Effective Field Theories for Nuclei and Compact-Star Matter

Chiral Nuclear Dynamics (CND-III)

Yong-Liang Ma, Mannque Rho

• Publisher: WSPC
• Year: 2018
• ISBN:
  9789813273337
• Topic: Physical Sciences
• Subtopic: Nuclear Physics

Effective field theories have been widely used in nuclear physics. This volume is devoted to exploring the intricate structure of compact-star matter inaccessible directly from QCD. It is principally anchored on hidden symmetries and topology presumed to be encoded in QCD. It differs from standard effective field theory and energy density functional approaches in that it exploits renormalization-group flow in the complex 'vacuum' sliding with density inferred from topology change identified as a manifestation of baryon-quark continuity in dense matter. It makes a variety of predictions that drastically differ from the conventional treatments that could be tested by upcoming terrestrial and astrophysical experiments.

This monograph recounts how to go, in one unique field theoretic formalism in terms of hadronic degrees of freedom, from finite nuclei to dense compact-star matter that could be explored in RIB-type machines in nuclear physics as well as in LIGO-type gravity waves in astrophysics.

Contents:

• Preface
• Notation and Conventions
• Introduction
• The 'Folk Theorem' in Nuclear Physics
• Hadron-Quark Continuity
• Effective Field Theories for Nuclear Interactions
• Hidden Symmetries in Dense Matter
• Scale-Chiral Symmetry
• From Skyrmions to Dense Matter
• Compressed Baryonic Matter
• Compact Stars
• Strangeness in Stars
• Epilogue
• Bibliography
• Index

Readership: Graduate students, researchers and professionals engaged in the fields of nuclear physics and particle physics.
Key Features:

• Effective theories
• Emergence of hidden symmetries
• Topology change and hadron-quark continuity

Chapter 1

Introduction

Where the proton (or generally nucleon) mass comes from remains, even after the discovery of Higgs boson, as one of the great mysteries of Nature. In this volume, we explore the possibility that the answer could perhaps be found in nuclear physics by way of unraveling the structure of highly dense matter present in the interior of massive compact stars.

The problem can be stated as follows. Given that the mass of the proton is very accurately measured, 938.272081±0.000006 MeV [Patrignani (2016)], more than 99.9% of the “visible” mass around us — all the way down to atoms — can be accounted for in great accuracy by adding the number of nucleons involved in the system. Even that of the nucleus which is in the core of atoms is accounted for up to 98%. The strong interactions taking place inside the nucleus are now quantitatively described by quantum chromodynamics (QCD). So the mass of a nucleus is nearly completely given by the sum of the mass of the nucleons in the nucleus with only a small correction of binding energy, less than 2% of the proton mass, and even that small value can be fairly well explained, though in a highly intricate way, by QCD. This additive accountability, however, ends abruptly — and singularly — at this point. The proton mass, the source for the nuclear mass, is no longer accounted for as a sum of “something.” In QCD, the relevant constituents are quarks, and for the nucleon the (current) quarks involved, “up” and “down,” are very light, less than 5 MeV. Thus how the proton mass arises from its constituents must be drastically different from how the mass of a nucleus comes about. Effectively, QCD for the proton is a theory for “mass without masses” [Wilczek (2006)].

For most of particle physicists, however, the proton mass is satisfactorily “explained.” Hence the end of the story. In Wilczek’s words [Wilczek (2006)], “Here there are no uncontrolled approximations, no perturbative theory, no cutoff, and no room for fudge factors. A handful of parameters, inserted into a highly constrained theory of extraordinary symmetry, either will or won’t account for the incredible wealth of measured phenomena in the strong interactions. And it certainly appears that they do.” Indeed lattice simulation with QCD with no mass terms and with the heavy quarks c, b and t ignored, termed “QCDLite” by Wilczek, predicts ∼ 95% of the proton mass. If pressed to explain in more detail, they will then say it comes from the massless gluons interacting with the nearly massless, highmomentum quarks, winding up confined in a “bag.” In a nutshell, one may say the mass is generated due to the breaking of chiral symmetry associated with the nearly massless quarks by the confinement [Casher (1979)]. In the standard paradigm, the chiral symmetry spontaneously broken leading to the mass generation is characterized by the non-zero quark condensate, 〈q̄q〉 ≠ 0, a potential chiral order parameter.

