Finite Quark Chemical Potential Research Articles

Functional renormalization group study of thermodynamic geometry around the phase transition of quantum chromodynamics

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, T, and quark number chemical potential, μ. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization group approach. We use recent developments to recast the flow equation into the form of an advection-diffusion equation. We adopt the local potential approximation for the effective average action. We focus on the thermodynamic curvature, R, in the (μ,T) plane, in proximity of the chiral crossover, up to the critical point of the phase diagram. We find that the inclusion of fluctuations results in a smoother behavior of R near the chiral crossover. Moreover, for small μ, R remains negative, signaling the fact that bosonic fluctuations reduce the capability of the system to completely overcome the fermionic statistical repulsion of the quarks. We investigate in more detail the small μ region by analyzing a system in which we artificially lower the pion mass, thus approaching the chiral limit in which the crossover is actually a second order phase transition. On the other hand, as μ is increased and the critical point is approached, we find that R is enhanced and a sign change occurs, in agreement with mean field studies. Hence, we completely support the picture that R is sensitive to a crossover and a phase transition, and provides information about the effective behavior of the system at the phase transition. Published by the American Physical Society 2024

Momentum transport of chiral modes in a thermal QCD medium

We investigate the effect of a weak magnetic field on momentum transport in a thermal QCD medium at finite quark chemical potential using a semiclassical kinetic theory. In the presence of a magnetic field, the momentum transport coefficients acquire a tensor structure, reflected by the five shear ([Formula: see text] and [Formula: see text]) and two bulk viscous components ([Formula: see text] and [Formula: see text]). The weak magnetic field removes the degeneracy in the effective mass of flavors, leading to different masses for the left-handed (L) and right-handed (R) chiral modes of quarks. The coefficients, [Formula: see text] and [Formula: see text] decrease with magnetic field in L mode and increase in [Formula: see text] mode, whereas, [Formula: see text] and [Formula: see text] increase in both L and [Formula: see text] modes. The bulk viscous coefficients, [Formula: see text] and [Formula: see text] increase with magnetic field for both L and R modes. The shear and bulk viscous coefficients positively amplify with baryon asymmetry.

Fate of the topological susceptibility in two-color dense QCD

We explore the topological susceptibility at finite quark chemical potential and zero temperature in two-color QCD (QC2D) with two flavors. Through the Ward-Takahashi identities of QC2D, we find that the topological susceptibility in the vacuum solely depends on three observables: the pion decay constant, the pion mass, and the η mass in the low-energy regime of QC2D. Based on the identities, we numerically evaluate the topological susceptibility at finite quark chemical potential using the linear sigma model with the approximate Pauli-Gursey SU(4) symmetry. Our findings indicate that, in the absence of U(1)A anomaly effects represented by the Kobayashi-Maskawa-’t Hooft-type determinant interaction, the topological susceptibility vanishes in both the hadronic and baryon superfluid phases. On the other hand, when the U(1)A anomaly effects are present, the constant and nonzero topological susceptibility is induced in the hadronic phase, reflecting the mass difference between the pion and η meson. Meanwhile, in the superfluid phase it begins to decrease smoothly. The asymptotic behavior of the decrement is fitted by the continuous reduction of the chiral condensate in dense QC2D, which is similar to the behavior observed in hot three-color QCD matter. In addition, effects from the finite diquark source on the topological susceptibility are discussed. We expect that the present study provides a clue to shed light on the role of the U(1)A anomaly in cold and dense QCD matter.

Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model

We investigate modifications of hadron masses at finite quark chemical potential in two-flavor and two-color QCD, data of which are available from lattice simulations, within a linear sigma model based on approximate Pauli-Gursey $SU(4)$ symmetry. The model describes not only ground-state scalar diquarks and pseudoscalar mesons but also the excited pseudoscalar diquarks and scalar mesons; each ground-state diquark (meson) has the corresponding excited diquark (hadron) with opposite parity as a chiral partner. Effects of chiral symmetry breaking and diquark condensates are incorporated by a mean-field treatment. We show that various mixings among the hadrons, which are triggered by the breakdown of baryon number conservation in the superfluid phase, lead to a rich hadron mass spectrum. We discuss the influence of $U(1{)}_{A}$ anomaly on the density dependence of the mass spectrum and also manifestations of the chiral partner structures as the density increases in the superfluid phase. The predicted hadron masses are expected to provide future lattice simulations with useful information on such symmetry properties in dense two-color QCD.

