Kenji Fukushima

Initial singularity of the little bang

Abstract The Color Glass Condensate (CGC) predicts the form of the nuclear wavefunction in QCD at very small x . Using this, we compute the wavefunction for the collision of two nuclei, infinitesimally in the forward light cone. We show that the Wigner transformation of this wavefunction generates rapidity dependent fluctuations around the boost invariant classical solution which describe the glasma in the forward light cone.

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense quark matter using an effective model with four-Fermi interactions. We find that the gap parameters representing the predominant pairing between the different quark flavors show oscillatory behavior as a function of the magnetic field. We point out that due to electric and color neutrality constraints the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure at a zero magnetic field.

Analytical and numerical evaluation of the Debye and Meissner masses in dense neutral three-flavor quark matter

We calculate the Debye and Meissner masses and investigate chromomagnetic instability associated with the gapless color superconducting phase changing the strange quark mass M{sub s} and the temperature T. Based on the analytical study, we develop a computational procedure to derive the screening masses numerically from curvatures of the thermodynamic potential. When the temperature is zero, from our numerical results for the Meissner masses, we find that instability occurs for A{sub 1} and A{sub 2} gluons entirely in the gapless color-flavor locked (gCFL) phase, while the Meissner masses are real for A{sub 4}, A{sub 5}, A{sub 6}, and A{sub 7} until M{sub s} exceeds a certain value that is larger than the gCFL onset. We then handle mixing between color-diagonal gluons A{sub 3}, A{sub 8}, and photon A{sub {gamma}}, and clarify that, among three eigenvalues of the mass squared matrix, one remains positive, one is always zero because of an unbroken U(1){sub Q-}t{sub ilde} symmetry, and one exhibits chromomagnetic instability in the gCFL region. We also examine the temperature effects that bring modifications into the Meissner masses. The instability found at large M{sub s} for A{sub 4}, A{sub 5}, A{sub 6}, and A{sub 7} persists at finite T into themorexa0» u-quark color superconducting (uSC) phase which has u-d and s-u but no d-s quark pairing and also into the two-flavor color superconducting (2SC) phase characterized by u-d quark pairing only. The A{sub 1} and A{sub 2} instability also goes into the uSC phase, but the 2SC phase has no instability for A{sub 1}, A{sub 2}, and A{sub 3}. We map the unstable region for each gluon onto the phase diagram as a function of M{sub s} and T.«xa0less

Model study of the sign problem in the mean-field approximation

We consider the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from quantum chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle point of which we can estimate the expectation value of the Polyakov loop.

Characterizing the Larkin-Ovchinnikov-Fulde-Ferrel phase induced by the chromomagnetic instability

We discuss possible destinations from the chromomagnetic instability in color superconductors with Fermi surface mismatch {delta}{mu}. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials A{sub {alpha}} which are interpreted as the net momenta q of pairing in the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) phase. When 1/{radical}(2)<{delta}{mu}/{delta}<1 where {delta} is the gap energy, the effective potential suggests that the instability leads to a LOFF-like state which is characterized by color-rotated phase oscillations with small q. In the vicinity of {delta}{mu}/{delta}=1/{radical}(2) the magnitude of q continuously increases from zero as the effective potential has negative larger curvature at vanishing A{sub {alpha}} that is the Meissner mass squared. In the gapless 2SC (g2SC) phase, in contrast, the effective potential has a minimum at gA{sub {alpha}}{approx}{delta}{mu}{approx}{delta} even when the negative Meissner mass squared is infinitesimally small. Our results imply that the chromomagnetic instability found in the gapless phase drives the system toward the LOFF state with q{approx}{delta}{mu}.

Light projectile scattering off the color glass condensate

We systematically compute the Gaussian average of Wilson lines inherent in the Color Glass Condensate, which provides useful formulae for evaluation of the scattering amplitude in the collision of a light projectile and a heavy target.

Gauge-invariant source terms in QCD

Abstract We discuss how to implement the source terms in Quantum Chromodynamics (QCD) respecting gauge invariance and noncommutativity of color charge density operators. We start with decomposing the generating functional of QCD into constituents projected to have specified color charge density. We demonstrate that such a projection leads to the gauge-invariant source terms consisting of a naive form accompanied by the density of states which cancels the gauge dependence. We then illustrate that this form is equivalently rewritten into a manifestly gauge-invariant expression in terms of the Wilson line. We confirm that noncommutativity of color charge density operators is fulfilled in both representations of the source terms. We point out that our results are useful particularly to consider the problems of the quantum evolution in high energy QCD.

Deriving the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equation with classical and quantum source terms

Abstract We discuss the high-energy evolution equation in quantum chromodynamics (QCD) in the framework of the color glass condensate. We rewrite the generating functional of QCD with the color glass condensate into a representation with the density of states and a simple eikonal coupling. In this representation we introduce an auxiliary variable which is identified as the quantum color charge density consistent with non-commutativity in the operator formalism. We revisit the derivation of the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner (JIMWLK) equation to clarify how the non-commutative nature among the color charge density operators can be disregarded in the regime where the gluon density is high.

Phase Structure and Instability Problem in Color Superconductivity

We address the phase structure of color superconducting quark matter at high quark density. Under the electric and color neutrality conditions there appear various phases as a result of the Fermi surface mismatch among different quark flavors induced by finite strange quark mass; the color-flavor locked (CFL) phase where quarks are all energy gapped, the u-quark superconducting (uSC) phase where u-quarks are paired with either d- or s-quarks, the d-quark superconducting (dSC) phase that is the d-quark analogue of the uSC phase, the two-flavor superconducting (2SC) phase where u- and d-quarks are paired, and the unpaired quark matter (UQM) that is normal quark matter without pairing. Besides these possibilities, when the Fermi surface mismatch is large enough to surpass the gap energy, the gapless superconducting phases are expected. We focus our discussion on the chromomagnetic instability problem related to the gapless CFL (gCFL) onset and explore the instability regions on the phase diagram as a function of the temperature and the quark chemical potential. We sketch how to reach stable physical states inside the instability regions.

Phase Diagram and Instability of Dense Neutral Three‐Flavor Quark Matter

We address the phase structure of color superconducting quark matter at high quark density. Under the electric and color neutrality conditions there appear various phases as a result of the Fermi surface mismatch among different quark flavors induced by finite strange quark mass; the color‐flavor locked (CFL) phase, the u‐quark superconducting (uSC) phase, the d‐quark superconducting (dSC) phase, the two‐flavor superconducting (2SC) phase, and the unpaired quark matter (UQM). Besides, when the Fermi surface mismatch is large enough to surpass the gap energy, the gapless superconducting phase is expected. We discuss the chromomagnetic instability problem and explore the instability regions on the phase diagram.