The long-standing puzzle of the quenched [Formula: see text] in nuclei is shown to have an extremely simple resolution in a renormalization-group (RG) treatment of a hidden local symmetric (HLS) and scale-symmetric (HSS) chiral Lagrangian. It is shown that the Landau–Migdal fixed-point approximation in nuclear matter (or [Formula: see text] in finite nuclei) in RG approach to strong correlations of fermionic hadrons on the Fermi surface exactly reproduces the superallowed Gamow–Teller transitions in the “Extreme Single-Particle (shell-)Model (ESPM)” in doubly-magic closed shell nuclei. One arrives at the quenching factor [Formula: see text] giving the quenched [Formula: see text]. This resolution exposes scale-chiral symmetry, hidden in QCD in the vacuum, emerging in nuclear matter from low density to high compact-star density. It has important implications on “first principles” approaches to nuclear physics, such as the role of multi-body exchange currents in weak axial-current matrix elements in nuclei and in neutrinoless double [Formula: see text] decays for going Beyond the Standard Model. This resolution could put in serious doubt the most recent improved measurement of the superallowed Gamow–Teller transition in the doubly-magic closed shell nucleus [Formula: see text]Sn which if confirmed would require a “fundamental quenching” [Formula: see text].

How to arrive at the densest matter in massive compact stars starting from Walecka's linear ω-σ mean-field model is described in a series of arguments anchored on hidden local symmetry, hidden scale symmetry and emergent parity-doublet symmetry. I follow the bottom-up approach from chiral symmetry with pions, coupled to hidden local and scale symmetry degrees of freedom. Exploiting the renormalization-group treatment à la Shankar and Polchinski of the fermionic interactions on the Fermi sphere, leading to Landau-Migdal Fermi-liquid, one obtains a sort of generalized “Density Functional" that allows via a topology change hadrons transform to quarks without phase changes at the center of massive stars. The highly dense matter is “pseudo-conformal" with the sound velocity v_pcs^2/c^2≈ 1/3 but the trace of the energy-momentum tensor is not equal to zero, hence the matter is non-conformal.

A novel idea is developed that the long-standing mystery in nuclear physics of the effective axial-current coupling constant in nuclei, gAeff≈1, could be interpreted in terms of an emerging hidden scale symmetry in dense compact-star matter. Arguments are presented using an effective field theory, referred to as Fermi-liquid fixed point (FLFP) approach, anchored on a renormalization group to interacting baryons on the Fermi surface coupled with hidden symmetric heavy mesonic degrees of freedom that enables one to go beyond Weinberg’s nuclear effective field theory χEFTπ involving nucleon and pion fields only. Both hidden local and scale symmetries, the former involving the vector mesons ρ and ω and the latter the hidden scalar meson, a dilaton σˆ (i.e., f0(500)), play the key role. Going beyond the density regime applicable to normal nuclear matter n0, the notion of “hadron–quark continuity HQC)” is brought in via the skyrmion structure of the nucleon argued to be valid in QCD at large Nc limit and the large N′ limit of the Grassmannian model G/H=[O(N′)/O(N′−p)×O(p)] where N′=4 and p=2 for hidden local symmetry and the IR fixed point in QCD for Nf≤3 involving “genuine/QCD-conformal dilaton (GD/QCD-CD) ” for hidden scale symmetry. The arguments presented give a strong support, in the total absence of lattice QCD at large density and furthermore in the impossibility of ab initio exact calculation of strong correlations in nuclear matter, for a possible equivalence between the FLFP approximation and the “Extreme Single Particle Shell Model (EPSM)” approach in heavy doubly-magic closed shell nuclei. The connection between the quenched gA and the sound speed vs2/c2≈1/3 expected inside dense compact stars could be interpreted as a (coarse-grained) signal for emergent “pseudo-conformal” symmetry in nuclear medium.

The V_lowk-renormalization group approach on the surface of Fermi liquid for nuclear matter to which Tom Kuo made a pioneering contribution at Stony Brook is found to inject the pivotal input in the formulation of the generalized nuclear effective field theory with acronym “GnEFT" applicable to superdense compact-star physics. A topology change in terms of skyrmions and half-skyrmions is shown to play the role of the “putative" hadron-quark continuity (HQC)" conjectured in QCD. Crucially involved are hidden local symmetry (“HLS") and hidden scale symmetry (“HSS") with the vacuum sliding with density in nuclear medium, with the nuclear tensor force emerging as a Landau Fermi-liquid fixed-point quantity. A possibly novel paradigm, a “Cheshire Catism," in nuclear correlations is suggested.

