Towards the Hadron-Quark Continuity Via a Topology Change in Compact Stars

Abstract

We review an effective field theory approach to dense compact-star matter that exploits the Cheshire Cat Principle for hadron-quark continuity at high density, adhering only to hadronic degrees of freedom, hidden topology and hidden symmetries of QCD. No Landau-Ginzburg-Wilsonian-type phase transition is involved in the range of densites involved. The microscopic degrees of freedom of QCD, i.e., quarks and gluons, possibly intervening at high baryonic density are traded in for fractionalized topological objects. Essential in the description are symmetries invisible in QCD in the matter-free vacuum: Scale symmetry, flavor local symmetry and parity-doubling. The partial emergence of scale symmetry is signaled by a dilatonic scalar in a "pseudo-conformal" structure. Flavor gauge symmetry manifests with the ρ meson mass going toward a Wilsonian RG fixed point identified with the "vector manifestation fixed point (VMFP)" at which the flavor gauge boson mass goes to zero. Parity doubling is to take place as the quasi-nucleon mass converges to the chiral invariant m 0 . The theory with a few controllable parameters accounts satisfactorily for all known properties of normal nuclear matter and makes certain predictions that are drastically different from what's available in the literature. In particular, it provides a topological mechanism, argued to be robust, for the cross-over from soft-to-hard equation of state that predicts the star properties in overall agreement with the presently available data, including the maximum star mass M max ∼ 2.3M and the recent LIGO/Virgo gravity-wave data. What is most glaringly different from all other approaches known, however, is the prediction for the rapid convergence to a sound velocity of star v 2 s ≈ 1/3 (in unit c = 1) at a density n ∼ > 3n 0 , far from the asymptotic density ∼ > 50n 0 expected in perturbative QCD. We interpret this to signal the precocious emergence in compact-star matter of a pseudo-conformal structure associated with the hidden symmetries.

The Quenched ${g_A}$ in Nuclei and Emergent Scale Symmetry in Baryonic Matter

“…It has been shown recently [12] that the result obtained in Ref. [9] corresponds precisely to what one obtains in the LOSS approximation in GσEFT [3]. The result obtained in [9] was in agreement with (2).…”

“…As described in great detail in Ref. [3], we find it far more powerful and predictive to resort to a higher cutoff, ∼ > 700 MeV, in particular for going to high densities relevant to massive compact stars. The relevant degrees of freedom with such a cutoff are the lowest-lying vector mesons V µ = (ρ, ω) with mass ∼ > 700 MeV possessing "hidden local symmetry (HLS)" and a scalar meson with mass ∼ 600 MeV denoted χ as a dilaton of broken scale symmetry 1 .…”

“…It has been established that this GσEFT in what is referred to as a "leading order scale symmetry (LOSS)" approximation, as described in detail in Ref. [3] and briefly below, is surprisingly successful, with very few parameters, for describing not only nuclear matter at the equilibrium density n 0 ≃ 0.16 fm −3 but also the compact-star matter at n ∼ (5 − 7)n 0 [3]. So far there seems to be no conflict with Nature…”

“…Our proposal is that it is the super-allowed GT decay of the doubly magic nucleus 100 Sn. 3 What is crucial here is that it provides the "extreme single-particle shell-model (ESPM)" -as explained in Ref. [5] -to be identified with the result of GσEFT.…”

“…Prediction in GσEFT -Let us see what we get in the GσEFT [3]. The calculation was first done a long time ago [9] with a model that incorporates chiral-scale symmetry [10] in the Landau-Migdal Fermi-liquid approach to nuclei [11].…”