Color Superconductivity Research Articles

Holographic model with power-law Maxwell field for color superconductivity

Studying the color superconductivity (CSC) phase is important to understand the physics in the core of the neutron stars which is the only known context where the CSC phase might appear due to the gravitational force squeezing the matter to a sufficiently high density. We propose a simple holographic dual description of the CSC phase transition in the realistic Yang-Mills theory with the power-law Maxwell field. We find the CSC phase transition with the large color number in the deconfinement phase, which is not found in the case of the usual Maxwell field, if the power parameter characterizing for the power-law Maxwell field is sufficiently lower than one but above $1/2$ and the chemical potential is above a critical value. However, the power parameter is not arbitrary below one because when this parameter is sufficiently far away from one it leads to the occurrence of the CSC state in the confinement phase which is not compatible with a nonzero vacuum expectation value of the color nonsinglet operator.

Recovering the Conformal Limit of Color Superconducting Quark Matter within a Confining Density Functional Approach

We generalize a recently proposed confining relativistic density-functional approach to the case of density-dependent vector and diquark couplings. The particular behavior of these couplings is motivated by the non-perturbative gluon exchange in dense quark matter and provides the conformal limit at asymptotically high densities. We demonstrate that this feature of the quark matter EoS is consistent with a significant stiffness in the density range typical for the interiors of neutron stars. In order to model these astrophysical objects, we construct a family of hybrid quark-hadron EoSs of cold stellar matter. We also confront our approach with the observational constraints on the mass–radius relation of neutron stars and their tidal deformabilities and argue in favor of a quark matter onset at masses below 1.0M⊙.

Semiclassical Effects in Color Flavor Locked Strange Stars

Strange stars in the color flavor locked phase, as described by a generalization of the phenomenological MIT bag model proposed in the context of color superconductivity, are studied through a model motivated by the semiclassical solutions for hydrostatic equilibrium. Results show that within this framework it is possible to find ultracompact configurations situated between regular compact stars and black holes.

A new class of hybrid EoS with multiple critical endpoints for simulations of supernovae, neutron stars and their mergers

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a stiff quark matter EoS with color superconductivity at high densities within a finite region of baryonic chemical potentials mu _B^h< mu _B < mu _B^q. We consider two scenarios corresponding to a cross-over and a strong first-order transition between quark and hadron phases considered at finite and zero temperatures. This allows us to analyze the effects of finite entropy on the EoS and mass-radius relation of NS. We demonstrate that the formation of a color superconducting state of quark matter drives the evolution of matter in supernovae explosions under the condition of entropy conservation to higher temperatures than in the case of deconfinement to normal quark matter. Within the presented hybrid EoS scenario, regions of the QCD phase diagram may be accessible to supernovae and NS mergers that can be reached also in terrestrial experiments with relativistic heavy ion collisions.

Influence of chiral chemical potential μ5 on phase structure of the two-color quark matter

In this paper the influence of chiral chemical potential $\mu_5$ on the phenomenon of diquark condensation and phase structure of dense quark matter altogether is contemplated in the framework of effective two-color and two-flavor Nambu--Jona-Lasinio model. We show that the duality relations, found $\mu_5=0$, are also valid for any value of $\mu_5\neq0$. Hence the dualities seem to be a real fundamental feature of the phase diagram of two color quark matter, and besides they are a very powerful tool of studying the phase structure. In terms of dualities and the influence on the phase diagram chiral imbalance $\mu_5$ stands alone from other chemical potentials. Two regimes in the phase diagram could be discerned, the first one, rather small or moderate values of chemical potentials $\mu_B$, $\mu_I$ and $\mu_{I5}$, where the picture is rather concise and elegant: each of the above phenomena is in one-to-one correspondence with some chemical potential ($\mu_{I5}$ induces chiral symmetry breaking, $\mu_I$ propels charged pion condensation and $\mu_B$ leads to diquark condensation). In this regime chiral chemical potential $\mu_5$ does not break this correspondence, it has a property of being universal catalyzer, i.e. it {\it catalyzes/enhances} all the phenomena on equal footing. The feature of chiral imbalance $\mu_5$ to catalyze chiral symmetry breaking phenomenon was known before but its catalytic properties appeared to be more universal and it can catalyze also diquark and charged pion condensation. These happen due to the dual properties. In the second regime, when several chemical potentials reach rather large values, one could observe a rather complicated and rich phase structure, and $\mu_5$ can be a factor that not so much catalyzes as {\it triggers} rather peculiar phases. For example, it can lead to the formation of diquark condensation at zero baryon chemical potential.

