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From pQCD to neutron stars: matching equations of state to constrain global star properties
Abstract
The equation of state (EoS) of quantum chromodynamics (QCD) at zero temperature can be calculated in two different perturbative regimes: for small values of the baryon chemical potential , one may use chiral perturbation theory (ChEFT); and for large values of , one may use perturbative QCD (pQCD). There is, however, a gap for , where these theories becomes non-perturbative, and where there is currently no known microscopic description of QCD matter. Unfortunately, this interval obscures the values of found within the cores of neutron stars (NSs). In this thesis, we argue that thermodynamic matching of the ChEFT and pQCD EoSs is a legitimate way to obtain quantitative constraints on the non-pertubative QCD EoS. Moreover, we argue that this method is effective, verifiable, and systematically improvable. First, we carry out a simplified matching procedure in QCD-like theories that can be simulated on the lattice without a sign problem. Our calculated pressure band serves as a prediction for lattice-QCD practitioners and will allow them to verify or refute the simplified procedure. Second, we apply the state-of-the-art matched EoS of Kurkela et al. (2014) to rotating NSs. This allows us to obtain bounds on observable NS properties, as well as point towards future observations that would more tightly constrain the current state-of-the-art EoS band. Finally, as evidence of the ability to improve the procedure, we carry out calculations in pQCD to improve the zero-temperature pressure. We calculate the full contribution to the pQCD pressure for massless quarks, as well as a significant portion of the piece and even some of the piece.
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Recent progress in direct simulations of QCD at nonzero chemical potentials is reported upon. After a brief introduction to the sign problem in lattice QCD and a quick description of the complex Langevin equation we show recent results and discuss open questions.
A set of theoretical mass-radius relations for rigidly rotating neutron stars
with exotic cores, obtained in various theories of dense matter, is reviewed.
Two basic observational constraints are used: the largest measured rotation
frequency is 716 Hz and the maximum measured mass is .
Present status of measuring the radii of neutron stars is described. The theory
of rigidly rotating stars in general relativity is reviewed and limitations of
the slow rotation approximation are pointed out. Mass-radius relations for
rotating neutron stars with hyperon and quark cores are illustrated using
several models. Problems related to the non-uniqueness of the crust-core
matching are mentioned. Limits on rigid rotation resulting from the
mass-shedding instability and the instability with respect to the axisymmetric
perturbations are summarized. The problem of instabilities and of the
back-bending phenomenon are discussed in detail. Metastability and instability
of a neutron star core in the case of a first-order phase transition, both
between pure phases, and into a mixed-phase state, are reviewed. The case of
two disjoint families (branches) of rotating neutron stars is discussed and
generic features of neutron-star families and of core-quakes triggered by the
instabilities are considered.
TikZ-Feynman is a LaTeX package allowing Feynman diagrams to be easily generated within LaTeX with minimal user instructions and without the need of external programs. It builds upon the TikZ package and leverages the graph placement algorithms from TikZ in order to automate the placement of many vertices. TikZ-Feynman still allows fine-tuned placement of vertices so that even complex diagrams can be generated with ease. Program summary Program title: TikZ-Feynman Catalogue identifier: AFBF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 6727 No. of bytes in distributed program, including test data, etc.: 413779 Distribution format: tar.gz Programming language: TeX, LaTeX, Lua. Computer: PC's or workstations. Operating system: Any capable of processing LaTeX. Classification: 4.4. External routines: TikZ Nature of problem: Existing methods for drawing Feynman diagrams in LaTeX usually require external programs and are not very user friendly thereby making it difficult and time consuming to generate even simple diagrams. Solution method: TikZ-Feynman provides an easier way to draw Feynman diagrams by building on TikZ and using graph drawing algorithms to automatically place vertices. This can be combined with some positioning to produce complicated diagrams with relative ease. Running time: Depends on the size
These lecture notes contain an elementary introduction to lattice QCD at
nonzero chemical potential. Topics discussed include chemical potential in the
continuum and on the lattice; the sign, overlap and Silver Blaze problems; the
phase boundary at small chemical potential; imaginary chemical potential; and
complex Langevin dynamics. An incomplete overview of other approaches is
presented as well. These lectures are meant for postgraduate students and
postdocs with an interest in extreme QCD. A basic knowledge of lattice QCD is
assumed but not essential. Some exercises are included at the end.
