Quark-hadron Continuity Research Articles

Topology and Emergent Symmetries in Dense Compact Star Matter

It has been found that the topology effect and the possible emergent hidden scale and hidden local flavor symmetries at high density reveal a novel structure of compact star matter. When Nf≥2, baryons can be described by skyrmions when the number of color Nc is regarded as a large parameter and there is a robust topology change—the transition from skyrmion to half-skyrmion—in the skyrmion matter approach to dense nuclear matter. The hidden scale and local flavor symmetries, which are sources introducing the scalar meson and vector mesons, are significant elements for understanding the nuclear force in nonlinear chiral effective theories. We review in this paper how the robust conclusions from the topology approach to dense matter and emergent hidden scale and hidden local flavor symmetries figure in generalized nuclear effective field theory (GnEFT), which is applicable to nuclear matter from low density to compact star density. The topology change encoded in the parameters of the effective field theory is interpreted as the hadron-quark continuity in the sense of the Cheshire Cat Principle. A novel feature predicted in this theory that has not been found before is the precocious appearance of the conformal sound velocity in the cores of massive stars, although the trace of the energy-momentum tensor of the system is not zero. That is, there is a pseudoconformal structure in the compact star matter and, in contrast to the usual picture, the matter is made of colorless quasiparticles of fractional baryon charges. A possible resolution of the longstanding gA quench problem in nuclei transition and the compatibility of the predictions of the GnEFT with the global properties of neutron star and the data from gravitational wave detections are also discussed.

Early Quark Deconfinement in Compact Star Astrophysics and Heavy-ion Collisions

Based on a recently developed relativistic density functional approach to color-superconducting quark matter and a novel quark-hadron transition construction which phenomenologically accounts for the effects of inhomogeneous pasta phases and quark-hadron continuity, we construct a class of hybrid equations of state applicable at the regimes typical for compact star astrophysics and heavy ion collisions. We outline that early quark deconfinement is a notable consequence of strong diquark pairing providing a good agreement with the observational data and driving the trajectories of the matter evolution during the supernovae explosions toward the regimes typical for the compact star mergers and heavy-ion collisions.

Pseudo-Conformal Sound Speed in the Core of Compact Stars

By implementing the putative “hadron-quark continuity” conjectured in QCD in terms of skyrmion-half-skyrmion topological change in an effective field theory for dense matter, we argue that (quasi-)baryons could “masquerade” deconfined quarks in the interior of compact stars. We interpret this phenomenon as a consequence of possible interplay between hidden scale symmetry and hidden local symmetry at high density. A surprising spin-off of the emerging symmetry that we call “pseudo-conformality” is that the long-standing puzzle of the quenched gA≈1 in nuclei can be given a simple resolution by the way the hidden symmetries impact nuclear dynamics at low density.

Cooling of neutron stars with quark-hadron continuity

Neutron stars are high-density objects formed by the gravitational collapse of massive stars, and the whole star can be likened to a giant nucleus. The interior of a neutron star is considered to contain exotic particles and states which do not appear in a normal nucleus. The internal states are constrained by observations of masses and radii via the equation of state of highly dense nuclear matter. Within these constraints, a variety of exotic states have been discussed. The internal state of neutron stars is closely related to its neutrino emission process, which cools the star from the inside. This effect can be compared with observations of the surface temperature of neutron stars. However, despite the wide range of observations of neutron stars, the nature of the neutron star matter remains uncertain. We consider quark matter as an exotic state and perform cooling calculations for neutron stars, incorporating the effects of nucleon superfluidity and quark colour superconductivity.We take into account the “quark-hadron continuity”, in which the neutron superfluidity is succeeded by thedquark pairing. Furthermore, we obtained the range of the neutron star cooling curve, taking into account the difference in surface temperature due to the composition of the surface layer. We found that the existence of quark matter causes strong neutrino emission from quarks, which is moderately suppressedbysuperfluidity and superconductivity, and canexplain the cold surface temperature of neutron stars.

