High Density Effective Theory Research Articles

Chiral kinetic theory from effective field theory revisited

We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the O(1/μ) expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.

Symmetry energy in cold dense matter

We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.

Spontaneous superfluid current generation in the kaon condensed color flavor locked phase at nonzero strange quark mass

We find that for a large enough strange quark mass, ${m}_{s}^{2}/4\ensuremath{\mu}\ensuremath{\Delta}g2/3(1\ensuremath{-}0.023)$ ($\ensuremath{\mu}$ is the quark number chemical potential, $\ensuremath{\Delta}$ is the superconducting gap), the kaon condensed color flavor locked (CFL) phase of asymptotically dense strongly interacting 3 flavor quark matter is unstable with respect to spontaneous generation of currents of Nambu Goldstone bosons due to spontaneous breaking of baryon number symmetry and hypercharge symmetry in the $\mathrm{CFL}{K}^{0}$ ground state. The total baryon and hypercharge currents vanish in the ground state. We find that $\mathrm{CFL}{K}^{0}$ and the new state are separated by a first order phase transition. The result is derived in the mean field approximation of high density effective theory with electromagnetic interactions turned off.

Massive high density effective theory

I derive an effective theory for dense, cold, and massive quark matter. To this end, I employ a general effective action formalism where antiquarks and quarks far from the Fermi surface, as well as hard gluons, are integrated out explicitly. I show that the resulting effective action depends crucially on the projectors used to separate quarks from antiquarks. If one neglects the quark masses in these projectors, the Feynman rules of the effective theory involve quark mass insertions which connect quark with antiquark propagators. Including the quark masses into these projectors, mass insertions do not appear and the Feynman rules are identical to those found in the zero-mass limit.

Effective Theory of Color Superconductivity

We briefly review an effective theory of QCD at high baryon density, describing the relevant modes near the Fermi surface. The high density effective theory has properties of reparametrization invariance and gauge invariance, maintained in a subtle way. It also has a positive measure, allowing lattice simulations at high baryon density. We then apply it to gapless superconductors and discuss recent proposals to resolve the magnetic instability of gapless superconductivity.

Non-Fermi liquid effects in QCD at high density

We study non-Fermi liquid effects due to the exchange of unscreened magnetic gluons in high density QCD by using an effective field theory. A one-loop calculation gives the well known result that magnetic gluons lead to a logarithmic enhancement in the fermion self energy near the Fermi surface. The self energy is of the form $\Sigma(\omega)\sim \omega\gamma\log(\omega)$, where $\omega$ is the energy of the fermion, $\gamma=O(g^2)$, and $g$ is the coupling constant. Using an analysis of the Dyson-Schwinger equations we show that, in the weak coupling limit, this result is not modified by higher order corrections even in the regime where the logarithm is large, $\gamma\log(\omega)\sim 1$. We also show that this result is consistent with the renormalization group equation in the high density effective field theory.

High density effective theory confronts the Fermi liquid

The high density effective theory recently introduced by Hong and Hsu to describe ultradense relativistic fermionic matter is used to calculate the tree-level forward scattering amplitude between two particles at the Fermi surface. While the direct term correctly reproduces that of the underlying gauge theory, the exchange term has the wrong sign. The physical consequences are discussed in the context of Landau's theoretical description of the Fermi liquid.

High Density Effective Theory of QCD

We discuss the salient features of the high density effective theory (HDET) of QCD, elaborating more on the matching for vector-vector correlators and axial-vector-vector correlators, which are related to screening mass and axial anomaly, respectively. We then apply HDET to discuss various color-superconducting phases of dense QCD. We also review a recent proposal to solve the sign problem in dense fermionic matter, using the positivity property of HDET. Positivity of HDET allows us to establish rigorous inequalities in QCD at asymptotic density and to show vector symmetry except the fermion number is not spontaneously broken at asymptotic density.