We present a first look at the spectroscopy of SU(4) gauge theory coupled to
two flavors of Dirac fermions in the two-index antisymmetric representation,
which is a real representation. We compute meson and diquark masses, the
pseudoscalar and vector meson decay constants, and the masses of six-quark
baryons. We make comparisons with large-Nc expectations.
We summarise recent progress in simulating QCD at nonzero baryon density
using complex Langevin dynamics. After a brief outline of the main idea, we
discuss gauge cooling as a means to control the evolution. Subsequently we
present a status report for heavy dense QCD and its phase structure, full QCD
with staggered quarks, and full QCD with Wilson quarks, both directly and using
the hopping parameter expansion to all orders.
It has been conjectured that the velocity of sound in any medium is smaller
than the velocity of light in vacuum divided by . Simple arguments
support this bound in non-relativistic and/or weakly coupled theories. The
bound has been demonstrated in several classes of strongly coupled theories
with gravity duals and is saturated only in conformal theories. We point out
that the existence of neutron stars with masses around two solar masses
combined with the knowledge of the equation of state of hadronic matter at
"low" densities is in strong tension with this bound.
We present results for the equation of state in (2+1)-flavor QCD using the
highly improved staggered quark action and lattices with temporal extent
, and 12. We show that these data can be reliably
extrapolated to the continuum limit and obtain a number of thermodynamic
quantities and the speed of sound in the temperature range MeV. We
compare our results with previous calculations, and provide an analytic
parameterization of the pressure, from which other thermodynamic quantities can
be calculated, for use in phenomenology. We show that the energy density in the
crossover region, MeV, defined by the chiral
transition, is , i.e.,
. At high temperatures, we compare our
results with resummed and dimensionally reduced perturbation theory
calculations. As a byproduct of our analyses, we obtain the values of the scale
parameters from the static quark potential and from the gradient
flow.
We study lattice QCD with four flavors of staggered quarks. In the limit of
infinite gauge coupling, "dual" variables can be introduced, which render the
finite-density sign problem mild and allow a full determination of the
phase diagram by Monte Carlo simulations, also in the chiral limit. However,
the continuum limit coincides with the weak coupling limit. We propose a
strong-coupling expansion approach towards the continuum limit. We show first
results, including the phase diagram and its chiral critical point, from this
expansion truncated to next-to-leading order.
We highlight the progress, current status, and open challenges of QCD-driven
physics, in theory and in experiment. We discuss how the strong interaction is
intimately connected to a broad sweep of physical problems, in settings ranging
from astrophysics and cosmology to strongly-coupled, complex systems in
particle and condensed-matter physics, as well as to searches for physics
beyond the Standard Model. We also discuss how success in describing the strong
interaction impacts other fields, and, in turn, how such subjects can impact
studies of the strong interaction. In the course of the work we offer a
perspective on the many research streams which flow into and out of QCD, as
well as a vision for future developments.
We present the spectrum of baryons in a new SU(4) gauge theory with
fundamental fermion constituents. The spectrum of these bosonic baryons is of
significant interest for composite dark matter theories. Here, we compare the
spectrum and properties of SU(3) and SU(4) baryons, and then compute the
dark-matter direct detection cross section via Higgs boson exchange for
TeV-scale composite dark matter arising from a confining SU(4) gauge sector.
Comparison with the latest LUX results leads to tight bounds on the fraction of
the constituent-fermion mass that may arise from electroweak symmetry breaking.
Lattice calculations of the dark matter mass spectrum and the Higgs-dark matter
coupling are performed on quenched , ,
, and lattices with three different
lattice spacings, using Wilson fermions with moderate to heavy pseudoscalar
meson masses. Our results lay a foundation for future analytic and numerical
study of composite baryonic dark matter.