Stiffening of matter in quark-hadron continuity

We discuss stiffening of matter in quark-hadron continuity. We introduce a model that relates quark wave functions in a baryon and the occupation probability of states for baryons and quarks in dense matter. In a dilute regime, the confined quarks contribute to the energy density through the masses of baryons but do not directly contribute to the pressure; hence, the equations of state are very soft. This dilute regime continues until the low momentum states for quarks get saturated; this may happen even before baryons fully overlap, possibly at density slightly above the nuclear saturation density. After the saturation, the pressure grows rapidly while changes in energy density are modest, producing a peak in the speed of sound. If we use baryonic descriptions for quark distributions near the Fermi surface, we reach a description similar to the quarkyonic matter model of McLerran and Reddy. With a simple adjustment of quark interactions to get the nucleon mass, our model becomes consistent with the constraints from 1.4-solar mass neutron stars, but the high density part is too soft to account for two-solar mass neutron stars. We delineate the relation between the saturation effects and short range interactions of quarks, suggesting interactions that leave low density equations of state unchanged but stiffen the high density part.

Phenomenological QCD equations of state for neutron star dynamics: Nuclear-2SC continuity and evolving effective couplings

We delineate the quark-hadron continuity by constructing QCD equations of state for neutron star dynamics, covering the wide range of charge chemical potential ($\mu_Q$) and temperatures ($T$). Based on the nuclear-2SC continuity scenario, we match equations of state for nuclear and two-flavor color-superconducting (2SC) quark matter, where the matching baryon density is $n_B\simeq 1.5n_0$ ($n_0\simeq 0.16\, {\rm fm^{-3}}$: nuclear saturation density). The effective vector and diquark couplings in a quark matter model evolve as functions of $n_B, \mu_Q, T$, whose low density values are constrained by the nuclear matter properties and neutron star radii, with the high density behavior by the two-solar mass ($2M_\odot$) constraint. With couplings dependent on $n_B$, we examined how smooth the nuclear-2SC continuity can be, and found problems in matching nuclear and 2SC entropies at low temperatures. To proceed with the continuity scenario, we enforce smooth matching by making the couplings ($n_B, \mu_Q, T$)-dependent. In effect, this adds phenomenological contributions which we call "X". After the phenomenological matching, we take the rest as our predictions. The 2SC and color-flavor-locked (CFL) phases computed with these evolving couplings are called 2SCX and CFLX. The CFLX appears around $n_B\simeq 2$-$4n_0$ and, in contrast to the conventional CFL, has non-negligible dependence on $(\mu_Q,T)$. To examine the astrophysical consequences of our modeling, we add charged leptons and neutrinos, and study the composition of matter for lepton fractions relevant for protoneutron stars and neutron star mergers. The abundance of neutrinos and thermal effects reduce the strangeness fraction and stiffen equations of state. For a neutrino trapped neutron star at $T\simeq 30 $ MeV with a lepton fraction $Y_L\simeq 0.05$, the mass is larger than its cold static counterpart by $\sim 0.1M_\odot$.

Multifarious Roles of Hidden Chiral-Scale Symmetry: “Quenching” gA in Nuclei

I discuss how the axial current coupling constant gA renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The “quenched” gA observed in nuclear superallowed Gamow–Teller transitions, a long-standing puzzle in nuclear physics, is shown to encode the emergence of chiral-scale symmetry hidden in QCD in the vacuum. This enables one to explore how trace-anomaly-induced scale symmetry breaking enters in the renormalized gA in nuclei applicable to certain non-unique forbidden processes involved in neutrinoless double beta decays. A parallel is made between the roles of chiral-scale symmetry in quenching gA in highly dense medium and in hadron–quark continuity in the EoS of dense matter in massive compact stars. A systematic chiral-scale EFT, presently lacking in nuclear theory and potentially crucial for the future progress, is suggested as a challenge in the field.

Vortices penetrating two-flavor quark-hadron continuity

Alice and Boojums are both representative characters created by Lewis Carroll. We show that they possibly meet in cores of rotating neutron stars. Recent studies of quark-hadron continuity suggest that neutron superfluid matter can connect smoothly to two-flavor symmetric quark matter at high densities. We study how this can be maintained in the presence of the vortices. In the neutron matter, quantized superfluid vortices arise. In the two-flavor dense quark matter, vortices carrying color magnetic fluxes together with fractionally quantized superfluid circulations appear as the most stable configuration, and we call these as the non-Abelian Alice strings. We show that three integer neutron superfluid vortices and three non-Abelian Alice strings of different color magnetic fluxes with total color flux canceled out are joined at a junction called a Boojum.