Chirality dependence in charge and heat transport in thermal QCD

As the strength of the magnetic field ($B$) becomes weak, novel phenomena, similar to the Hall effect in condensed matter physics, emerges both in charge and heat transport in a thermal QCD medium with a finite quark chemical potential ($\ensuremath{\mu}$). So we have calculated the transport coefficients in a kinetic theory within a quasiparticle framework, wherein we compute the effective mass of quarks for the aforesaid medium in a weak magnetic field (B) limit ($|eB|\ensuremath{\ll}{T}^{2}$; $T$ is temperature) by the perturbative thermal QCD up to one loop, which depends on $T$ and $B$ differently to left-handed (L) and right-handed (R) chiral modes of quarks, lifting the prevalent degeneracy in L and R modes in strong magnetic field limit ($|eB|\ensuremath{\gg}{T}^{2}$). Another implication of weak $B$ is that the transport coefficients assume a tensorial structure: The diagonal elements represent the usual (electrical and thermal) conductivities (${\ensuremath{\sigma}}_{\text{Ohmic}}$ and ${\ensuremath{\kappa}}_{0}$ as the coefficients of charge and heat transport, respectively) and the off-diagonal elements denote their Hall counterparts (${\ensuremath{\sigma}}_{\text{Hall}}$ and ${\ensuremath{\kappa}}_{1}$, respectively). It is found in charge transport that the magnetic field acts on L and R modes of the Ohmic part of electrical conductivity in an opposite manner, viz. ${\ensuremath{\sigma}}_{\text{Ohmic}}$ for L mode decreases and for R mode, increases with $B$ whereas the Hall-part ${\ensuremath{\sigma}}_{\text{Hall}}$ for both L and R modes always increases with $B$. In heat transport too, the effect of the magnetic field on the usual thermal conductivity (${\ensuremath{\kappa}}_{0}$) and Hall-type coefficient (${\ensuremath{\kappa}}_{1}$) in both modes is identical to the above-mentioned effect of $B$ on charge transport coefficients. We have then derived some coefficients from the above transport coefficients, namely Knudsen number ($\mathrm{\ensuremath{\Omega}}$ is the ratio of the mean-free path to the length scale of the system) and Lorenz number in Wiedemann-Franz law. The effect of $B$ on $\mathrm{\ensuremath{\Omega}}$ either with ${\ensuremath{\kappa}}_{0}$ or with ${\ensuremath{\kappa}}_{1}$ for both modes is identical to the behavior of ${\ensuremath{\kappa}}_{0}$ and ${\ensuremath{\kappa}}_{1}$ with $B$. The value of $\mathrm{\ensuremath{\Omega}}$ is always less than unity for the entire temperature range, validating our calculations. Lorenz number (${\ensuremath{\kappa}}_{0}/{\ensuremath{\sigma}}_{\text{Ohmic}}T$) and Hall-Lorenz number (${\ensuremath{\kappa}}_{1}/{\ensuremath{\sigma}}_{\text{Hall}}T$) for L mode increases and for R mode decreases with magnetic field. It also does not remain constant with temperature hence violating the Wiedemann-Franz law.

Passage of heavy quarks through the fluctuating hot QCD medium

The change in the energy of the moving heavy (charm and bottom) quarks due to field fluctuations present in the hot QCD medium has been studied. A finite quark chemical potential has been considered while modeling the hot QCD medium counting the fact that the upcoming experimental facilities such as Facility for Anti-proton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA) are expected to operate at finite baryon density and moderate temperature. The effective kinetic theory approach has been adopted where the collisions have been incorporated using the well-defined collisional kernel, known as Bhatnagar–Gross–Krook (BGK). To incorporate the non-ideal equations of state (EoSs) effects/medium interaction effects, an extended effective fugacity model has been adopted. The momentum dependence of the energy change due to fluctuation for the charm and bottom quark has been investigated at different values of collision frequency and chemical potential. The results are exciting as the heavy quarks are found to gain energy due to fluctuations while moving through the produced medium at finite chemical potential and collision frequency.