Baryons in finite nuclei, nuclear matter and dense compact-star matter are described in terms of Cheshire Cat for QCD. A potential conceptual link, admittedly short in mathematical rigor, between their manifestations is made by what’s called Cheshire Cat Principle. Put in terms “dual” to QCD variables, going to very high density exposes quantum Hall droplets – or pancakes – at which the dilaton-limit fixed-point (DLFP) with gA→1, fπ→fχ – where fπ and fχ are respectively the pion and dilaton decay constants – and the baryon parity-doubling are reached. This scenario suggests a thus-far totally unexplored structure of dual baryonic matter at high density which does neither require nor rule out (rapid) first-order phase transitions from hadrons to quarks in the core of compact stars on the verge of gravitational collapse.

The possible consequence of an infrared (IR) fixed point in QCD for Nf=2, 3 in nuclear matter is discussed. It is shown in terms of d(ilaton)-χ effective field theory (dχEFT) incorporated in a generalized effective field theory implemented with hidden local symmetry and hidden scale symmetry that the superallowed Gamow–Teller transition in the doubly magic-shell nucleus 100Sn recently measured at RIKEN indicates a large anomaly-induced quenching identified as a fundamental renormalization of gA from the free-space value of 1.276 to ≈0.8. Combined with the quenching expected from strong nuclear correlations “snc”, the effective coupling in nuclei gAeff would come to ∼1/2. If this result were reconfirmed, it would impact drastically not only nuclear structure and dense compact-star matter—where gA figures in π-N coupling via the Goldberger-Treiman relation—but also in search for physics Beyond the Standard Model (BSM), e.g., 0νββ decay, where the fourth power of gA figures.

We calculated in nonlinear bosonized theory $1/\bar{N}$ corrections to the Landau Fermi-liquid fixed-point (FLFP) axial-vector coupling constant in nuclear matter $g_A^L\approx 1$ to which the Landau parameter $F_1^\omega$ predominantly contributes. We obtain the correction to $F_1^\omega$ to calculate the correction $\delta g_A^L$ to the axial-vector coupling constant $g_A^L$ at the nuclear saturation density. It comes out to be extremely small, $\delta g_A^L\sim O(10^{-4})$. We discuss how the "dilaton-limit fixed-point (DLFP)" result $g_A=1$ can be preserved from finite nuclei to high densities relevant to massive neutron stars and its possible impact on $0\nu\beta\beta$ decay processes involved in going beyond the Standard Model.

This brief note is to point out that the recent measurements at GSI and RIKEN of the superallowed Gamow-Teller transition in the doubly magic closed-shell nucleus ^100Sn could give an indication for a possibly important fundamental quenching, thus-far unrecognized, of g_A, unambiguously distinct from nuclear correlation effects in the framework of nuclear effective field theory. The result, either confirmed or ruled out both experimentally and theory, can have strong impacts on nuclear physics vis-à-vis with nuclear effective field theory as well as on particle physics relevant for going beyond the Standard Model.

How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to the “Extreme Single Particle (shell) Model” (acronym ESPM) in superallowed Gamow–Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1−qssb)≠0—that one might identify as “fundamental quenching (FQ)”—in certain experiments seems to be alarmingly significant. I present arguments for how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow–Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In.

The World-Class University/Hanyang Project launched in Korea in 2008 led to what is now called the "pseudo-conformal model" that addresses dense compact star matter and is confronted in this short note with the presently available astrophysical observables, with focus on those from gravity waves. The predictions made nearly free of parameters by the model involving "topology change" remain more or less intact "un-torpedoed" by the data.

The superallowed Gamow-Teller transition in the doubly-magic-shell nucleus ^100Sn and the high resolution spectral shape analysis in the fourth-forbidden nonunique transition in ^115In indicate as much as ∼ 40% fundamental quenching in the axial-current coupling constant g_A in nuclei. This can be attributed to an effect of the trace anomaly in QCD "emerging" in nuclear medium. If confirmed, this would signal a major revamping to do in nuclear interactions consistent with chiral-scale symmetry in nuclear medium and a big impact on 0ν and νν double β decays for BSM. I present an argument that such a big anomaly-induced quenching is incompatible with how hidden scale symmetry manifests in nuclear medium, A possible means to resolve this issue is discussed in terms of hidden scale symmetry permeating in baryonic matter from normal nuclear matter to massive compact-star matter.

The Standard Model, comprising electroweak (EW) and strong (QCD) interactions, has been established and tested with great accuracy [...]