To nuclear physicists, ironically, this explanation raises more questions than answers. This may be due to the fact that confinement is very poorly — if at all — understood. For mathematicians, it is “One-Million Dollar Clay Millenium Problem”, still to be solved. It may even be, as some argue, that “deconfinement”, corollary to confinement, does not take place within the framework of QCD. For nuclear physicists, it presents numerous puzzles, some of which bear directly on observables as we will describe below.

How to decipher the mystery of the proton mass is the most fundamental issue in nuclear physics.

In this volume, we address this issue by means of “un-breaking” the spontaneously broken — or, more precisely, “unhiding” the hidden — chiral symmetry. The idea is to “dial” the quark condensate to zero. This could be done by heating hadronic matter to high temperature and/or crushing baryonic matter to high density. Hadrons have been heated in heavy-ion collisions to high temperature, say, several hundreds of MeV, allowing us to have a glimpse of the Universe at the age of ∼ 10⁻⁶ second after the Big Bang. Baryonic matter is being, and will be soon more strongly, compressed to a density several times the normal nuclear matter density n₀ ≃ 0.16 fm⁻³, mimicking the conditions that are supposed to be present in the interior of compact stars. These processes bring hadronic matter to a temperature or density at which the spontaneously broken chiral symmetry is restored and/or the quarks and gluons get deconfined. Along the way the matter experiences a variety of conditions in which the mass and coupling constants get modified significantly, influencing crucially the properties of hadrons living in these environments. Lattice QCD, the only trustful tool known for highly correlated strongly-interacting matter, has, backed by heavy-ion accelerators, beautifully shed light on hadronic matter at high temperature. The near perfect quark-gluon liquid has been discovered, exposing a picture drastically different from, and far more exciting than, what was naively expected, weakly interacting quark-gluon plasma. But the situation at high density is totally different. Since the lattice technique cannot yet access — and there are no other known nonperturbative tools to describe — highly dense matter, the strongly compressed baryonic matter relevant in the interior of massive compact stars remains largely unknown.

The assertion in this volume is that effective field theories (EFTs for short) offer the most promising approach to access dense baryonic matter.

The approach adopted in this volume is anchored on the “Folk Theorem (FT)” on EFTs championed by Steven Weinberg [Weinberg (1997)]. This theorem, briefly stated in Chapter 2, will be the underlying strategy throughout the volume. In fact nuclear physics offers a surprisingly convincing “folk proof ” of this theorem, perhaps even better than in particle physics. The early “proof ” of this theorem was recounted in the volume CNDII [Rho (2008)] and there have been more recent impressive developments, in various nuclear structure phenomena, that reconfirm the early vindication of the FT in nuclear physics. In this volume the aim is to venture further, boldly, into that direction for accessing the uncharted domain of high density. It will inevitably involve certain uncertainties and complications that need to be lifted by future experiments and of course theoretical progress. The import of this development is that EFT, not only making a connection to QCD, can supplement and improve on — not just replace — the standard nuclear physics approach (SNPA for short). What makes EFT more powerful than the SNPA in its framework is that it can make predictions that go beyond what was feasible in standard nuclear physics approaches. In doing this, we revisit certain concepts treated in CNDI and CNDII, sharpening them — and correcting errors committed therein — with more recent theoretical insight and contact with nature.

