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

Color-Neutral Superconducting Quark Matter

We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter at zero temperature, color neutrality guarantees that the number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL) phase will be equal even with physical current quark masses. Electric charge neutrality follows as a consequence and without the presence of electrons. In contrast, electric charge neutrality in the less symmetric 2-flavor superconducting (2SC) phase with ud pairing requires more electrons than the normal quark phase. The free energy density cost of enforcing color and electric charge neutrality in the CFL phase is lower than that in the 2SC phase, which favors the formation of the CFL phase. With increasing temperature and neutrino content, an unlocking transition occurs from the CFL phase to the 2SC phase with the order of the transition depending on the temperature, the quark and lepton number chemical potentials. The astrophysical implications of this rich structure in the phase diagram, including estimates of the effects from Goldstone bosons in the CFL phase, are discussed.Comment: 20 pages, 4 figures; version to appear in Phys. Rev.

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

Illuminating interfaces between phases of a U(1) x U(1) gauge theory

We study reflection and transmission of light at the interface between different phases of a U(1) x U(1) gauge theory. On each side of the interface, one can choose a basis so that one generator is free (allowing propagation of light), and the orthogonal one may be free, Higgsed, or confined. However, the basis on one side will in general be rotated relative to the basis on the other by some angle alpha. We calculate reflection and transmission coefficients for both polarizations of light and all 8 types of boundary, for arbitrary alpha. We find that an observer measuring the behavior of light beams at the boundary would be able to distinguish 4 different types of boundary, and we show how the remaining ambiguity arises from the principle of complementarity (indistinguishability of confined and Higgs phases) which leaves observables invariant under a global electric/magnetic duality transformation. We also explain the seemingly paradoxical behavior of Higgs/Higgs and confined/confined boundaries, and clarify some previous arguments that confinement must involve magnetic monopole condensation.Comment: RevTeX, 12 page

Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops

This is an exploratory study of the lightest non-singlet scalar $q\bar q$ state on the lattice with two dynamical quarks. Domain Wall fermions are used for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$ and N_f=2. Since this statistical error-bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the Partially Quenched ChPT and find it describes lattice correlators well. The leading unphysical contribution in Partially Quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass 1.51(19) GeV from the partially quenched correlators is consistent with the dynamical result and has appreciably smaller error-bar.Comment: 23 pages, 8 figure

Bulk viscosity in a cold CFL superfluid

We compute one of the bulk viscosity coefficients of cold CFL quark matter in the temperature regime where the contribution of mesons, quarks and gluons to transport phenomena is Boltzmann suppressed. In that regime dissipation occurs due to collisions of superfluid phonons, the Goldstone modes associated to the spontaneous breaking of baryon symmetry. We first review the hydrodynamics of relativistic superfluids, and remind that there are at least three bulk viscosity coefficients in these systems. We then compute the bulk viscosity coefficient associated to the normal fluid component of the superfluid. In our analysis we use Son's effective field theory for the superfluid phonon, amended to include scale breaking effects proportional to the square of the strange quark mass m_s. We compute the bulk viscosity at leading order in the scale breaking parameter, and find that it is dominated by collinear splitting and joining processes. The resulting transport coefficient is zeta=0.011 m_s^4/T, growing at low temperature T until the phonon fluid description stops making sense. Our results are relevant to study the rotational properties of a compact star formed by CFL quark matter.Comment: 19 pages, 2 figures; one reference added, version to be published in JCA

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 $1/p_F$ 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 $g$ 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

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding

Meson Exchange Effect on Color Superconductivity

We investigate the effects of pion and gluon exchanges on the formation of two-flavor color superconductivity at moderate density, $\mu <1 GeV$. The chiral quark model proposed by Manohar and Georgi containing pions as well as gluons is employed to show that the pion exchange reduces substantially the value of the superconducting gap gotten with the gluon exchange only. It turns out that the pion exchanges produce a repulsion between quark-quark pair in a spin and isospin singlet state. We suggest that the phase consisiting of pions, gluons and quarks is one of the candidates of in-medium QCD phase at moderate density.Comment: 8 pages, 1 figure, minor correction

Bulk viscosity in the nonlinear and anharmonic regime of strange quark matter

The bulk viscosity of cold, dense three-flavor quark matter is studied as a function of temperature and the amplitude of density oscillations. The study is also extended to the case of two different types of anharmonic oscillations of density. We point several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. We also find that, in most regions of the parameter space, with the exception of the case of a very large amplitude of density oscillations (i.e. 10% and above), nonlinear effects and anharmonicity have a small effect on the interplay of the nonleptonic and semileptonic processes in the bulk viscosity.Comment: 14 pages, 6 figures; v2: Appendix B is omitted, a few new discussions added and some new references adde