via QCD preheating with nonadiabatic baryon chemical potential

The chiral phase transition in QCD can be supercooled in the thermal history of the universe to be instantaneously out-of equilibrium, if QCD is coupled to a dark QCD sector exhibiting the dark chiral phase transition of the first order. In that case the QCD sigma meson field (as the chiral order parameter, or the light quark condensate) starts to roll in a nonadiabatic way down to the true QCD vacuum. Meanwhile a dynamic baryonic chemical potential can be generated solely within QCD, which is governed by the dynamic motion of the QCD sigma meson field, analogously to the spontaneous baryogenesis or the leptogenesis via the Higgs or axionlike relaxation scenario. When QCD is further allowed to communicate with a dark fermion with mass of order of 1 GeV and the baryon number violating coupling to neutron, the nonadiabatic QCD sigma motion along with the nonadiabatic baryon chemical potential can trigger the preheating and produce the baryon number asymmetry. We discuss this scenario in details to find that the QCD-induced dynamic baryon chemical potential plays a significant role for the QCD preheating and the baryogenesis, which yields the desired amount of the asymmetry today consistently with current astrophysical, cosmological, and terrestrial experimental constraints. Cosmological and phenomenological consequences characteristic to the present scenario are also addressed.

Estimates on the convergence of expansions at finite baryon chemical potentials

Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Padé approximants, and the T′ expansion proposed recently in lattice QCD simulations, have been investigated in a low energy effective theory within the functional renormalization group approach. It is found that the convergence of the T′ expansion and the Padé approximants is consistent with the conventional Taylor expansion, within the expansion orders considered in this work. Furthermore, we find that the consistent regions of the three different expansions are in agreement with the convergence radius of the Lee-Yang edge singularities. Published by the American Physical Society 2024

QCD critical point, Lee-Yang edge singularities, and Padé resummations

I analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential (μB) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in μB and various resummation techniques that blend in Padé expansions and conformal maps. By extrapolating from this information, I estimate for the location of the QCD critical point: Tc≈100 MeV, μc≈580 MeV. I also estimate the crossover slope at the critical point to be α1≈9∘ and further constrain the nonuniversal mapping parameters between the three-dimensional Ising model and QCD equations of state. Published by the American Physical Society 2024

Baryonic vortex phase and magnetic field generation in QCD with isospin and baryon chemical potentials

We propose a novel baryonic vortex phase in low energy dense QCD with finite baryon and isospin chemical potentials. It is known that the homogeneous charged pion condensate emerges as a ground state at finite isospin chemical potential, and therein arises the Abrikosov vortex lattice with an applied magnetic field. We first demonstrate that a vortex with the same quantized magnetic flux as the conventional Abrikosov vortex, carries a baryon number captured by the third homotopy group of Skyrmions, once we take into account a modulation of the neutral pion inside the vortex core. Such a vortex-Skyrmion state is therefore dubbed the baryonic vortex. We further reveal that when the baryon chemical potential is above a critical value, the baryonic vortex has negative tension measured from the charged pion condensation. It implies that the phase, in which such vortices emerge spontaneously without an external magnetic field, would take over the ground state at high baryon density. Such a new phase contributes to the comprehension of QCD phase diagram and relates to the generation of magnetic fields inside neutron stars.

Effective potential of composite operators in the first order region of the QCD phase transition

We propose a method to determine the effective potential of QCD from the gap equation by introducing the homotopy method between the solutions of the equation of motion. Via this method, the effective potential beyond the bare vertex approximation is obtained, which then generalizes the Cornwall-Jackiw-Tomboulis effective potential for the bilocal composite operators. Moreover, the extended effective potential is set to be a function of self-energy instead of the propagator, which is the key point for the potential to be bounded from below. We then investigate the extended effective potential in the cases of phase transition of the QCD vacuum with a small current quark mass, the first order phase transition of QCD at finite temperature, and high baryon chemical potential. In the former case, the effective potential shows as an inflection point at the critical mass where the multiple solutions of the Dyson-Schwinger equation (DSE) vanishes, which is consistent with that obtained by solving the DSE directly. For the latter case, the in-medium properties, such as the latent heat and the difference of trace anomaly, of QCD is obtained. Published by the American Physical Society 2024

Electrobaryonic axion: hair of neutron stars

Axion-like particles are predicted in many physics scenarios beyond the Standard Model (SM). Their interactions with SM particles may arise from the triangle anomaly of the associated global symmetry, along with other SM global and gauge symmetries, including anomalies with the global baryon number and electromagnetic gauge symmetries. We initiate the phenomenological study of the corresponding “electrobaryonic axion”—a particle that couples with both the baryon chemical potential and the electromagnetic field. Neutron stars, particularly magnetars, possessing high baryon density and strong magnetic fields, can naturally develop a thin axion hair around their surface. In this study, we calculate this phenomenon, considering the effects of neutron star rotation and general relativity. For axion particles lighter than the neutron star rotation frequency, the anomalous interaction can also induce the emission of axion particles from the neutron star. In the light axion regime, this emission can significantly contribute to the neutron star cooling rate.

