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Kenji Fukushima

Publications and source records attributed to Kenji Fukushima.

At least 145 records · Page 8Linked to original sources
arXiv2008

Initial energy density and gluon distribution from the Glasma in heavy-ion collisions

We estimate the energy density and the gluon distribution associated with the classical fields describing the early-time dynamics of the heavy-ion collisions. We first decompose the energy density into the momentum components exactly in the McLerran-Venugopalan model, with the use of the Wilson line correlators. Then we evolve the energy density with the free-field equation, which is justified by the dominance of the ultraviolet modes near the collision point. We also discuss the improvement with inclusion of nonlinear terms into the time evolution. Our numerical results at RHIC energy are fairly consistent with the empirical values.

hep-ph↗
arXiv2008

Two-Gluon Production and Longitudinal Correlations in the Color Glass Condensate

We derive an analytical expression for the two-gluon production in the pA (light-heavy) collisions, and focus specifically on the rapidity dependent part. We approximate the gauge field from the heavy target as the Color Glass Condensate which interacts with the light projectile whose source density allows for a perturbative expansion. We discuss the longitudinal correlations of produced particles. Our calculation goes in part beyond the eikonal limit for the emitted gluons so that we can retain the exponential terms with respect to the rapidity difference. Our expression can thus describe the short-range correlations as well as the long-range ones for which our formula is reduced to the known expression. In a special case of two high-pt gluons in the back-to-back kinematics we find that dependence on the rapidity separation is only moderate even in the diagrammatically connected part.

hep-ph↗
arXiv2008

The Chiral Magnetic Effect

Topological charge changing transitions can induce chirality in the quark-gluon plasma by the axial anomaly. We study the equilibrium response of the quark-gluon plasma in such a situation to an external magnetic field. To mimic the effect of the topological charge changing transitions we will introduce a chiral chemical potential. We will show that an electromagnetic current is generated along the magnetic field. This is the Chiral Magnetic Effect. We compute the magnitude of this current as a function of magnetic field, chirality, temperature, and baryon chemical potential.

hep-ph↗
arXiv2008

Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the Polyakov loop

We present extensive studies on hot and dense quark matter with two light and one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop (so-called PNJL model). First we discuss prescription dependence in choosing the Polyakov loop effective potential and propose a simple and rather sensible ansatz. We look over quantitative comparison to the lattice measurement to confirm that the model captures thermodynamic properties correctly. We then analyze the phase structure with changing the temperature, quark chemical potential, quark masses, and coupling constants. We particularly investigate how the effective U_A(1) restoration and the induced vector-channel interaction at finite density would affect the QCD critical point.

hep-ph↗
arXiv2008

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential μfor a given gauge configuration on the finite-volume lattice. First, we elaborate the Banks-Casher relations in the complex plane extended for the diquark condensate as well as the chiral condensate to relate the eigenvalue spectral density to the physical observable. Next, we evaluate the condensates and clarify the characteristic spectral change corresponding to the phase transition. Assuming the strong coupling limit, we exhibit the numerical results for a random gauge configuration in two-color QCD implemented by the staggered fermion formalism and confirm that our results agree well with the known estimate quantitatively. We then exploit our method in the case of the Wilson fermion formalism with two flavors. Also we elucidate the possibility of the Aoki (parity-flavor broken) phase and conclude from the point of view of the spectral density that the artificial pion condensation is not induced by the density effect in strong-coupling two-color QCD.

hep-ph↗
arXiv2008

Chiral Symmetry and Heavy-Ion Collisions

I revisit the phase structure of hot and dense matter out of quarks and gluons with some historical consideration on the color deconfinement and chiral phase transitions. My goal is to make clear which part of the QCD phase diagram is under theoretical control and which part is not. I demonstrate that an uncommon but logically possible scenario other than the standard phase diagram cannot be ruled out. My emphasis is on the concern that one should correctly understand what kind of phenomenon occurs associated with the phase boundary line on the diagram. It is not quite obvious, in particular, where chiral symmetry restoration plays a phenomenological role in the temperature and baryon density plane except at the QCD (chiral) critical point.

hep-ph↗
arXiv2008

Randomness in infinitesimal extent in the McLerran-Venugopalan model

We study discrepancy between the analytical definition and the numerical implementation of the McLerran-Venugopalan (MV) model. The infinitesimal extent of a fast-moving nucleus should retain longitudinal randomness in the color source distribution even when the longitudinal extent approximates zero due to the Lorentz contraction, which is properly taken into account in the analytical treatment. We point out that the longitudinal randomness is lost in numerical simulations because of lack of the path-ordering of the Wilson line along the longitudinal direction. We quantitatively investigate how much the results with and without longitudinal randomness differ from each other. We finally mention that the discrepancy could be absorbed in a choice of the model parameter in the physical unit, and nevertheless, it is important for a full theory approach.

