arXiv subjects
Publications and source records attributed to Mannque Rho.
Following Golterman and Shamir, we develop scale-chiral perturbation theory in the large $N_c$ and large $N_f$ Veneziano limit that incorporates both light-quark baryons and hidden local symmetric bosons and derive a leading-order scale symmetry Lagrangian applicable in nuclear physics. Some applications in the medium-free space and baryonic matter are discussed.
Drawing largely from my work with co--workers, I present arguments that strangeness does not play an {\it explicit} role in compact-star matter. They are based on the skyrmion description of dense matter combined with Wilsoninan renormalization group approach to kaon nuclear interactions. The key idea is that quark degrees of freedom, carrying strangeness, can be traded in by topology for hadron degrees of freedom.
By incorporating hidden scale symmetry and hidden local symmetry in nuclear effective field theory, combined with double soft-pion theorem, we predict that the Gamow-Teller operator coming from the space component of the axial current should remain unaffected by the QCD vacuum change caused by baryonic density whereas the first forbidden beta transition operator coming from the time component should be strongly enhanced. While the latter has been confirmed since some time, the former is given a support by a powerful recent {\it ab initio} quantum Monte Carlo calculation in light nuclei, also confirming the old "chiral filter hypothesis." Formulated in terms of Fermi-liquid fixed point structure of strong-coupled nuclear interactions, we offer an extremely simple resolution to the long-standing puzzle of "quenched $g_A$", $g_A^{\rm eff}\approx 1$~\cite{quenched}, in nuclear Gamow-Teller beta transitions, giant Gamow-Teller resonances and double beta decays.
The in-medium property of the axial-vector coupling constant $g_A$ in nuclei and dense baryonic matter, a long standing problem in nuclear physics, is reformulated in terms of the recently constructed scale-invariant hidden local symmetric ($bs$HLS) Lagrangian that encompasses the physics of baryon density ranging from nuclear matter $n_0$ to that of massive compact stars, $\sim 6n_0$. It is shown that unlike the pion decay constant $f_π$ that slides with the vacuum change induced by, and dropping with, increasing density, the axial-current constant $g_A$ should remain more or less unaffected by the decrease of chiral condensate in nuclear Gamow-Teller transitions (involving the space component of the axial current) whereas it gets strongly enhanced in axial-charge transitions (involving the time component of the axial current) as density increases. This phenomenon confirms the "chiral filter hypothesis" inferred from the current algebras in 1970's. These phenomena can be taken as a "nuclear physics proof" of Weinberg's folk theorem on quantum effective field theories. The implications of these predictions on giant Gamow-Teller resonances in nuclei and on first-forbidden beta transitions (relevant to nuclear astrophysical processes) are discussed.
This is a brief history of what I consider as very important, some of which truly seminal, contributions made by young Korean nuclear theorists, mostly graduate students working on PhD thesis in 1990's and early 2000's, to nuclear effective field theory, nowadays heralded as the first-principle approach to nuclear physics. The theoretical framework employed is an effective field theory anchored on a scale-invariant hidden local symmetric Lagrangian constructed along the line of Weinberg's "Folk Theorem" on effective field theory. The problems addressed are the high-precision calculations on the thermal $np$ capture, the solar $pp$ fusion process, the solar $hep$ process -- John Bahcall's challenge to nuclear theorists -- and the quenching of $g_A$ in giant Gamow-Teller resonances and the whopping enhancement of first-forbidden beta transitions in astrophysical processes. Extending adventurously the strategy to a wild uncharted domain in which a systematic implementation of the "theorem" is far from obvious, the same effective Lagrangian is applied to the structure of compact stars. A surprising result on the properties of massive stars, totally different from what has been obtained up to day in the literature, is predicted, such as the precocious onset of conformal sound velocity together with the possible emergence of hidden symmetries such as scale symmetry and hidden local symmetry.
A scale-invariant chiral effective Lagrangian is constructed for octet pions and a dilaton figuring as Nambu-Goldstone bosons with vector mesons incorporated as hidden gauge fields. The Lagrangian is built to the next-to-leading order in chiral-scale counting without baryon fields and then to leading order including baryons. The resulting theory is hidden scale-symmetric and local symmetric. We also discuss some possible applications of the present Lagrangian.