We present a full result for the 2+1 flavor QCD equation of state. All the
systematics are controlled, the quark masses are set to their physical values,
and the continuum extrapolation is carried out. This extends our previous
studies [JHEP 0601:089 (2006); 1011:077 (2010)] to even finer lattices and now
includes ensembles with Nt = 6,8,10,12 up to Nt = 16. We use a Symanzik
improved gauge and a stout-link improved staggered fermion action. Our findings
confirm our earlier results. In order to facilitate the direct use of our
equation of state we make our tabulated results available for download.
The complex Langevin method is extended to full QCD at non-zero chemical
potential. The use of gauge cooling stabilizes the simulations for smooth
lattices. At large fermion mass the results are compared to HQCD limit, where
the spatial hoppings are neglected, and good agreement is found. The method
allows simulations also at high densities, all the way up to saturation.
We discuss macroscopic aspects of quark matter phase transition in cold dense stellar matter, considering global charge neutrality and baryonic charge conservation. We determine the critical condition for the phase transition between the strange quark matter, SQM, and the color-flavor locked, CFL, superconducting phase. We also discuss the sensitivity of our results to variations in the gap energy, D, and in the current strange quark mass, ms0. The phase transition is calculated taking into account the baryonic density dependence of the quark masses in dense baryonic medium.
The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g5. We compute here the last contribution which can be determined perturbatively, g6ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g6ln(1/g) terms, once they are summed together with the so far unknown perturbative and nonperturbative g6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.
We compute the dimensionally regularised four-loop vacuum energy density of the SU(Nc) gauge + adjoint Higgs theory, in the disordered phase. "Scalarisation", or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining master integrals are evaluated in d = 3 - 2ε dimensions, by expanding in ε ≪ 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders script O sign(g6ln(1/g)), script O sign(g6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems.
This book discusses the physical phases of Quantum Chromodynamics (QCD) in ordinary environments, as well as in extreme environments with high temperatures and high baryon numbers. Under such extreme conditions, new phases are thought to exist: the quark-gluon plasma and color superconductivity. After introducing lattice gauge theory, John Kogut and Mikhail Stephanov emphasize the application of QCD to the study of matter in extreme environments through a host of methods. These include lattice gauge theory, lower dimensional model field theories and effective Lagrangians.
At nonzero chemical potential the numerical sign problem in lattice field
theory limits the use of standard algorithms based on importance sampling.
Complex Langevin dynamics provides a possible solution, but it has to be
applied with care. In this review, we first summarise our current understanding
of the approach, combining analytical and numerical insight. In the second part
we study SL(N,C) gauge cooling, which was introduced recently as a tool to
control complex Langevin dynamics in nonabelian gauge theories. We present new
results in Polyakov chain models and in QCD with heavy quarks and compare
various adaptive cooling implementations.
We present the results of a systematic, first-principles study of the
spectrum and decay constants of mesons for different numbers of color charges
N, via lattice computations. We restrict our attention to states in the
non-zero isospin sector, evaluating the masses associated with the ground-state
and first excitation in the pseudoscalar, vector, scalar, and axial vector
channels. Our results are based on a new set of simulations of four dimensional
SU(N) Yang-Mills theories with the number of colors ranging from N=2 to N=17;
the spectra and the decay constants are computed in the quenched approximation
(which becomes exact in the 't Hooft limit) using Wilson fermions. After
discussing the extrapolations to the chiral and large-N limits, we present a
comparison of our results to some of the numerical computations and analytical
predictions available in the literature - including, in particular, those from
holographic computations.
It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but—quite surprisingly—most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five-dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.