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 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, Tpc(μB). We find that the chiral crossover line starts to deviate significantly from the chemical freeze-out line already for μB>400MeV. Furthermore, we find that the chiral pseudocritical line can be parametrized as Tpc(μB)/Tpc(0)=1−κ2[μB/Tpc(0)]2−κ4[μB/Tpc(0)]4 with κ2=0.0150(2) and κ4=3.1(6)×10−5, which are in agreement with lattice QCD results for small values of μB. For the first time we find a tiny but nonzero value of κ4 in our study. Published by the American Physical Society 2024

Cold isospin asymmetric baryonic rich matter in nonlocal NJL-like models

We study the features of low energy strong interactions for a system at zero temperature and finite baryon and isospin chemical potentials, in the framework of a Nambu–Jona-Lasinio-like model that includes nonlocal four-point interactions. We analyze the phase transitions corresponding to chiral symmetry restoration and pion condensation, comparing our results with those obtained from local NJL-like models and lattice QCD calculations. Published by the American Physical Society 2024

Baryon Electric Charge Correlation as a Magnetometer of QCD.

The correlation between net baryon number and electric charge, χ_{11}^{BQ}, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of M_{π}=135 MeV on N_{τ}=8 and 12 lattices. We find that χ_{11}^{BQ} along the transition line starts to increase rapidly with magnetic field strength eB≳2M_{π}^{2} and by a factor 2 at eB≃8M_{π}^{2}. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, μ_{Q}/μ_{B}, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both χ_{11}^{BQ} and μ_{Q}/μ_{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.

Polyakov loop models in the large N limit: Correlation function and screening masses

We explore the ’t Hooft-Veneziano limit of the Polyakov loop models at finite baryon chemical potential. Using methods developed by us earlier we calculate the two- and N-point correlation functions of the Polyakov loops. This gives a possibility to compute the various potentials in the confinement phase and to derive the screening masses outside the confinement region. In particular, we establish the existence of complex masses and an oscillating decay of correlations in a certain range of parameters. Furthermore, it is shown that the calculation of the N-point correlation function in the confinement phase reduces to the geometric median problem. This leads to a large N analog of the Y law for the baryon potential. Published by the American Physical Society 2024

Investigating the fractional wave function and the impact of topological defects with anisotropic plasma on the dissociation of bottomonium in the fractional non-relativistic quark model

Incorporating a topological defect and anisotropic plasma, this work used the generalized fractional of the Nikiforov–Uvarov technique to solve the fractional-radial Schrödinger equation in the longitudinal-transverse plane. The study produced wave functions and energy eigenvalues in their fractional forms. The results showed that the presence of an anisotropic plasma and a topological defect increases the dissociation energy of bottomonium. Furthermore, regardless of whether the fractional or classical models are taken into account, it was shown that the effect of temperature on the dissociation energy is stronger than the effect of baryonic chemical potential. In addition, the dissociation energy of bottomonium is significantly larger at lower chemical potential levels. Last but not least, the energy of bottomonium is only little influenced by magnetic auxiliaries.

Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes

The ground state of QCD with two flavors at a finite baryon chemical potential under rapid rotation is a chiral soliton lattice (CSL) of the η meson, consisting of a stack of sine-Gordon solitons carrying a baryon number, due to the anomalous coupling of the η meson to the rotation. In a large parameter region, the ground state becomes a non-Abelian CSL, in which due to the neutral pion condensation each η soliton decays into a pair of non-Abelian sine-Gordon solitons carrying S2 moduli originated from Nambu-Goldstone (NG) modes localized around it, corresponding to the spontaneously broken vector symmetry SU(2)V. There, the S2 modes of neighboring solitons are anti-aligned, and these modes should propagate in the transverse direction of the lattice due to the interaction between the S2 modes of neighboring solitons. In this paper, we calculate excitations including gapless NG modes and excited modes around non-Abelian and Abelian (η) CSLs, and find three gapless NG modes with linear dispersion relations (type-A NG modes): two isospinons (S2 modes) and a phonon corresponding to the spontaneously broken vector SU(2)V and translational symmetries around the non-Abelian CSL, respectively, and only a phonon for the Abelian CSL because of the recovering SU(2)V. We also find in the deconfined phase that the dispersion relation of the isospinons becomes of the Dirac type, i.e. linear even at large momentum.

Pearcey integrals, Stokes lines and exact baryonic layers in the low energy limit of QCD

The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the (μB−Bext) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.

Chiral Soliton Lattice turns into 3D crystal

Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ methods from type-II superconductivity and construct a three-dimensional pion (and baryon) crystal perturbatively, close to the instability curve of the Chiral Soliton Lattice. We find an analogue of the usual type-I/type-II transition in superconductivity: along the instability curve for magnetic fields eB > 0.12 GeV2 and chemical potentials μ < 910 MeV, this crystal can continuously supersede the Chiral Soliton Lattice. For smaller magnetic fields the instability curve must be preceded by a discontinuous transition.