3,124 research outputs found
Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state
Lack of Lorentz invariance of QCD at finite quark chemical potential in
general implies the need of Lorentz non-invariant condensates for the
self-consistent description of the color-superconducting ground state.
Moreover, the spontaneous breakdown of color SU(3) in this state naturally
leads to the existence of SU(3) non-invariant non-superconducting expectation
values. We illustrate these observations by analyzing the properties of an
effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the
possibility of color-superconducting states with effectively gapless fermionic
excitations. It turns out that the effect of condensates so far neglected can
yield new interesting phenomena.Comment: 16 pages, 3 figure
Illuminating Dense Quark Matter
We imagine shining light on a lump of cold dense quark matter, in the CFL
phase and therefore a transparent insulator. We calculate the angles of
reflection and refraction, and the intensity of the reflected and refracted
light. Although the only potentially observable context for this phenomenon
(reflection of light from and refraction of light through an illuminated quark
star) is unlikely to be realized, our calculation casts new light on the old
idea that confinement makes the QCD vacuum behave as if filled with a
condensate of color-magnetic monopoles.Comment: 4 pages, 1 figur
Mass-Induced Crystalline Color Superconductivity
We demonstrate that crystalline color superconductivity may arise as a result
of pairing between massless quarks and quarks with nonzero mass m_s. Previous
analyses of this phase of cold dense quark matter have all utilized a chemical
potential difference \delta\mu to favor crystalline color superconductivity
over ordinary BCS pairing. In any context in which crystalline color
superconductivity occurs in nature, however, it will be m_s-induced. The effect
of m_s is qualitatively different from that of \delta\mu in one crucial
respect: m_s depresses the value of the BCS gap \Delta_0 whereas \delta\mu
leaves \Delta_0 unchanged. This effect in the BCS phase must be taken into
account before m_s-induced and \delta\mu-induced crystalline color
superconductivity can sensibly be compared.Comment: 12 pages, 4 figures. v2: very small change onl
Mass Terms in Effective Theories of High Density Quark Matter
We study the structure of mass terms in the effective theory for
quasi-particles in QCD at high baryon density. To next-to-leading order in the
expansion we find two types of mass terms, chirality conserving
two-fermion operators and chirality violating four-fermion operators. In the
effective chiral theory for Goldstone modes in the color-flavor-locked (CFL)
phase the former terms correspond to effective chemical potentials, while the
latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone
bosons in the CFL phase, confirming earlier results by Son and Stephanov as
well as Bedaque and Sch\"afer. We show that to leading order in the coupling
constant there is no anti-particle gap contribution to the mass of
Goldstone modes, and that our results are independent of the choice of gauge.Comment: 22 pages, 4 figure
Anisotropic admixture in color-superconducting quark matter
The analysis of color-superconducting two-flavor deconfined quark matter at
moderate densities is extended to include a particular spin-1 Cooper pairing of
those quarks which do not participate in the standard spin-0 diquark
condensate. (i) The relativistic spin-1 gap Delta' implies spontaneous
breakdown of rotation invariance manifested in the form of the quasi-fermion
dispersion law. (ii) The critical temperature of the anisotropic component is
approximately given by the relation T_c'~ Delta'(T=0)/3. (iii) For massless
fermions the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes
effectively gapless and two-dimensional. Consequently, its specific heat
depends quadratically on temperature. (iv) All collective Nambu-Goldstone
excitations of the anisotropic phase have a linear dispersion law and the whole
system remains a superfluid. (v) The system exhibits an electromagnetic
Meissner effect.Comment: v2: references added, angular dependence of the gap clarified, v3:
extended discussion, typo in eq. (5) corrected, version accepted for
publication in PR
Quark description of nuclear matter
We discuss the role of an adjoint chiral condensate for color superconducting
quark matter. Its presence leads to color-flavor locking in two-flavor quark
matter. Color is broken completely as well as chiral symmetry in the two-flavor
theory with coexisting adjoint quark-antiquark and antitriplet quark-quark
condensates. The qualitative properties of this phase match the properties of
ordinary nuclear matter without strange baryons. This complements earlier
proposals by Schafer and Wilczek for a quark description of hadronic phases. We
show for a class of models with effective four-fermion interactions that
adjoint chiral and diquark condensates do not compete, in the sense that
simultaneous condensation occurs for sufficiently strong interactions in the
adjoint chiral channel.Comment: 15 pages, 3 figure
Colour superconductivity in finite systems
In this paper we study the effect of finite size on the two-flavour colour
superconducting state. As well as restricting the quarks to a box, we project
onto states of good baryon number and onto colour singlets, these being
necessary restrictions on any observable ``quark nuggets''. We find that
whereas finite size alone has a significant effect for very small boxes, with
the superconducting state often being destroyed, the effect of projection is to
restore it again. The infinite-volume limit is a good approximation even for
quite small systems.Comment: 14 pages RevTeX4, 12 eps figure
The Stability of Strange Star Crusts and Strangelets
We construct strangelets, taking into account electrostatic effects,
including Debye screening, and arbitrary surface tension sigma of the interface
between vacuum and quark matter. We find that there is a critical surface
tension sigma_crit below which large strangelets are unstable to fragmentation
and below which quark star surfaces will fragment into a crystalline crust made
of charged strangelets immersed in an electron gas. We derive a
model-independent relationship between sigma_crit and two parameters that
characterize any quark matter equation of state. For reasonable model equations
of state, we find sigma_crit typically of order a few MeV/fm^2. If sigma <=
sigma_crit, the size-distribution of strangelets in cosmic rays could feature a
peak corresponding to the stable strangelets that we construct.Comment: 11 pages, LaTe
Dense quark matter in compact stars
The densest predicted state of matter is colour-superconducting quark matter,
in which quarks near the Fermi surface form a condensate of Cooper pairs. This
form of matter may well exist in the core of compact stars, and the search for
signatures of its presence is an ongoing enterprise. Using a bag model of quark
matter, I discuss the effects of colour superconductivity on the mass-radius
relationship of compact stars, showing that colour superconducting quark matter
can occur in compact stars at values of the bag constant where ordinary quark
matter would not be allowed. The resultant ``hybrid'' stars with colour
superconducting quark matter interior and nuclear matter surface have masses in
the range 1.3-1.6 Msolar and radii 8-11 km. Once perturbative corrections are
included, quark matter can show a mass-radius relationship very similar to that
of nuclear matter, and the mass of a hybrid star can reach 1.8 \Msolar.Comment: 11 pages, for proceedings of SQM 2003 conference; references added,
abstract reworde
Numerical solution of the color superconductivity gap in a weak coupling constant
We present the numerical solution of the full gap equation in a weak coupling
constant . It is found that the standard approximations to derive the gap
equation to the leading order of coupling constant are essential for a secure
numerical evaluation of the logarithmic singularity with a small coupling
constant. The approximate integral gap equation with a very small should be
inverted to a soft integral equation to smooth the logarithmic singularity near
the Fermi surface. The full gap equation is solved for a rather large coupling
constant . The approximate and soft integral gap equations are solved
for small values. When their solutions are extrapolated to larger
values, they coincide the full gap equation solution near the Fermi surface.
Furthermore, the analytical solution matches the numerical one up to the order
one O(1). Our results confirm the previous estimates that the gap energy is of
the order tens to 100 MeV for the chemical potential MeV. They
also support the validity of leading approximations applied to the full gap
equation to derive the soft integral gap equation and its analytical solution
near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe
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