We numerically investigate global properties of rotating neutron stars using the allowed band of QCD equations of state derived by Kurkela et al. This band is constrained by chiral effective theory at low densities and perturbative QCD at high densities, and is thus, in essence, a controlled constraint from first-principles physics. Previously, this band of equations of state was used to investigate non-rotating neutron stars only; in this work, we extend these results to any rotation frequency below the mass-shedding limit. We investigate mass--radius curves, allowed mass--frequency regions, radius--frequency curves for a typical 1.4-solar-mass star, and the values of the moment of inertia of the double pulsar PSR J0737-3039A, a pulsar whose moment of inertia may be constrained observationally in a few years. We present limits on observational data coming from these constraints, and identify values of observationally-relevant parameters that would further constrain the allowed region for the QCD equation of state. We also discuss how much this region would be constrained by a measurement of the moment of inertial of the double pulsar PSR J0737-3039A.
DOI:http://dx.doi.org/10.1103/PhysRevC.93.049905
Many physically motivated extensions to general relativity (GR) predict significant deviations at energies present in massive neutron stars. We report the measurement of a 2.01 0.04 solar mass (M) pulsar in a 2.46-h orbit around a 0.172 0.003 M white dwarf. The high pulsar mass and the compact orbit make this system a sensitive laboratory of a previously untested strong-field gravity regime. Thus far, the observed orbital decay agrees with GR, supporting its validity even for the extreme conditions present in the system. The resulting constraints on deviations support the use of GR-based templates for ground-based gravitational wave detection experiments. Additionally, the system strengthens recent constraints on the properties of dense matter and provides novel insight to binary stellar astrophysics and pulsar recycling.
A precise moment of inertia measurement for PSR J0737-3039A in the double pulsar system is expected within the next five years. We present here a new method of mapping the anticipated measurement of the moment of inertia directly into the neutron star structure. We determine the maximum and minimum values possible for the moment of inertia of a neutron star of a given radius based on physical stability arguments, assuming knowledge of the equation of state only at densities below the nuclear saturation density. If the equation of state is trusted up to the nuclear saturation density, we find that a measurement of the moment of inertia will place absolute bounds on the radius of PSR J0737-3039A to within ±1 km. The resulting combination of moment of inertia, mass, and radius measurements for a single source will allow for new, stringent constraints on the dense-matter equation of state.
We present our final results for the Lambda parameter and strange quark mass of QCD with two dynamical quark flavors following the ALPHA collaboration's long-term strategy to compute fundamental parameters of QCD. This strategy includes non-perturbative renormalization and a recursive finite-size scaling procedure in the continuum to compute the renormalization group invariant quantities Λ and Ms. Here perturbation theory enters at scales of O(100GeV) where it is well controlled. The last missing piece in this setup, namely the lattice scale has been recently determined via the kaon decay constant on large volume simulations (mπL ≥ 4) made available through the Coordinated Lattice Simulations (CLS) effort.
We use quantum Monte Carlo (QMC) techniques to calculate the static structure function S(q) of a one-component ion lattice and use it to calculate the thermal conductivity κ of high-density solid matter expected in the neutron star crust. By making detailed comparisons with the results for the thermal conductivity obtained using standard techniques based on the one-phonon approximation (OPA) valid at low temperatures and the multiphonon harmonic approximation expected to be valid over a wide range of temperatures, we assess the temperature regime where S(q) from the QMC can be used directly to calculate κ. We also compare the QMC results to those obtained using the classical Monte Carlo to quantitatively assess the magnitude of the quantum corrections. We found that quantum effects became relevant for the calculation of κ at a temperature of T0.3ΩP, where ΩP is the ion plasma frequency. At T≃0.1ΩP the quantum effects suppress κ by about 30%. The comparison with the results of the OPA indicates that dynamical information beyond the static structure is needed when T0.1ΩP. These quantitative comparisons help to establish QMC as a viable technique to calculate κ at moderate temperatures in the range of T=0.1-1ΩP of relevance to the study of accreting neutron stars. This finding is especially important because QMC is the only viable technique so far for calculating κ in multicomponent systems at low temperatures.
In this review article, we argue that our current understanding of the
thermodynamic properties of cold QCD matter, originating from first principles
calculations at high and low densities, can be used to efficiently constrain
the macroscopic properties of neutron stars. In particular, we demonstrate that
combining state-of-the-art results from Chiral Effective Theory and
perturbative QCD with the current bounds on neutron star masses, the Equation
of State of neutron star matter can be obtained to an accuracy better than 30%
at all densities.