Thermal quarks and gluon propagators in two-color dense QCD

We study Landau gauge gluon propagators in two-color QCD at finite quark chemical potential ($\mu_q$) and temperature ($T$). We include medium polarization effects at one-loop by quarks into massive gluon propagators, and compared the analytic results with the available lattice data. We particularly focus on the high density phase of color-singlet diquark condensates whose critical temperature is $\sim 100$ MeV with weak dependence on $\mu_q$. At zero temperature the color singlet condensates protect the IR limit of electric and magnetic gluon propagators from the medium screening effects. At finite temperature, this behavior remains true for the magnetic sector, but the electric screening mass should be generated by thermal, and hence gapless, particles which are unbound from the diquark condensates. Treating thermal excitations as quasi-quarks, we found that the electric screening develops too fast compared to the lattice results. Beyond the critical temperature for diquark condensates the analytic results are consistent with the lattice results.

In medium properties of an axion within a 2+1 flavor Polyakov loop enhanced Nambu–Jona-Lasinio model

We estimate the axion properties i.e. its mass, topological susceptibility and the self-coupling within the framework of Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical potential. PNJL model, where quarks couple simultaneously to the chiral condensate and to a background temporal quantum chromodynamics (QCD) gauge field, includes two important features of QCD phase transition, i.e. deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model plays an important role near the critical temperature. We have shown significant difference in the axion properties calculated in PNJL model compared to the same obtained using Nambu-Jona-Lasinio (NJL) model. We find that both the mass of the axion and its self-coupling are correlated with the chiral transition as well as the confinement-deconfinement transition. We have also estimated the axion properties at finite chemical potential. Across the QCD transition temperature and/or quark chemical potential axion mass and its self-coupling also changes significantly. Since the PNJL model includes both the fermionic sector and the gauge fields, it can give reliable estimates of the axion properties, i.e. it's mass and the self-coupling in a hot and dense QCD medium. We also compare our results with the lattice QCD results whenever available.

Masses and decay constants of (axial-)vector mesons at finite chemical potential

We update our previous results for (pseudo-)scalar mesons at zero temperature and finite quark chemical potential and generalize the investigation to include (axial-)vector mesons. We determine bound-state properties such as meson masses and decay constants up to chemical potentials far in the first-order coexistence region. To extract the bound-states properties, we solve the Bethe-Salpeter equation and utilize Landau-gauge quark and gluon propagators obtained from a coupled set of (truncated) Dyson-Schwinger equations with N_{text{ f }}=2+1 dynamical quark flavors at finite chemical potential and vanishing temperature. For multiple (pseudo-)scalar and (axial-)vector mesons, we observe constant masses and decay constants for chemical potentials up to the coexistence region of the first-order phase transition thus verifying explicitly the Silver-Blaze property of QCD. Inside the coexistence region the pion becomes more massive and its decay constants decrease, whereas corresponding quantities for the (axial-)vector mesons remain (almost) constant.

Energy loss of heavy quarks in the isotropic collisional hot QCD medium at a finite chemical potential

The present article is the followup of Eur. Phys. J. C 79, 761 (2019), where we studied the energy loss of the heavy quarks traversing through the isotropic collisional hot QCD medium. As the QCD phase diagram at finite baryon density and the moderate temperature is expected to be traced by the upcoming experimental facilities such as Anti-proton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA), the theoretical research needs the inclusion of finite chemical potential to study the hot QCD medium. Therefore, the aim here is to develop a formalism that investigates the collisional energy loss of heavy quarks moving in the hot QCD medium having small but a finite quark chemical potential. The calculation uses the extended effective fugacity quasi-particle model [1–3] and the effective kinetic theory with Bhatnagar-Gross-Krook (BGK) collisional kernel. The change in the energy of charm and bottom quarks with respect to their corresponding momenta has been investigated at different values of collisions frequency and chemical potential. We find that the bottom quark loses less energy than the charm quark for a fixed momentum, collisional frequency and chemical potential. The energy loss values are found to decrease with increasing chemical potential.