Non-Abelian Alice strings in two-flavor dense QCD

Quark-hadron continuity with two-flavor quarks that was proposed recently connects hadronic matter with neutron $^3P_2$ superfluidity and two-flavor dense quark matter. This two-flavor dense quark phase consists of the coexistence of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks, which gives rise to color superconductivity as well as superfluidity. We classify vortices in this phase. The most stable vortices are what we call the non-Abelian Alice strings, which are superfluid vortices with non-Abelian color magnetic fluxes therein, exhibiting so-called topological obstruction, or a non-Abelian generalization of the Alice property. We show that a single Abelian superfluid vortex is unstable against decay into three non-Abelian Alice strings. We discover that a non-Abelian Alice string carries orientational moduli of the real projective space $\mathbb{R}P^2$ corresponding to the color flux therein in the presence of the $P$-wave condensates alone. We calculate Aharanov-Bohm (AB) phases around the non-Abelian Alice string, and find that the 2SC condensates and string's orientational moduli must be aligned with each other because of single-valuedness of the AB phases of the 2SC condensates.

Manifestation of hidden symmetries in baryonic matter: From finite nuclei to neutron stars

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density [Formula: see text], the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise both to the long-standing “effective [Formula: see text]” in nuclear Gamow–Teller (GT) transitions at [Formula: see text] and to the pseudo-conformal sound velocity [Formula: see text] at [Formula: see text]. It is suggested that what has been referred to, since a long time, as “quenched [Formula: see text]” in light nuclei reflects what leads to the dilaton-limit [Formula: see text] at near the (putative) infrared fixed point of scale invariance. These properties are confronted with the recent observations in GT transitions and in astrophysical observations.

Continuity from neutron matter to color-superconducting quark matter with 3P2 superfluidity

I clarify how the concept of quark-hadron continuity, which was previously considered in the context of the asymptotic color-flavor locked phase with ideal three-flavor symmetry, is applied to two-flavor matter. Our observation is that neutron star matter can continuously be connected to two-flavor color-superconducting (2SC) phase with an additional condensate of d-quarks in the 3P2 channel. I discuss here two aspects of this novel phase. First, I introduce the notion of continuity based on the patterns of symmetry breaking and the corresponding order parameters, and then explain qualitatively the physics mechanism of d-quark 3P2 pairing in analogy to nuclear physics. Our finding serves as the theoretical underpinning for the phenomenological construction of the equation of state in the neutron star environment.

Holographic quarkyonic matter

We point out a new configuration in the Witten-Sakai-Sugimoto model, allowing baryons in the pointlike approximation to coexist with fundamental quarks. The resulting phase is a holographic realization of quarkyonic matter, which is predicted to occur in QCD at a large number of colors, and possibly plays a role in real-world QCD as well. We find that holographic quarkyonic matter is chirally symmetric and that, for large baryon chemical potentials, it is energetically preferred over pure nuclear matter and over pure quark matter. The zero-temperature transition from nuclear matter to the quarkyonic phase is of first order in the chiral limit and for a realistic pion mass. For pion masses far beyond the physical point we observe a quark-hadron continuity due to the presence of quarkyonic matter.

Topological term, QCD anomaly, and the \u03b7\u2032 chiral soliton lattice in rotating baryonic matter

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.

Continuity from neutron matter to two-flavor quark matter with S01 and P23 superfluidity

This study is performed with the aim of gaining insights into the possible applicability of the quark-hadron continuity concept, not only in the idealized case of three-flavor symmetric quark matter, but also for the transition from neutron matter to two-flavor quark matter. A key issue is the continuity between neutron superfluidity and a corresponding superfluid quark phase produced by $d$-quark pairing. Symmetry arguments are developed and relevant dynamical mechanisms are analyzed. It is pointed out that the $^3P_2$ superfluidity in dense neutron matter has a direct analogue in the $^3P_2$ pairing of $d$-quarks in two-flavor quark matter. This observation supports the idea that the quark-hadron continuity hypothesis may be valid for such systems. Possible implications for neutron stars are briefly discussed.