We construct equilibrium configurations of uniformly rotating neutron stars
for selected relativistic mean-field nuclear matter equations of state (EOS).
We compute in particular the gravitational mass (M), equatorial () and polar () radii, eccentricity, angular momentum (J),
moment of inertia (I) and quadrupole moment () of neutron stars stable
against mass-shedding and secular axisymmetric instability. By constructing the
constant frequency sequence f=716 Hz of the fastest observed pulsar, PSR
J1748-2446ad, and constraining it to be within the stability region, we obtain
a lower mass bound for the pulsar, -, for the
EOS employed. Moreover we give a fitting formula relating the baryonic mass
() and gravitational mass of non-rotating neutron stars,
[or
], which is independent on the
EOS. We also obtain a fitting formula, although not EOS independent, relating
the gravitational mass and the angular momentum of neutron stars along the
secular axisymmetric instability line for each EOS. We compute the maximum
value of the dimensionless angular momentum, (or "Kerr
parameter"), , found to be also independent on the
EOS. We compare and contrast then the quadrupole moment of rotating neutron
stars with the one predicted by the Kerr exterior solution for the same values
of mass and angular momentum. Finally we show that, although the mass
quadrupole moment of realistic neutron stars never reaches the Kerr value, the
latter is closely approached from above at the maximum mass value, as
physically expected from the no-hair theorem. In particular the stiffer the EOS
is, the closer the Kerr solution is approached.
We calculate the equation of state at non-zero temperature and density from
first principles in two-, three- and four-color QCD with two fermion flavors in
the fundamental and two-index, antisymmetric representation. By matching
low-energy results (from a `hadron resonance gas') to high-energy results from
(resummed) perturbative QCD, we obtain results for the pressure and trace
anomaly that are in quantitative agreement with full lattice-QCD studies for
three colors at zero chemical potential. Our results for non-zero chemical
potential at zero temperature constitute predictions for the equation of state
in QCD-like theories that can be tested by traditional lattice studies for
two-color QCD with two fundamental fermions and four-color QCD with two
two-index, antisymmetric fermions. We find that the speed of sound squared at
zero temperature can exceed one third, which may be relevant for the
phenomenology of high-mass neutron stars.
We present a study of spectroscopy of SU(4) lattice gauge theory coupled to
two flavors of Dirac fermions in the anti-symmetric two index representation.
The fermion representation is real, and the pattern of chiral symmetry breaking
is SU(2Nf) -> SO(2Nf) with Nf flavors of Dirac fermions. It is an interesting
generalization of QCD, for several reasons: it allows direct exploration of an
alternate large Nc expansion, it can be simulated at non-zero chemical
potential with no sign problem, and several UV completions of composite Higgs
systems are built on it. We present preliminary results on the baryon and meson
spectra of the theory and compare them with SU(3) results and with expectations
for large Nc scaling.
The strong coupling limit of staggered lattice QCD has been studied for decades, both via Monte Carlo and mean field. In this model, the finite density sign problem is mild and the full phase diagram can be studied, even in the chiral limit. However, in the strong coupling limit the lattice is maximally coarse. Here, we propose a method to go beyond the strong coupling limit with first results and discuss the consequences on the QCD phase diagram in the μ-T plane, in particular the existence of chiral critical end point which is sought in heavy ion collisions. We explain how to construct an effective theory for non-zero lattice coupling, valid to O{script}(β), and present Monte Carlo results incorporating these corrections.
Progress in simulating QCD at nonzero baryon density requires, amongst
others, substantial numerical effort. Here we propose two different expansions
to all orders in the hopping parameter, preserving the full Yang-Mills action,
which are much cheaper to simulate. We carry out simulations using complex
Langevin dynamics, both in the hopping expansions and in the full theory, for
two flavours of Wilson fermions, and agreement is seen at sufficiently high
order in the expansion. These results provide support for the use of complex
Langevin dynamics to study QCD at nonzero density, both in the full and the
expanded theory, and for the convergence of the latter.
