Yoshimasa Hidaka

Quarkyonic Chiral Spirals

Abstract We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as ∼ 1 / ( p → 2 ) 2 . We assume that the number of colors, N c , is large, and that the quark chemical potential, μ , is much larger than renormalization mass scale, Λ QCD . To leading order in 1 / N c and Λ QCD / μ , a gauge theory with N f flavors of massless quarks in 3 + 1 dimensions naturally reduces to a gauge theory in 1 + 1 dimensions, with an enlarged flavor symmetry of SU ( 2 N f ) . Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z , as 〈 ψ ¯ exp ( 2 i μ z γ 0 γ z ) ψ 〉 . Following Schon and Thies, we term this two-dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess–Zumino–Novikov–Witten model in 1 + 1 dimensions then generate strong infrared effects in 3 + 1 dimensions.

How wide is the transition to deconfinement

Pure SU(3) glue theories exhibit a deconfining phase transition at a nonzero temperature, T{sub c}. Using lattice measurements of the pressure, we develop a simple matrix model to describe the transition region, when T{>=}T{sub c}. This model, which involves three parameters, is used to compute the behavior of the t Hooft loop. There is a Higgs phase in this region, where off-diagonal color modes are heavy, and diagonal modes are light. Lattice measurements of the latter suggest that the transition region is narrow, extending only to about {approx}1.2T{sub c}. This is in stark contrast to lattice measurements of the renormalized Polyakov loop, which indicates a much wider width. The possible implications for the differences in heavy ion collisions between the Relativistic Heavy Ion Collider and the LHC are discussed.

Small shear viscosity in the semiquark gluon plasma

At nonzero temperature in QCD, about the deconfining phase transition there is a semiquark gluon plasma (semi-QGP), where the expectation value of the (renormalized) Polyakov loop is less than one. This can be modeled by a semiclassical expansion about a constant field for the vector potential, A{sub 0}, which is diagonal in color. We compute the shear viscosity in the semi-QGP by using the Boltzmann equation in the presence of this background field. To leading, logarithmic order in weak coupling, the dominant diagrams are given by the usual scattering processes of 2{yields}2 particles. For simplicity we also assume that both the number of colors and flavors are large. Near the critical temperature T{sub c}, where the expectation value of the Polyakov loop is small, the overall density of colored fields decreases according to their color representation, with the density of quarks vanishes linearly with the loop, and that of gluons, quadratically. This decrease in the overall density dominates changes in the transport cross section. As a result, relative to that in the perturbative QGP, near T{sub c} the shear viscosity in the semi-QGP is suppressed by two powers of the Polyakov loop. In a semiclassical expansion, the suppression of coloredmorexa0» fields depends only upon which color representation they lie in, and not upon their mass. That light and heavy quarks are suppressed in a common manner may help to explain the behavior of charm quarks at RHIC.«xa0less

Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop

We compute the simplest hard thermal loops for a spatial t Hooft loop in the deconfined phase of a SU(N) gauge theory. We expand to quadratic order about a constant background field A{sub 0}=Q/g, where Q is a diagonal, color matrix and g is the gauge coupling constant. We analyze the problem in sufficient generality that the techniques developed can be applied to compute transport properties in a semi-quark gluon plasma. Notably, computations are done using the double line notation at finite N. The quark self-energy is a Q-dependent thermal mass squared {approx}g{sup 2}T{sup 2}, where T is the temperature, times the same hard thermal loop as at Q=0. The gluon self-energy involves two pieces: a Q-dependent Debye mass squared, {approx}g{sup 2}T{sup 2}, times the same hard thermal loop as for Q=0, plus a new hard thermal loop {approx}g{sup 2}T{sup 3}, due to the color electric field generated by a spatial t Hooft loop.

Zero point energy of renormalized Wilson loops

The quark-antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.

The Dichotomous Nucleon: Some Radical Conjectures for the Large Nc Limit

Abstract We discuss some problems with the large N c approximation for nucleons which arise if the axial coupling of the nucleon to pions is large, g A ∼ N c . While g A ∼ N c in non-relativistic quark and Skyrme models, it has been suggested that Skyrmions may collapse to a small size, r ∼ 1 / f π ∼ Λ QCD − 1 / N c . (This is also the typical scale over which the string vertex moves in a string vertex model of the baryon.) We concentrate on the case of two flavors, where we suggest that to construct a nucleon with a small axial coupling, that most quarks are bound into colored diquark pairs, which have zero spin and isospin. For odd N c , this leaves one unpaired quark, which carries the spin and isospin of the nucleon. If the unpaired quark is in a spatial wavefunction orthogonal to the wavefunctions of the scalar diquarks, then up to logarithms of N c , the unpaired quark only costs an energy ∼ Λ QCD . This naturally gives g A ∼ 1 and has other attractive features. In nature, the wavefunctions of the paired and unpaired quarks might only be approximately orthogonal; then g A depends weakly upon N c . This dichotomy in wave functions could arise if the unpaired quark orbits at a size which is parametrically large in comparison to that of the diquarks. We discuss possible tests of these ideas from numerical simulations on the lattice, for two flavors and three and five colors; the extension of our ideas to more than three or more flavors is not obvious, though.

Renormalized linear kinetic theory as derived from quantum field theory: A novel diagrammatic method for computing transport coefficients

We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has the form of a linearized kinetic equation as usual, but our formalism enables us to incorporate higher-order corrections of the coupling systematically for the first time. Furthermore, it is clarified that the higher-order corrections are nicely summarized into that of the vertex function, spectral function, and collision term. We identify the diagrams up to the next-to-next-leading-order corrections in the weak coupling expansion of {phi}{sup 4} theory, which is a difficult task in kinetic approaches and other diagrammatic methods.

Spectral function of a fermion coupled with a massive vector boson at finite temperature in a gauge invariant formalism

We investigate spectral properties of a fermion coupled with a massive gauge boson with a mass m at finite temperature (T) in the perturbation theory. The massive gauge boson is introduced as a U(1) gauge boson in the Stueckelberg formalism with a gauge parameter {alpha}. We find that the fermion spectral function has a three-peak structure for T{approx}m irrespective of the choice of the gauge parameter, while it tends to have one faint peak at the origin and two peaks corresponding to the normal fermion and antiplasmino excitations familiar in QED in the hard thermal loop approximation for T>>m. We show that our formalism successfully describe the fermion spectral function in the whole T region with the correct high-T limit except for the faint peak at the origin, although some care is needed for choice of the gauge parameter for T>>m. We clarify that for T{approx}m, the fermion pole is almost independent of the gauge parameter in the one-loop order, while for T>>m, the one-loop analysis is valid only for {alpha}<<1/g where g is the fermion-boson coupling constant, implying that the one-loop analysis cannot be valid for large gauge parameters as in the unitary gauge.

Fast Vacuum Decay into Quark Pairs in Strong Color Electric and Magnetic Fields

We study quark‐pair creations in strong color electomagnetic fields. We point out that, for massless quarks, the vacuum persistency probability per unit space‐time volume is zero, i.e., the quark‐pair creation rate w is infinite, in general homogeneous color electromagnetic fields, while it is finite when the color magnetic field is absent. We find that the contribution from the lowest Landau level (LLL) dominates this phenomenon. With an effective theory of the LLL projection, we also discuss dynamics of the vacuum decay, taking into account the back reaction of pair creations.