Unlike the octet baryons for $N_f=3$, there is no skyrmion coming from the $\eta^\prime$ meson. It is instead described as a fractional quantum Hall droplet, a pancake or a pita involving a singular $\eta^\prime$ ring in which Chern-Simons fields live. By incorporating hidden local symmetry and hidden scale symmetry in nuclear dynamics, I describe how to access baryon-charged quantum Hall droplets in dense nuclear matter in terms of the nuclear scale-chiral effective field theory approach ``G$n$EFT" with the $U_A(1)$ anomaly taken into account. I discuss how the single-flavor baryon that I will call ${\cal B}^s$ could be exposed in superdense baryonic matter, figuring, perhaps, in ``quark stars" associated with the baryon-quark continuity involving CFL or phase transitions.

In this paper, we review how the “cusp” predicted in the nuclear symmetry energy generated by a topology change at density [Formula: see text] can have a surprising consequence, so far unrecognized in nuclear physics and astrophysics communities, on the structure of dense compact-star matter. The topology change translated into nuclear EFT with “effective” QCD degrees of freedom encoded in hidden local and scale symmetries predicts an EoS that is soft below and stiff above [Formula: see text], and yields the properties of neutron stars with no tension with all the astrophysical observations available up to date. Furthermore it describes the interior core of the massive stars populated by fractionally charged quasi-fermions that are neither baryonic nor quarkonic. It is argued that the cusp “buried” in the symmetry energy resulting from strong correlations with hidden heavy degrees of freedom leads, at [Formula: see text], to a “pseudo-conformal” sound speed, [Formula: see text], converged from below at [Formula: see text]. It is not conformal since the trace of energy–momentum tensor is not zero even in the chiral limit. It reflects an emergent scale symmetry. This observation with the topology change implies that the quantities accurately measured at [Formula: see text] cannot give a qualitatively stringent constraint for what takes place at the core density of compact stars [Formula: see text]. This is because there intervenes a change of degrees of freedom in the effective field theory. We discuss the implication of this on the recent PREX-II “dilemma” in the measured skin thickness of [Formula: see text].

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.

The answer is found in the way the hidden scale symmetry involving a dilaton emerges in strong nuclear correlations in nuclear matter. It is suggested that the same mechanism is at the origin at higher densities of the sound speed converging in the core of massive compact stars to what could be called “pseudo-conformal sound speed" v_s^2/c^2≈ 1/3. A precision measurement of the superallowed Gamow-Teller transitions in the doubly magic nucleus ^100Sn is suggested to confirm or falsify this prediction. It could also lead to the possible determination of genuine “fundamental renormalization" of g_A in nuclear medium.

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are “local flavor symmetry” of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden “quantum scale symmetry” with an IR fixed point with a “genuine dilaton (GD)” characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for Nf≥2 baryons and the fractional quantum Hall (FQH) droplet topology for Nf=1 baryons are unified in the “homogeneous/hidden” Wess–Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless.

We present the argument that "pseudo-conformal" symmetry permeates from low density near nuclear matter to high density in the core of massive neutron stars. As a support of this argument, we describe how the quenched g_A≈ 1 in nuclei and the sound speed v_s^2/c^2≈ 1/3 in compact stars are controlled by emerging scale invariance in nuclear interactions. In our description, quasi-baryons could "masquerade" de-confined quarks in the interior of compact stars.

Although largely unrecognized, Gerry Brown had played a seminal and prescient role for the development of the currently heralded “first-principles approach” to nuclear dynamics known as “nuclear effective field theory” (nEFT for short). I give a brief account in what way he entered – together with his Korean colleagues – at the earliest stage of its development and what he left behind for the future in paving the road to go way beyond the standard nEFT. I do this in the context of Gerry’s original conceptual ideas conceived after the “dilepton fiasco” that indicate a surprising new role of hidden local and scale symmetries in nuclear physics.

A chain of connections in compressed baryonic matter, up-to-date glaringly missing in nuclear effective field theory, between intrinsic or emergent symmetries of QCD, mesons-gluons dualities, vector meson dominance and Chern-Simons fields has recently been revealed, presaging a possible new paradigm in nuclear theory. It indicates a ubiquitous role, thus far unexplored, of hidden symmetries -- flavor-local and scale -- permeating from dilute baryonic systems to normal nuclear matter and then to compact-star matter. Here I give a brief account of the possibly indispensable relevance of the $\eta^\prime$ singular ring, a.k.a. fractional quantum Hall (FQH) droplet, to the properties of the lowest-lying vector mesons $\omega$ and $\rho$, relevant to dilepton production processes, argued to be Seiberg-dual to the gluons near the chiral restoration.