We define the appropriate languages to address this issue in Chapter 2. The notations that will figure in the volume are defined in this chapter. We revisit in Chapter 3 the thesis treated in both CNDI and CNDII on the Cheshire Cat phenomenon that addresses the hadron-quark continuity in nuclear processes, one of the principal themes of this volume. The reason for this is that that notion, so crucial for making contacts with the topological aspect of nucleon structure, reappears in holographic QCD and in a much broader context in the equation of state (EoS) that enters in the structure of compact stars. How EFT works in nuclear processes at a density in the vicinity of normal nuclear matter is outlined in Chapter 4 with the aim to extrapolate to high-density regime where the EFT has not been tested. Its connection to phenomenological approaches, such as “energy density functional (EDF)” popular in nuclear community, is pointed out there. Various symmetries hidden in QCD proper, such as scale symmetry, hidden local symmetry (HLS), “mended symmetries” are discussed in Chapter 5 with the suggestion that their tell-tale signals can emerge in strongly-correlated baryonic systems at high density. To apply the EFTs to dense matter to explore the pattern of the emerging symmetries, effective Lagrangians are constructed in Chapters 6-8. The notable case is the scale symmetry. Scale symmetry, manifest at the classical level in gauge theories, is broken explicitly at the quantum level by a quantum anomaly and can also be broken spontaneously. Whether and how it can manifest in QCD is highly controversial, and figures importantly at large number of flavors (N_f) for dilatonic Higgs for going beyond the Standard Model in particle physics. In this volume, it is argued to be a crucial element also in the EoS for dense matter and the origin of the nucleon mass.

Baryons as topological solitons, skyrmions, treated in both CNDI and CNDII, are revisited in Chapter 7. Skyrmions in lower dimensions are found to describe a variety of fascinating phenomena in condensed matter physics. And they are also figuring, in an intriguing way, in nuclear structure as one can see in [Rho and Zahed (2016)]. It turns out as one finds in this chapter that it plays an extremely important role in the EoS for dense matter with a hint at the source of the proton mass. There is a phase structure of baryonic matter that is not visible in models that do not resort to topology that appears at a density 2 or 3 times the normal nuclear matter density. There emerges, at high density, parity-doubling that indicates that the proton mass has an important component that is not directly associated with the spontaneous breaking of chiral symmetry. At this density, nothing much is known experimentally and hence whether such a phase change is real or not is not known. What is remarkable is that it has a significant qualitative impact on baryonic matter at a density relevant to massive compact stars. How the topology change influences the structure of the EFT Lagrangian in the wide range of densities involved is discussed in Chapter 8. In Chapter 9, the EFT so determined is applied, nearly parameter-free, to massive compact stars. The predictions made are the maximum star mass, the radius, the sound velocity and the tidal deformability in gravitational waves with an initial contact with the recently observed gravitational waves coming from merging neutron stars GW170817 [Abbott et al. (2017)]. The connection between the source of the proton mass and the emergence of hidden symmetries is inferred from these results. The notion that the hadron-quark continuity can be applied to the EoS of compact stars is put forward in this chapter. All the way to massive compact stars with the central density ∼ 6n₀, strangeness did not figure in the description. This matter will be treated in Chapter 10 where various arguments are given to the effect that explicit strangeness degrees of freedom need not figure in the density regime involved in the massive compact stars so far observed.

Chapter 2

The “Folk Theorem” in Nuclear Physics

2.1 Foreword

As stated in Introduction, our principal theoretical tool will be effective field theory (EFT). It will cover the whole range of nuclear physics, from finite nuclei and infinite nuclear matter to highly compressed baryonic matter relevant to compact stars. In the first part of this Chapter, we will give a precise definition of what EFT that concerns us is all about, then give a short account of how well EFT works in nuclear physics. In the second part of the chapter, we give the minimalistic list of the basic elements in the fundamental theory, put in non-rigorous terms, that are to figure in one or more of EFTs we want to construct. Those ingredients will then be implemented in the following chapters to the best that is feasible to capture a variety of different concepts that we deem indispensable in building the theoretical framework to address the range of phenomena that we are interested in. The ultimate aim is to have one unified approach with as few a set of parameters as feasible.

Quantum Chromodynamics (QCD) is undoubtedly the correct theory for strong interactions, as it is now widely recognized, so it should apply not only to elementary hadrons but also to nuclear physics as well as compactstar physics. But it cannot at present directly access the latter two with any degree of accuracy, particularly the complex structure of compact-star matter. It will be some time before it will be able to do so. EFTs in a variety of different guises are currently the only tools available to explore the wide variety of strong interactions that take place in going from quarks to hadrons to superdense matter involved. And the only promising one.

So what is effective quantum field theory?

Th...