Electrical conductivity and Hall conductivity of a hot and dense quark gluon plasma in a magnetic field: A quasiparticle approach

We estimate here the electrical and Hall conductivity using a quasiparticle approach for quark matter. We use a Boltzmann kinetic approach in presence of external magnetic field. We confront the results of model calculations with Lattice QCD simulations for vanishing magnetic field. In general electrical conductivity decreases with magnetic field. The Hall conductivity on the other hand can show a non monotonic behaviour with magnetic field due to an intricate interplay of behaviour of relaxation time and strength of the magnetic field. We argue for vanishing quark chemical potential Hall conductivity vanishes and quark gluon plasma with finite quark chemical potential can show Hall effect. Both electrical conductivity and Hall conductivity increases with increasing quark chemical potential.

Fierz-complete NJL model study. III. Emergence from quark-gluon dynamics

Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scalar-pseudoscalar interaction channel is dynamically rendered most dominant by the gauge degrees of freedom, indicating the formation of a chiral condensate. Moreover, the inclusion of quark-gluon interactions leaves a significant imprint on the dynamics as measured by the curvature of the finite-temperature phase boundary which we find to be in accordance with lattice QCD results. At large quark chemical potential, we then observe that the dominance pattern of the four-quark couplings is changed by the underlying quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In this regime, the scalar-pseudoscalar interaction channel becomes subleading and the dominance pattern suggests the formation of a chirally symmetric diquark condensate. In particular, our study confirms the importance of explicit $U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at high densities.

Thermodynamic potential for quark-qluon plasma with finite quark mass and chemical potential

We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite s-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. We describe various means to interpolate between the low and high chemical potential limits. Although physically well motivated, we show that the infinite series Padé rational polynomial interpolation scheme introduces spurious poles. Nevertheless, we show that lower order interpolation schemes such as polynomial interpolation reproduce the Padé result without the presence of spurious poles. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. This provides a new realistic bag-model treatment of the QCD equation of state. We compute the QCD phase diagram with up to the two-loop corrections. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. We also show, however, that the correction for finite s-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe.

Relaxation time for quark spin and thermal vorticity alignment in heavy-ion collisions

We compute the relaxation time for quark/antiquark spin and thermal vorticity alignment in a quark-gluon plasma at finite temperature and quark chemical potential. We model the interaction of quark/antiquark spin with thermal vorticity as driven by a phenomenological modification of the elementary quark interaction with gluons. We find that in a scenario where the angular velocity of the quark-gluon plasma produced in a peripheral heavy-ion collision is small, quarks/antiquarks take a long time to align their spin with the vorticity. However, when the angular velocity created in the reaction is large, the alignment is efficient and well within the lifetime of the system created in the reaction. The relaxation time is larger for antiquarks which points out to a difference for the polarization of hadrons and antihadrons when this alignment is preserved during hadronization.

Effects of Superstatistics on the Location of the Effective QCD Critical End Point

Effects of the partial thermalization during the chiral symmetry restoration at the finite temperature and quark chemical potential are considered for the position of the critical end point in an effective description of the QCD phase diagram. We find that these effects cause the critical end point to be displaced toward larger values of the temperature and lower values of the quark chemical potential, as compared to the case where the system can be regarded as completely thermalized. These effects may be important for relativistic heavy ion collisions, where the number of subsystems making up the whole interaction volume can be linked to the finite number of participants in the reaction.

Quarks and light (pseudo-)scalar mesons at finite chemical potential

We investigate the properties of light scalar and pseudoscalar mesons at finite (light) quark chemical potential. To this end we solve a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators in Landau-gauge QCD and extend earlier results for $ N_{\mathrm{f}} = 2+1$ dynamical quark flavors to finite chemical potential at zero temperature. We then determine the meson bound state masses, wave functions, and decay constants for chemical potentials below the first-order phase transition from their homogeneous Bethe-Salpeter equation. We study the changes in the quark dressing functions and Bethe-Salpeter wave functions with chemical potential. In particular, we trace charge-conjugation parity breaking. Furthermore, we confirm the validity of the Silver-Blaze property: all dependencies of colored quantities on chemical potential cancel out in observables and we observe constant masses and decay constants up to and into the coexistence region of the first-order chiral phase transition.