Anomalous enhancement of dilepton production as a precursor of color superconductivity

Abstract We compute the modification of the photon self-energy due to dynamical diquark fluctuations developed near the critical temperature of two-flavor superconductivity, which is one of the color superconducting phases, through the Aslamasov–Larkin, Maki–Thompson, and density of states terms, which are responsible for the paraconductivity in metals at vanishing energy and momentum. The analysis is performed through an investigation of the diquark fluctuations within the normal phase determined by the mean-field approximation in the massless two-flavor Nambu–Jona-Lasinio model. It is shown that the rate has a significant enhancement in low-invariant-mass regions over a rather wide range of temperatures in the normal phase. This enhancement is worth exploring in the relativistic heavy-ion collisions, which may thereby reveal the significance of the diquark fluctuations in dense quark matter.

Thermal relaxation and cooling of quark stars with a strangelet crust

Context. In this article we explore the cooling of isolated quark stars. These objects are structured from a homogeneous quark matter core and crusted by ordinary matter or by strangelets. Aims. Our main purpose is to quantify the effects of a strangelet crust on the cooling and relaxation times of these strange stars. Methods. We adopt two kinds of crust: (i) a crust made of purely nuclear matter following the Baym-Pethick-Sutherland equation of state (EOS) and (ii) a crust made of nuggets of strange quark matter (strangelets). Both models have the same quark matter core, described by the MIT bag model EOS. Our study also includes the possible effects of color superconductivity in the quark core. Results. We have found that objects with a strangelet crust have a significantly different thermal relaxation time.

Density functional approach to quark matter with confinement and color superconductivity

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to a large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

Oscillating Magnetized Color Superconducting Quark Stars

The main objective of this work is to study the structure, composition, and oscillation modes of color superconducting quark stars with intense magnetic fields. We adopted the MIT bag model within the color superconductivity CFL framework, and we included the effects of strong magnetic fields to construct the equation of state of stable quark matter. We calculated observable quantities, such as the mass, radius, frequency, and damping time of the oscillation fundamental f mode of quark stars, taking into account current astrophysical constraints. The results obtained show that color superconducting magnetized quark stars satisfy the constraints imposed by the observations of massive pulsars and gravitational wave events. Furthermore, the quantities associated with the oscillation f mode of these objects fit the universal relationships for compact objects. In the context of the new multi-messenger gravitational wave astronomy era and the future asteroseismology of neutron stars, we hope that our results contribute to the understanding of the behavior of dense matter and compact objects.

Quark-nuclear hybrid equation of state for neutron stars under modern observational constraints

We study a family of equations of state for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the "DD2" class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu-Jona-Lasinio model in SU(2)$_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4 - 0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR J0740+6620 and tidal deformability from GW170817 it is necessary to consider a $\mu$-dependent bag pressure that mimics confinement.

The Phase Structure of Two Color QCD and Charged Pion Condensation Phenomenon

The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $${{\mu }_{{\text{B}}}}$$ , isospin $${{\mu }_{{\text{I}}}}$$ and chiral isospin $${{\mu }_{{{\text{I5}}}}}$$ chemical potentials. It has been shown in the mean-field approximation that there exist three dualities, one of them between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case. The other two dual symmetries between the phase with condensation of charged pions and the phase with diquark condensation and between chiral symmetry breaking and diquark condensation phenomena. It has been demonstrated that due to the duality properties the phase diagram is extremely symmetric and the whole phase diagram in two color case can be obtained just by dualities from the phase structure of three color case. This shows that the dualities are rather usefull tool. It is shown that chiral imbalance generates charged pion condensation phenomenon in conditions of matter in neutron stars, i. e. electrically neutral and $$\beta $$ -equilibrated dense quark matter. And that diquark condensation does not prohibit the generation of the charged PC phase by chiral imbalance at least in the two color case.