Zero point energy of composite particles: The medium effects

We analyze the zero point energy of composite particles (or resonances) which are dynamically created from relativistic fermions. We compare the zero point energies in medium to the vacuum one, taking into account the medium modification of the constituent particles. Treating composite particles as if quasi-particles, their zero point energies contain the quadratic and logarithmic UV divergences even after the vacuum subtraction. The coefficients of these divergences come from the difference between the vacuum and in-medium fermion propagators. We argue that such apparent divergences can be cancelled by consistently using fermion propagators to compute the quasi-particle contributions as well as their interplay, provided that the self-energies of the constituents at large momenta approach to the vacuum ones sufficiently fast. In the case of quantum chromodynamics, mesons and baryons, which may be induced or destroyed by medium effects, yield the in-medium divergences in the zero point energies, but the divergences are assembled to cancel with those from the quark zero-point energy. This is particularly important for unified descriptions of hadronic and quark matter which may be smoothly connected by the quark-hadron continuity.

Quark-Hadron Continuity beyond the Ginzburg-Landau Paradigm.

Quark-hadron continuity is a scenario in which hadronic matter is continuously connected to a color superconductor without phase transitions as the baryon chemical potential increases. This scenario is based on Landau's classification of phases, since they have the same symmetry breaking pattern. We address the question of whether this continuity is true as quantum phases of matter, which requires treatment beyond the Ginzburg-Landau description. To examine the topological nature of a color superconductor, we derive a dual effective theory for U(1) Nambu-Goldstone (NG) bosons and vortices of the color-flavor locked phase and discuss the fate of emergent higher-form symmetries. The theory has the form of a topological BF theory coupled to NG bosons, and fractional statistics of test quarks and vortices arise as a result of an emergent Z_{3} two-form symmetry. We find that this symmetry cannot be spontaneously broken, indicating that quark-hadron continuity is still a consistent scenario.

Quark-hadron continuity under rotation: Vortex continuity or boojum?

Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the limit of a light strange-quark mass, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was proposed that this conjecture could be generalized in the presence of superfluid vortices penetrating both phases (arXiv:1803.05115 [hep-ph]), and it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non-Abelian vortex (color magnetic flux tube) in the CFL phase. Here, we argue that their proposal is consistent only at large distances; instead, we show that three hadronic superfluid vortices must combine with three non-Abelian vortices with different colors with the total color magnetic fluxes canceled out, where the junction is called a colorful boojum. We rigorously prove this in both a macroscopic theory based on the Ginzburg-Landau description in which symmetry and excitations match (including vortex cores), and a microscopic theory in which the Aharonov-Bohm phases of quarks around vortices match.

Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter

We study how vortices in dense superfluid hadronic matter can connect to vortices in superfluid quark matter, as in rotating neutron stars, focusing on the extent to which quark-hadron continuity can be maintained. As we show, a singly quantized vortex in three-flavor symmetric hadronic matter can connect smoothly to a singly quantized non-Abelian vortex in three-flavor symmetric quark matter in the color-flavor locked (CFL) phase, without the necessity for boojums appearing at the transition.

QCD Equations of State in Hadron–Quark Continuity

The properties of dense matter in quantum chromodynamics (QCD) are delineated through equations of state constrained by the neutron star observations. The two solar mass constraint, the radius constraint of ≃11–13 km, and the causality constraint on the speed of sound, are used to develop the picture of hadron–quark continuity in which hadronic matter continuously transforms into quark matter. A unified equation of state at zero temperature and β-equilibrium is constructed by a phenomenological interpolation between nuclear and quark matter equations of state.

New Type of Crossover Physics in Three-Component Fermi Gases

A three-component Fermi gas near a broad Feshbach resonance does not have a universal ground state due to the Thomas collapse, while it does near a narrow Feshbach resonance. We explore its universal phase diagram in the plane of the inverse scattering length 1/ak(F) and the resonance range R(*)k(F). For a large R(*)k(F), there exists a Lifshitz transition between superfluids with and without an unpaired Fermi surface as a function of 1/ak(F). With decreasing R(*)k(F), the Fermi surface coexisting with the superfluid can change smoothly from that of atoms to trimers ("atom-trimer continuity"), corresponding to the quark-hadron continuity in a dense nuclear matter. Eventually, there appears a finite window in 1/ak(F) where the superfluid is completely depleted by the trimer Fermi gas, which gives rise to a pair of quantum critical points. The boundaries of these three quantum phases are determined in regions where controlled analyses are possible and are also evaluated based on a mean-field plus trimer model.