Conformal perturbation theory confronts lattice results in the vicinity of a critical point

We study the accuracy and predictive power of conformal perturbation theory by a comparison with lattice results in the neighborhood of the finite-temperature deconfinement transition of SU(2) Yang-Mills theory, assuming that the infrared properties of this non-Abelian gauge theory near criticality can be described by the Ising model. The results of this comparison show that conformal perturbation theory yields quantitatively accurate predictions in a broad temperature range. We discuss the implications of these findings for the description of the critical point (belonging to the same universality class) of another strongly coupled, non-supersymmetric non-Abelian gauge theory: the critical end-point in the phase diagram of QCD at finite temperature and finite quark chemical potential.

Two-loop perturbative corrections to the constrained effective potential in thermal QCD

In this paper, we compute the constrained QCD effective potential up to two-loop order with finite quark mass and chemical potential. We present the explicit calculations by using the double line notation and analytical expressions for massless quarks are obtained in terms of the Bernoulli polynomials or Polyakov loops. Our results explicitly show that the constrained QCD effective potential is independent on the gauge fixing parameter. In addition, as compared to the massless case, the constrained QCD effective potential with massive quarks develops a completely new term which is only absent when the background field vanishes. Furthermore, we discuss the relation between the one- and two- loop constrained effective potential. The surprisingly simple proportionality that exists in the pure gauge theories, however, is in general no longer true when fermions are taken into account. On the other hand, for high baryon density μB and low temperature T, in the massless limit, we do also find a similar proportionality between the one- and two-loop fermionic contributions in the constrained effective potential up to mathcal{O}left(T/{mu}_Bright) .

Mass sensitivity of the three-flavor chiral phase transition

The mass sensitivity of the chiral phase transition of QCD with and without axial $U_A(1)$-symmetry breaking at vanishing and finite quark chemical potential is investigated. To focus on the low-energy sector of QCD, a quark-meson model with three dynamical quark flavors is employed. Non-perturbative quantum fluctuations are taken into account with the functional renormalization group. The inherent ambiguities in fixing the low-energy model parameters away from the physical mass point and their consequences for spontaneous chiral symmetry breaking are discussed in detail and a heuristic parameter fixing scheme motivated by chiral perturbation theory is proposed. The influence of vacuum and thermal fluctuations of quarks and mesons on the order of the chiral phase transition is additionally assessed with a mean-field analysis.

The quark chemical potential of QCD phase transition and the stochastic background of gravitational waves

The detection of stochastic background of gravitational waves (GWs), produced by cosmological phase transitions (PTs), is of fundamental importance because allows to probe the physics related to PT energy scales. Motivated by the decisive role of non-zero quark chemical potential towards understanding physics in the core of neutron stars, quark stars and heavy-ion collisions, in this paper we qualitatively explore the stochastic background of GW spectrum generated by a cosmological source such as high-density QCD first order PT during the early Universe. Specifically, we calculate the frequency peak fpeak redshifted at today time and the fractional energy density Ωgwh2 in light of equation-of-state improved by the finite quark (baryon) chemical potential (we consider an effective three flavor chiral quarks model of QCD). Our calculations reveal a striking increase in fpeak and Ωgwh2 due to the quark chemical potential, which means to improve the chances of detection, in possible future observations (in particular SKA/PTA experiments), of the stochastic background of GWs from QCD first order PT. Even if the improvements could be weak, by updating the sensitivity of relevant detectors in the future, we can still remain hopeful. Concerning the phenomenological contribution of QCD equation-of-state, and in particular the possibility to detect a stochastic GW signal, we further show that the role of the quark chemical potential is model-dependent. This feature allows to discriminate among possible QCD effective models depending on their capability to shed light on the dynamic of QCD-PT through future observations of primordial GWs. In this perspective, the results are indeed encouraging to employ the GWs to study the QCD PT in high density strong interaction matter.