Exploiting certain robust topological inputs from the skyrmion description of compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict the equation of state that is consistent with the properties of nuclear matter at the equilibrium density, supports the maximum mass of massive compact star $\sim 2 M_\odot$ and surprisingly gives the sound velocity close to the "conformal velocity" $1/\sqrt{3}$ at densities $\gtrsim 3 n_0$. At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above $\sim 2n_0$ with a chiral-singlet mass $m_0 \sim (0.6-0.9) m_N$, hinting at a possible up-to-date unsuspected source of proton mass and an emergence at high density of scale symmetry and flavor local symmetry, both hidden in the QCD vacuum.
This is a brief account of the chief accomplishment of the 5-year activity (2008-2013) in the World Class University III Program at Hanyang University with the theme of exploring "From Dense Matter to Compact Stars." The principal objective was to explore and foresee what could be a break-through research that could be initiated at the RIB machine in project "RAON" at the upcoming ambitious Institute for Basic Science (IBS) in Korea. What came out was a possibility for unraveling the mystery of proton's "mass without mass" via nuclear matter and its impact on RAON-type physics and compact stars.
When a light scalar dilaton $σ$ and the light-quark vector mesons $V=(ρ,ω)$ are incorporated into an effective scale-invariant hidden local symmetric (sHLS) Lagrangian, scale symmetry for $σ$ and local gauge symmetry for $V$, both invisible in QCD in the vacuum, arise as emergent symmetries at a density above $n_{1/2}\sim 2n_0$, a phenomenon highly relevant for massive compact stars, hitherto unobserved in standard chiral pertubative approaches. What takes place involves a topology change at $n_{1/2}$, and as the density increases beyond, (1) exposes a parity doubling in the nucleon structure, (2) triggers drastic change in the nuclear tensor force and (3) stiffens the nuclear symmetry energy as density exceeds $n_{1/2}$. It results from an intricate interplay between the two hidden symmetries that the $ρ$ meson moves toward the vector manifestation (VM) fixed point where $m_ρ\rightarrow 0$ and the velocity of sound $v_s$ in the dense matter approaches the conformal symmetry value $v_s/c=\sqrt{1/3}$, indicating a presence of an infrared fixed point at which the dilaton mass vanishes.
With a light dilaton $σ$ and the light-quark vector mesons $V=(ρ,ω)$ incorporated into an effective scale-invariant hidden local symmetric Lagrangian, scale-chiral symmetry -- hidden in QCD -- arises at a high density, $n_{1/2}$, as an "emergent" symmetry, a phenomenon absent in standard chiral perturbative approaches but highly relevant for massive compact stars. What takes place as the density increases beyond $n_{1/2}\sim 2n_0$ in compressed baryonic matter is (1) a topology change from skyrmions to half-skyrmions, (2) parity doubling in the nucleon structure, (3) the maximum neutron star mass $M\simeq 2.01 M_{\odot}$ and the radius $R\simeq 12.0$ km and (4) the sound velocity $v_s^2/c^2\simeq 1/3$ due to the "vector manifestation (VM)" fixed point of $ρ$ and a "walking" dilaton condensate, which is intricately connected to the source of the proton mass.
The Skyrme model provides a novel unified approach to nuclear physics. In this approach, single baryon, baryonic matter and medium-modified hadron properties are treated on the same footing. Intrinsic density dependence (IDD) reflecting the change of vacuum by compressed baryonic matter figures naturally in the approach. In this article, we review the recent progress on accessing dense nuclear matter by putting baryons treated as solitons, namely, skyrmions, on crystal lattice with accents on the implications in compact stars.
It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension ($γ_{G^2}$) of the gluon field strength tensor squared ($G^2$) that represents the quantum trace anomaly should be $0 <γ_{G^2} <3$.
