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Kenji Fukushima

Publications and source records attributed to Kenji Fukushima.

At least 163 records · Page 9Linked to original sources
arXiv2006

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 $δμ$. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials $A_α$ which are interpreted as the net momenta $q$ of pairing in the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) phase. When $1/\sqrt{2}<δμ/Δ<1$ where $Δ$ 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 $δμ/Δ=1/\sqrt{2}$ the magnitude of $q$ continuously increases from zero as the effective potential has negative larger curvature at vanishing $A_α$ that is the Meissner mass squared. In the gapless 2SC (g2SC) phase, in contrast, the effective potential has a minimum at $gA_α\simδμ\simΔ$ 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 $q\simδμ$.

hep-ph↗
arXiv2006

Gauge invariant source terms in QCD

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.

hep-ph↗
arXiv2005

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.

hep-ph↗
arXiv2005

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 $M_s$ 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 $A_1$ and $A_2$ gluons entirely in the gapless color-flavor locked (gCFL) phase, while the Meissner masses are real for $A_4$, $A_5$, $A_6$, and $A_7$ until $M_s$ exceeds a certain value that is larger than the gCFL onset. We then handle mixing between color-diagonal gluons $A_3$, $A_8$, and photon $A_γ$, and clarify that, among three eigenvalues of the mass squared matrix, one remains positive, one is always zero because of an unbroken $U(1)_\tilde{Q}$ 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 $M_s$ for $A_4$, $A_5$, $A_6$, and $A_7$ persists at finite $T$ into the $u$-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 $A_1$ and $A_2$ instability also goes into the uSC phase, but the 2SC phase has no instability for $A_1$, $A_2$, and $A_3$. We map the unstable region for each gluon onto the phase diagram as a function of $M_s$ and $T$.

hep-ph↗
arXiv2005

Collective excitations in a superfluid of color-flavor locked quark matter

We investigate collective excitations coupled with baryon density in a system of massless three-flavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we derive the spectra both for the normal and color-flavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, when the excitation energy, $ω$, is smaller than the threshold given by twice the pairing gap $Δ$ ($ω<2Δ$), a phonon corresponding to fluctuations in the U(1) phase of $Δ$ appears as a sharp peak in the particle-particle ($H$) channel. We reproduce the property known from low energy effective theories that this mode propagates at a velocity of $v_H=1/\sqrt{3}$ in the low momentum regime; the decay constant $f_H$ in the NJL model is identical with the QCD result in the mean-field approximation. We also find that as the momentum of the phonon increases, the excitation energy goes up and asymptotically approaches $ω=2Δ$. Above the threshold for pair excitations ($ω>2Δ$), zero sound manifests itself in the vector channel. By locating the zero sound pole of the vector propagator in the complex energy plane we investigate the attenuation and energy dispersion relation of zero sound. In the long wavelength limit, the phonon mode has its spectral weight in the $H$ channel alone, while the spectral function vanishes in the vector channel. We finally extend our study to the case of nonzero temperature.

hep-ph↗
arXiv2004

Deconfinement and Chiral Restoration in Hot and Dense Matter

We propose a picture that the chiral phase transition at zero quark mass and the deconfinement transition at infinite quark mass are continuously connected. This gives a simple interpretation on the coincidence of the pseudo-critical temperatures observed in lattice QCD. We discuss a possible dynamical mechanism behind the simultaneous crossovers and show the results in a model study.

hep-lat↗
arXiv2004

Quark description of the Nambu-Goldstone bosons in the color-flavor locked phase

We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative difference between the flavor octet pions and the singlet phason. We propose a conjecture that superfluid H matter undergoes a crossover to a superconductor with tightly-bound diquarks, and then a crossover to superconducting matter with diquarks dissociated.

hep-ph↗
arXiv2004

Heating (Gapless) Color-Flavor Locked Quark Matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.

hep-ph↗
arXiv2004

Thermodynamics of strong coupling 2-color QCD with chiral and diquark condensates

2-color QCD (quantum chromodynamics with N_c=2) at finite temperature T and chemical potential μis revisited in the strong coupling limit on the lattice with staggered fermions. The phase structure in the space of T, μ, and the quark mass m is elucidated with the use of the mean field approximation and the 1/d expansion (d being the number of spatial dimensions). We put special emphasis on the interplay among the chiral condensate <\bar{q}q>, the diquark condensate , and the quark density in the T-μ-m space. Simple analytic formulae are also derived without assuming μnor m being small. Qualitative comparisons are made between our results and those of recent Monte-Carlo simulations in 2-color QCD.