Topological nature of the transition between the gap and the gapless superconducting states

Recently it was demonstrated that the long-known transition between the gap and gapless superconducting states in the Abrikosov-Gor'kov theory of superconducting alloy with paramagnetic impurities is of the Lifshitz's type, i.e., at zero temperature this is the order phase transition. Since transitions of this kind in a normal metal are always associated to certain topological changes, then below we clarify the topological nature of the transition under consideration. Namely, we demonstrate that the topological invariant which in process of the transition undergoes the change is nothing but the Euler characteristic. Alternatively, in terms of the theory of catastrophes one can relate this transition to appearance of the cuspidal edge at the corresponding surface of the density of states as the function of energy and superconducting order parameter. The concept of experiments for the confirmation of order topological phase transition is proposed. The obtained theoretical results can be applied for the explanation of recent experiments with lightwave-induced gapless superconductivity, for the interpretation of the disorder-induced transition states via gapless phase in two-band superconductors, and the emergence of gapless color superconductivity in quantum chromodynamics.

Topological phase transition between the gap and the gapless superconductors

It is demonstrated that the known for a long time transition between the gap and the gapless states in the Abrikosov-Gor’kov theory of a superconductor with paramagnetic impurities is of the Lifshitz type, i.e. of the 2\frac12212 order phase transition. We reveal the emergence of a cuspidal edge at the density of states surface N(\omega,\Delta_0)N(ω,Δ0) (\Delta_0Δ0 is the value of the superconducting order parameter in the absence of magnetic impurities) and the occurrence of the catastrophe phenomenon at the transition point. We study the stability of such a transition with respect to the spatial fluctuations of the magnetic impurities critical concentration n_sns and show that the requirement for validity of its mean field description is unobtrusive: \nabla \left( {\ln{n_s}} \right) \ll \xi^{-1}∇(lnns)≪ξ−1 (here \xiξ is the superconducting coherence length). Finally, we show that, similarly to the Lifshitz transition, the transition between gap and gapless states should be accompanied by the corresponding singularities. For instance, the superconducting thermoelectric effect has a giant peak exceeding the normal value of the Seebeck coefficient by the ratio of the Fermi energy and the superconducting gap. The concept of the experiment for the confirmation of 2\frac12212 order transition nature is proposed. The obtained theoretical results can be applied for the explanation of recent experiments with lightwave-driven gapless superconductivity, for the new interpretation of the disorder induced transition s_{\pm}s±-s_{++}s++ states via gapless state in multi-band superconductors, for better understanding of the gapless color superconductivity in quantum chromodynamics, the string theory.

From quarks and gluons to color superconductivity at supranuclear densities

We study the emergence of color superconductivity in the theory of the strong interaction at supranuclear densities. To this end, we follow the renormalization group (RG) flow of dense strong-interaction matter with two massless quark flavors from the fundamental quark and gluon degrees of freedom at high energies down to the non-perturbative low-energy regime which is found to be governed by the dynamical formation of diquark states. With the strong coupling at the initial RG scale as the only input parameter, we compute the (chirally symmetric) scalar diquark condensate and analyze its scaling behavior over a wide range of the quark chemical potential. Approximations entering our computations are critically assessed. Since our approach naturally allows us to study the scale dependence of couplings, we also monitor the strength of couplings appearing in low-energy models of dense strong-interaction matter. The observed dependence of these couplings on the quark chemical potential may help to amend model studies in the future. Finally, we estimate the speed of sound of dense QCD matter. Our results indicate that the speed of sound exceeds the value of the noninteracting quark gas at high densities and even increases as the density is decreased, across a wide range, suggesting the existence of a maximum at supranuclear densities.

Mesons and diquarks in a color superconducting regime

The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model them in this regime. This paper focuses on the scalar and pseudoscalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at zero strange density. An objective of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses and the coupling constants of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, [Formula: see text] and the diquarks [ud] whose color is rg. This reveals that the inclusion of the color superconductivity in the modeling is relevant to describe the mesons and diquarks near the first-order chiral phase transition.

Critical fluctuations of QCD phase transitions and their related observables

We study how the dilepton production rate and the electric conductivity are affected by the soft modes inherently associated with the second-order phase transitions at the critical temperature of color superconductivity and QCD critical point. It is shown that the soft modes modify the photon self-energy significantly through the so called Aslamasov-Larkin, Maki-Thompson and density of states terms, which are known responsible for the paraconductivity in the metallic superconductivity, and they lead to an anomalous enhancement of the production rate in the low energy/momemtum region and the divergence of conductivity at the critical temperature.