I describe a possible scenario for the origin of proton mass in terms of Cheshire Cat, half-skyrmions, topology change and interplay between hidden chiral-scale symmetry and induced local symmetry. This differs from the standard constituent-quark scenario. As the baryonic matter density is increased toward the vector manifestation (VM) fixed-point at which the $ρ$ mass is to vanish, the effective in-medium mass ratio $m^*_ρ/m^*_N$ is to tend to zero proportionally to $g^*_ρ$ where $g^*_ρ$ is the in-medium hidden gauge coupling constant. I develop the thesis that the intricacy involved in the mass generation could be decoded from experiments at RIB accelerators and massive compact stars.
I describe the long-standing search for a "smoking-gun" signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown's last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ($ρ$,$ω$) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau-Migdal fixed point interaction $G_0^\prime$, the nuclear tensor forces and Brown-Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, "run the show and make all forces equal."
When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar $f_0(500)$ may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudo-scalar pNG bosons $π$ and the matter fields $V=(ρ,ω)$ as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large $N_c$ in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent (IDD) "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale $Λ_M$. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group $V_{lowk}$ formalism. We satisfactorily post-dict the properties of normal nuclear matter and more significantly {\it predict} the EoS of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.
The hadronic matter described as a skyrmion matter embedded in an FCC crystal is found to turn into a half-skyrmion matter with vanishing (in the chiral limit) quark condensate and {\it non-vanishing} pion decay constant {$f_π$} at a density $n_{1/2}$ lower than or near the critical density $n_c$ at which hadronic matter changes over to a chiral symmetry restored phase with possibly deconfined quarks. When hidden local gauge fields and a dilaton scalar of spontaneously broken scale symmetry with decay constant $f_χ$ are incorporated, this half-skyrmion phase is characterized by $f_χ\approx f_π\neq 0$ with the hidden gauge coupling $g\neq 0$ but $\ll 1$. While chiral symmetry is restored {\it globally} in this region in the sense that space-averaged, $\la\bar{q}q\ra$ vanishes, quarks are still confined in massive hadrons and massless pions. This phase is shown to play a crucial role in the model for a smooth transition from a soft EoS at low density to a stiffer EoS at high density, the changeover taking place at $n_{1/2} \sim 2n_0$. It resembles the "quarkyonic phase" predicted in large $N_c$ QCD and represents the "hadronic freedom" regime which figures as a doorway to chiral restoration. The fractionization of skyrmion matter into half-skyrmion matter has a tantalizing analogy to what appears to happen in condensed matter in (2+1) dimensions where half-skyrmions or "merons" enter as relevant degrees of freedom at the interface.
Chiral symmetry, first entering in nuclear physics in the 1970's for which Gerry Brown played a seminal role, has led to a stunningly successful framework for describing strongly-correlated nuclear dynamics both in finite and infinite systems. We review how the early germinal idea, conceived with the soft-pion theorems in the pre-QCD era, has evolved into a highly predictive theoretical framework for nuclear physics, aptly assessed by Steven Weinberg: "it (chiral effective field theory) allows one to show in a fairly convincing way that what they (nuclear physicists) have been doing all along... is the correct first step in a consistent approximation scheme." Our review recounts both how the theory presently fares in confronting Nature and how one can understand its extremely intricate workings in terms of the multifaceted aspects of chiral symmetry, namely, chiral perturbation theory, skyrmions, Landau Fermi-liquid theory, the Cheshire cat phenomenon, and hidden local and mended symmetries.
The notion that the scalar listed as $f_0 (500)$ in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. That notion which puts the scalar -- that we shall identify as a "dilaton" -- on the same footing as the pseudo-scalar pseudo-NG bosons, i.e., octet $π$, while providing a simple explanation for the $ΔI=1/2$ rule for kaon decay, generalizes the standard chiral perturbation theory (S$χ$PT) to "scale chiral perturbation theory," denoted $χ$PT$_σ$, with {\it one infrared mass scale for both symmetries}, with the $σ$ figuring as a chiral singlet NG mode in non-strange sector. Applied to nuclear dynamics, it is seen to provide possible answers to various hitherto unclarified nuclear phenomena such as the success of one-boson-exchange potentials (OBEP), the large cancellation of strongly attractive scalar potential by strongly repulsive vector potential in relativistic mean field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson $ω$ in dense skyrmion matter, the BPS skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.