hep-ph↗
arXiv2004

Linking the chiral and deconfinement phase transitions

We show that the electric glueball becomes critical at the end-point of the deconfinement phase transition in finite temperature QCD. Based on this observation and existing lattice data, we argue that the chiral phase transition at a zero quark mass and the deconfinement phase transition at an infinite quark mass are continuously connected by the glueball-sigma mixing.

hep-ph↗
arXiv2004

Chiral effective model with the Polyakov loop

We discuss how the simultaneous crossovers of deconfinement and chiral restoration can be realized. We propose a dynamical mechanism assuming that the effective potential gives a finite value of the chiral condensate if the Polyakov loop vanishes. Using a simple model, we demonstrate that our idea works well for small quark mass, though there should be further constraints to reach the perfect locking of two phenomena.

hep-ph↗
arXiv2003

Order parameters with higher dimensionful composite fields

We discuss the possibility of the spontaneous symmetry breaking characterized by order parameters with higher dimensionful composite fields. By analyzing general Ginzburg-Landau potential for a complex scalar field ϕ=ϕ_1 + i ϕ_2 with O(2) symmetry, we demonstrate that a phase characterized by < ϕ_1^2 - ϕ_2^2 > \neq 0 with < ϕ_1 >=< ϕ_2 >=0 is realized in a certain parameter region. To clarify the driving force to favor this phase, we study the O(2) ϕ^6 theory in three dimensions.

hep-th↗
arXiv2003

Toward understanding the lattice QCD results from the strong coupling analysis

This is a review of strong coupling approaches to grasp the nature of the phase transition in finite temperature and density QCD. We commence with classics of the center symmetry and the Polyakov loop in pure gauge theories. The effective action derived in the strong coupling limit gives qualitatively plausible behavior for the deconfinement transition at finite temperature. We can apply the strong coupling analysis to describe the chiral phase transition with the help of large dimensional expansion. In order to make this article as self-contained as possible, we elucidate the computational procedure and its physical meaning in detail. Also the relation between the Polyakov loop behavior and the chiral dynamics, the phase structure of two-color QCD, and future possibilities to be pursued in the strong coupling analysis are discussed.

hep-ph↗
arXiv2003

On the nature of thermal QCD phase transitions

We argue that the chiral phase transition and the deconfinement phase transition in finite temperature QCD are just different limits of a single crossover phase transition driven by the lightest scalar field which is a mixture of the glueball and the sigma meson. The key mechanism, the level repulsion between the sigma and the glueball, gives not only a unified description of the finite temperature phase transitions, but also a consistent characterization of the entire QCD phase diagram in the temperature-quark mass plane.

hep-ph↗
arXiv2003

Relation between color-deconfinement and chiral restoration

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.

hep-ph↗
arXiv2003

Thermodynamic limit of the canonical partition function with respect to the quark number in QCD

We investigate QCD in the canonical ensemble with respect to the quark number. We reveal that the canonical description in which the quark number is fixed would be reduced to the grand canonical description under the thermodynamic limit. Since the grand canonical ensemble contains fluctuations of the quark number, the idea of the canonical ensemble is of no use for the purpose of defining order parameters for the deconfinement transition. We clarify the origin of such reduction and propose an idea to define the order parameter. The Monte-Carlo simulation by means of the spin system, which is an effective model of QCD at finite temperature, shows prosperous behaviors though the results suffer from the severe statistical error due to the sign problem.

hep-ph↗
arXiv2003

Relation between the Polyakov loop and the chiral order parameter at strong coupling

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using the Gocksch-Ogilvie model with fundamental or adjoint quarks. The model is based on the double expansion of strong coupling and large dimensionality on the lattice. In an analytic way with the mean field approximation employed, we show that the confined phase must be accompanied by the spontaneous breaking of the chiral symmetry for both fundamental and adjoint quarks. Then we proceed to numerical analysis to look into the coupled dynamics of the Polyakov loop and the chiral order parameter. In the case of fundamental quarks, the pseudo-critical temperature inferred from the Polyakov loop behavior turns out to coincide with the pseudo-critical temperature of the chiral phase transition. We discuss the physical implication of the coincidence of the pseudo-critical temperatures in two extreme cases; one is the deconfinement dominance and the other is the chiral dominance. As for adjoint quarks, the deconfinement transition of first order persists and the chiral phase transition occurs distinctly at higher temperature than the deconfinement transition does. The present model study gives us a plausible picture to understand the results from the lattice QCD and aQCD simulations.

hep-ph↗