Constraints on the maximum mass of quark star and the GW 190814 event

Gravitational-waves (GWs) data have widely been used for testing preferred modified gravity theories. In this paper, we investigate the possibility of testing them in the strong gravity regime by looking at the properties of compact objects in dense matter physics. In this direction modified gravity theories such as f(R, T) gravity can be tested with the recently discovered compact binary merger, GW 190814, containing a compact object with mass 2.50–2.67 M_{odot }. By considering these constraints on maximum mass of such an object, we predict the existence of quark stars (QSs) made of quark matter in the color-flavor-locked (CFL) phase of color superconductivity. Such a state is significantly more bound than ordinary quark matter and enhances the possibility of the existence of a pure stable QS. We focus on the following aspects in particular: mass–radius profile, mass-central mass density relation, compactness and the corresponding effective adiabatic index for stability related issues. Our result implies that predicted properties for QSs are well consistent with GW 190814 observational data that helps us to impose constraints on the theoretical models of dense nuclear matter.

Chiral condensates for neutron stars in hadron-quark crossover: From a parity doublet nucleon model to a Nambu–Jona-Lasinio quark model

We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 \gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B \sim 2-3n_0$ ($n_0\simeq 0.16\,{\rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B \gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.

Stellar structure and stability of charged interacting quark stars and their scaling behavior

We explore the stellar structure and radial stability of charged quark stars composed of interacting quark matter (IQM) in three classes of commonly used charge models. We adopt a general parametrization of IQM equation of state that includes the corrections from perturbative QCD, color superconductivity, and the strange quark mass into one parameter $\lambda$, or one dimensionless parameter $\bar{\lambda}=\lambda^2/(4B_{\rm eff})$ after being rescaled with the effective bag constant $B_{\rm eff}$. We find that increasing charge tends to increase the mass and radius profiles, and enlarges the separation size in mass between the maximum mass point and the point where zero eigenfrequencies $\omega^2_0=0$ of the fundamental radial oscillation mode occur. The sign of the separation in central density depends on the charge model; this separation also has a dependence on $\lambda$ such that increasing $\lambda$ (which can occur for either large color superconductivity or small strange quark mass) tends to decrease this separation size for the first and third classes of charge models monotonically. Moreover, for the second and third classes of charge models, we manage to numerically and analytically identify a new kind of stellar structure with a zero central pressure but a finite radius and mass. All the calculations and analysis are performed in a general dimensionless rescaling approach so that the results are independent of explicit values of dimensional parameters.

Gravitational wave echoes from interacting quark stars

We show that interacting quark stars (IQSs) composed of interacting quark matter (IQM), including the strong interaction effects such as perturbative QCD corrections and color superconductivity, can be compact enough to feature a photon sphere that is essential to the signature of gravitational wave echoes. We utilize an IQM equation of state unifying all interacting phases by a simple reparametrization and rescaling, through which we manage to maximally reduce the number of degrees of freedom into one dimensionless parameter $\overline{\ensuremath{\lambda}}$ that characterizes the relative size of strong interaction effects. It turns out that gravitational wave echoes are possible for IQSs with $\overline{\ensuremath{\lambda}}\ensuremath{\gtrsim}10$ at large center pressure. Rescaling the dimension back, we illustrate its implication on the dimensional parameter space of the effective bag constant ${B}_{\mathrm{eff}}$ and the superconducting gap $\mathrm{\ensuremath{\Delta}}$ with variations of the perturbative QCD parameter ${a}_{4}$ and the strange quark mass ${m}_{s}$ in their empirical range. We calculate the rescaled gravitational wave echo frequencies ${\overline{f}}_{\mathrm{echo}}$ associated with IQSs, from which we obtain a simple scaling relation for the minimal echo frequency ${f}_{\mathrm{echo}}^{\mathrm{min}}\ensuremath{\approx}5.76\sqrt{{B}_{\mathrm{eff}}/{(100\text{ }\text{ }\mathrm{MeV})}^{4}}\text{ }\text{ }\mathrm{kHz}$ at the large $\overline{\ensuremath{\lambda}}$ limit.