hep-ph↗
arXiv2007

Erratum: Initial fields and instability in the classical model of the heavy-ion collision

We correct a mistake in the analytical expression for the energy density given in Phys. Rev. C76, 021902 (2007) [arXiv:0704.3625 [hep-ph]]. The expression should be multiplied by 16. One question then arises; how could it be possible to explain this difference between the analytical and numerical results in the same model if both are correct? We find a subtle problem in the treatment of the randomness of the color source along the longitudinal direction and the treatment of the longitudinal extent of the color source.

hep-ph↗
arXiv2007

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters Delta_1, Delta_2, and Delta_3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic field B that can penetrate the color superconducting medium. Without applying electric and color neutrality we find Delta_2 \approx Delta_3 >> Delta_1 for 2 e B / mu_q^2, where e is the modified electromagnetic coupling constant and mu_q is one third of the baryon chemical potential. Because the average Fermi surface for each pairing is affected by taking into account neutrality, the gap structure changes drastically in this case; we find Delta_1 >> Delta_2 \approx Delta_3 for 2 e B > mu_q^2. We point out that the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure Delta_1 \approx Delta_2 \approx Delta_3 at zero magnetic field.

hep-ph↗
arXiv2007

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.

hep-ph↗
arXiv2007

Initial fields and instability in the classical model of the heavy-ion collision

Color Glass Condensate (CGC) provides a classical description of dense gluon matter at high energies. Using the McLerran-Venugopalan (MV) model we calculate the initial energy density ε(τ) in the early stage of the relativistic nucleus-nucleus collision. Our analytical formula reproduces the quantitative results from lattice discretized simulations and leads to an estimate ε(τ=0.1fm)=40-50GeV/fm^3 in the Au-Au collision at RHIC energy. We then formulate instability with respect to soft fluctuations that violate boost invariance inherent to hard CGC backgrounds. We find unstable modes arising as a result of ensemble average over the initial CGC fields.

hep-ph↗
arXiv2007

Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter

We explore the phase structure of two-color and two-flavor QCD in the space of the quark chemical potential μ_q and the isospin chemical potential μ_I. Using a mean-field model we calculate the chiral and diquark condensates, σand Δ, self-consistently. In weak coupling and in the chiral limit, we confirm the interval of the isospin chemical potential, 0.71Δ_0<μ_I<0.75Δ_0, in which a single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic superfluidity and normal quark matter. The LOFF window becomes slightly wider at high density. For stronger coupling with nonzero quark mass, which is relevant to currently available numerical simulations in lattice two-color QCD, the single plane-wave LOFF phase appears only at sufficiently high density. The prediction obtained for the LOFF region could be tested with lattice since we can prove that the present system is free from the fermion sign problem. We draw the energy landscape on which local minima corresponding to the isotropic superfluid phase and the LOFF phase and a local maximum corresponding to the gapless phase are manifest. Our results clearly illustrate the path from the the unstable gapless phase down to the LOFF phase.

hep-ph↗
arXiv2007

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

We argue 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.

hep-ph↗
arXiv2007

Initial Singularity of the Little Bang

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.

hep-ph↗
arXiv2006

A description of the target wave-function encoded in the source terms

We argue that the gauge invariant source terms in the formalism of the Color Glass Condensate (CGC) should properly describe the target wave-function if the microscopic structure is concerned in the regime where the parton distribution is not quite dense. The quantum property of color charge density is incorporated in the quantum weight function defined with the source terms. We sketch that the logarithmic source terms encompass a meaningful picture of the microscopic structure of the target wave-function.

hep-ph↗
arXiv2006

Instability of a gapless color superconductor with respect to inhomogeneous fluctuations

We systematically apply density functional theory to determine the kind of inhomogeneities that spontaneously develop in a homogeneous gapless phase of neutral two-flavor superfluid quark matter. We consider inhomogeneities in the quark and electron densities and in the phases and amplitude of the order parameter. These inhomogeneities are expected to lead the gapless phase to a BCS-normal coexisting phase, a Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state with phase oscillations alone, and a LOFF state with amplitude oscillations. We find that which of them the homogeneous system tends towards depends sensitively on the chemical potential separation between up and down quarks and the gradient energies.

hep-ph↗
arXiv2006

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

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.

hep-ph↗