Part I. Field Theory: 1. Microscopic theory of radiation; 2. Lorentz invariance and second quantization; 3. Classical Field Theory; 4. Old-fashioned perturbation theory; 5. Cross sections and decay rates; 6. The S-matrix and time-ordered products; 7. Feynman rules; Part II. Quantum Electrodynamics: 8. Spin 1 and gauge invariance; 9. Scalar QED; 10. Spinors; 11. Spinor solutions and CPT; 12. Spin and statistics; 13. Quantum electrodynamics; 14. Path integrals; Part III. Renormalization: 15. The Casimir effect; 16. Vacuum polarization; 17. The anomalous magnetic moment; 18. Mass renormalization; 19. Renormalized perturbation theory; 20. Infrared divergences; 21. Renormalizability; 22. Non-renormalizable theories; 23. The renormalization group; 24. Implications of Unitarity; Part IV. The Standard Model: 25. Yang─Mills theory; 26. Quantum Yang-Mills theory; 27. Gluon scattering and the spinor-helicity formalism; 28. Spontaneous symmetry breaking; 29. Weak interactions; 30. Anomalies; 31. Precision tests of the standard model; 32. QCD and the parton model; Part V. Advanced Topics: 33. Effective actions and Schwinger proper time; 34. Background fields; 35. Heavy-quark physics; 36. Jets and effective field theory; Appendices; References; Index.
The hyperfine mass splittings of baryons in large N QCD are proved to be
proportional to J2. Hyperfine mass splittings are first
allowed at order 1/N in the 1/N expansion.
We calculate the three-loop thermodynamic potential of QCD at finite
temperature and chemical potential using the hard-thermal-loop perturbation
theory (HTLpt) reorganization of finite temperature and density QCD. The
resulting analytic thermodynamic potential allows us to compute the pressure,
energy density, and entropy density of the quark-gluon plasma. Using these we
calculate the trace anomaly, speed of sound, and second-, fourth-, and
sixth-order quark number susceptibilities. For all observables considered we
find good agreement between our three-loop HTLpt calculations and available
lattice data for temperatures above approximately 300 MeV.
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount - or even presence - of quark matter inside the stars. © 2014. The American Astronomical Society. All rights reserved.
This text introduces the theoretical framework for describing the
quark-gluon plasma, an important new state of matter. The first part of
the book is a self-contained introduction to relativistic thermal field
theory. Topics include the path integral approach, the real and
imaginary time formalisms, fermion fields and gauge fields at finite
temperature. The author illustrates useful techniques such as the
evaluation of frequency sums and the use of cutting rules. The second
part of the book is devoted to recent developments, and gives a detailed
account of collective excitations (bosonic and fermionic), showing how
they give rise to energy scales that imply a reorganization of
perturbation theory. The author also explains the relation with kinetic
theory. He works out in detail applications to processes that occur in
heavy ion collisions and in astrophysics. Each chapter ends with
exercises and a guide to the literature. Graduate students and
researchers in nuclear, particle, and astrophysics will benefit from
this book.
Preface; Inputs to the standard model; Interactions of the standard
model; Symmetries and anomalies; Introduction to effective Lagrangians;
Leptons; Very low energy QCD - Pions and photons; Introducing kaons and
etas; Kaons and the ∆S=1 interaction; Kaon mixing and CP
violation; The large N expansion; Phenomenological models; Baryon
properties; Hadron spectroscopy; Weak interactions of heavy quarks; The
Higgs boson; The electroweak gauge bosons; Appendices; References;
Index.
Lattice QCD studies of the thermodynamics of the hot quark-gluon plasma (QGP)
demonstrate the importance of accounting for the interactions of quarks and
gluons, if one wants to investigate the phase structure of strongly interacting
matter. Motivated by this observation and using state-of-the-art results from
perturbative QCD, we construct a simple effective equation of state for cold
quark matter that consistently incorporates the effects of interactions and
furthermore includes a built-in estimate of the inherent systematic
uncertainties. This goes beyond the MIT bag model description in a crucial way,
yet leads to an equation of state that is equally straightforward to use.