Hard loops, soft loops, and high density effective field theory

We study several issues related to the use of effective field theories in QCD at large baryon density. We show that the power counting is complicated by the appearance of two scales inside loop integrals. Hard dense loops involve the large scale μ 2 and lead to phenomena such as screening and damping at the scale gμ. Soft loops only involve small scales and lead to superfluidity and non-Fermi liquid behavior at exponentially small scales. Four-fermion operators in the effective theory are suppressed by powers of 1/ μ, but they get enhanced by hard loops. As a consequence their contribution to the pairing gap is only suppressed by powers of the coupling constant, and not powers of 1/ μ. We determine the coefficients of four-fermion operators in the effective theory by matching quark–quark scattering amplitudes. Finally, we introduce a perturbative scheme for computing corrections to the gap parameter in the superfluid phase.

Aspects of the color flavor locking phase of QCD in the Nambu–Jona-Lasinio approximation

We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\mu)^2 after checking that its numerical validity is very good already at first order.

Phonons and gluons in the crystalline color superconducting phase of QCD

The High Density Effective Theory formalism is used to calculate the low energy properties of the phonons and gluons in the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD. The effective phonon Lagrangian for the cubic crystal structure, which is favored according to a recent study, depends, at the second order in the derivatives, on three parameters which we calculate in this paper. We also compute for soft momenta the effective lagrangian for the gluons of the unbroken SU(2)_c group, both for a single plane wave structure and for the cube. In both cases the Meissner gluon mass vanishes as in the case of complete isotropy; on the other hand there is a partial Debye screening due to the existence of blocking regions on the Fermi spheres. For the single plane wave structure the gluon dielectric tensor is non isotropic, while it is isotropic for the cubic crystal, in spite of the intrinsic anisotropy of the structure.

Massive quark effects in two flavor color superconductors

The high density effective theory formalism (HDET) is employed to describe high density QCD with two massive flavors (2SC). The gap equation is derived and explicitly solved for the gap parameter. The parameters associated to the pseudo Nambu–Goldstone boson of U(1)A are evaluated in the limit μ→∞ and m/μ fixed. In particular, we find for the velocity of the NG boson the relation v2=μ12−m12μ22−m22/3μ1μ2.

Positivity of high density effective theory

We show that the effective field theory of low energy modes in dense QCD has positive Euclidean path integral measure. The complexity of the measure of QCD at finite chemical potential can be ascribed to modes which are irrelevant to the dynamics at sufficiently high density. Rigorous inequalities follow at asymptotic density. Lattice simulation of dense QCD should be possible using the quark determinant calculated in the effective theory.

Crystalline color superconductivity and high density effective theory

Crystalline color superconductivity and high density effective theory

Effective description of QCD at very high densities

We describe the effective lagrangian approach to the color superconductivity. The effective description that arises if one considers only the leading terms in the expansion for very high densities is particularly simple. It is based on a lagrangian whose effective fermion fields are velocity-dependent; moreover strong interactions do not change quark velocity and the effective lagrangian does not contain spin matrices. All these features render the effective theory similar to the Heavy Quark Effective Theory, which is the limit of Quantum ChromoDynamics for infinite quark masses. For this reason one can refer to the effective lagrangian at high density as the High Density Effective Theory (HDET). In some cases HDET results in analytical, though approximate, relations that are particularly simple to handle. After a pedagogical introduction, several topics are considered. They include the treatment of the Color-Flavor-Locking and the 2SC model, with evaluation of the gap parameters by the Nambu-Gorkov equations, approximate dispersion laws for the gluons and calculations of the Nambu-Goldstone Bosons properties. We also discuss the effective lagrangian for the crystalline color superconductive (LOFF) phase and we give a description of the phonon field related to the breaking of the rotational and translational invariance. Finally a few astrophysical applications of color superconductivity are discussed.

Aspects of high density effective theory in QCD

We study an effective theory of QCD at high density in detail, including the finite temperature effects and the leading order correction in $1/\mu$ expansion. We investigate the Cooper pair gap equation and find that the color-flavor locking phase is energetically preferred at high density. We also find the color-superconducting phase transition occurs in dense quark matter when the chemical potential is larger than $250\pm 100~{\rm MeV}$ and the temperature is lower than 0.57 times the Cooper pair gap in the leading order in the hard-dense-loop approximation. The quark-neutrino four-Fermi coupling and the quark-axion coupling receive significant corrections in dense quark matter.