Thoroughly revised and updated, this new edition develops the basic formalism and theoretical techniques for studying relativistic field theory at finite temperature and density. It starts with the path-integral representation of the partition function and then proceeds to develop diagrammatic perturbation techniques. The standard model is discussed, along with the nature of the phase transitions in strongly interacting systems and applications to relativistic heavy ion collisions, dense stellar objects, and the early universe. First Edition Hb (1989): 0-521-35155-3 First Edition Pb (1994): 0-521-44945-6
We study a class of models of dynamical weak-interaction symmetry breaking suggested by the work of Weinberg and Susskind. We demonstrate in these models some simple relations which determine the alignment of weakly gauged subgroups and the masses of pseudo-Goldstone bosons. We illustrate these methods by computing the spectrum of pseudo-Goldstone bosons in three models recently examined by Dimopoulos. These models are seen to contain a very light charged Higgs boson, whose mass we estimate by the use of chiral perturbation theory. In one of these models, we observe that the energetically preferred vacuum is a phenomenologically unpleasant one. Junior Fellow, Harvard Society of Fellows.
This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions. Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction. After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations. The book will be valuable for graduate students and researchers in theoretical physics, elementary particle physics, and field theory, interested in non-perturbative approximations and numerical simulations of quantum field phenomena.
We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for use in supernova simulations. The properties of nuclear matter with both uniform and non-uniform distributions are studied consistently. We tabulate the outcome in terms of the pressure, free energy, entropy, etc. at a sufficiently large number of mesh points in the density range ϱB = 105.1 ∼ 1015.4g/cm3, the temperature range T = 0 ∼ 100 MeV and the proton fraction range Yp = 0 ∼ 0.56 to be used for supernova simulations. We also discuss the EOS of neutron star matter at zero temperature in a wide density range including hyperons.
We consider the particle spectrum that QCD with n flavors of massless quarks would have if a quark-quark condensate formed in the color triplet channel, rather than a quark-antiquark condensate in the color singlet channel. We find observable massless fermions which carry baryon number +/-1. We also consider an arbitrary number of colors, and find similar results when the number of colors is odd. Our results always satisfy 't Hooft's anomaly constraints. Supported in part by NSF Grant PHY78-26847.
Infrared properties of quark gas at finite density are studied using renormalization-group-improved perturbation theory. The running coupling constant shows color charge screening in the infrared region and asymptotic freedom in the ultraviolet region. Color density correlations are finite. Instanton contributions to the partition function are estimated and found to be large at low density. Possible ambiguities of the perturbation expansion in the many-body medium are discussed.
We discuss the observational consistency, possible properties, and detection of collapsed nuclei CA. These may be considered as elementary particles with mass number A>1 and of much smaller radius than ordinary nuclei NA. The existence of CA of (perhaps much) lower energy than NA is observationally consistent if NA are very long-lived isomers against collapse because of a "saturation" barrier between CA and NA. Barrier-penetrability estimates show that sufficiently long lifetimes ≳1031 sec are plausible for A≳16-40. The properties of CA are discussed using composite baryon and quark models; small charges and hypercharges and, especially, neutral CA are possible. CA can be effectively a source or sink of baryons. Some astrophysical implications are briefly discussed, in particular the possible large scale presence of CA and the possibility that accelerated collapse in massive objects may be a source of energy comparable to the rest mass.
We calculate the ground-state energy of a quark gas up to and including effecs of fourth order in the quark-gluon coupling. Renormalization-group techniques are used to rewrite the results of the fourth-order calculation in terms of a chemical-potential-dependent coupling. The chemical-potential-dependent coupling approaches zero at high densities. We argue that at hadronic matter densities a phase transition between quark matter and hadronic matter occurs. We show the existence of this phase transition for a three-color, one-flavor quark gas. We find a close correspondence between the results of quantum chromodynamics at large coupling with no bag constant and quantum chromodynamics at small coupling with a bag constant.