arXiv subjects

Takumi Iritani

Publications and source records attributed to Takumi Iritani.

69 records · Page 4Linked to original sources

arXiv2013

SU(3) lattice QCD study of the gluon propagator in maximally Abelian gauge: off-diagonal gluon mass generation and infrared Abelian dominance

We investigate gluon propagators and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \times$ U(1)$_8$ Landau gauge fixing in SU(3) lattice QCD. The Monte Carlo simulation is performed on $16^4$ at $β$=5.7, 5.8 and 6.0 and $32^4$ at $β=$5.8 and 6.0 at the quenched level. To calculate the propagators, we adopt a method to extract gauge fields from link-variables analytically in the SU(3) case. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\rm off} \simeq 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and the propagation is limited within a short range. On the other hand, the diagonal gluons behave as light vector bosons with $M_{\rm diag}\simeq 0.3 {\rm GeV} $ and the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function ${\rm exp}(-m_{\rm off} r)/r$ with $m_{\rm off} = 1.3 -1.4 {\rm GeV}$ for $r = 0.1- 0.8{\rm fm}$. This also indicates that the spectral function of off-diagonal gluons has the negative-value region.

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arXiv2012

Analytical derivation of gauge fields from link variables in SU(3) lattice QCD and its application in maximally Abelian gauge

In SU(3) lattice QCD, we improve a method to extract gauge fields from link variables analytically. With this method, we perform the first study on the effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. We investigate the propagator and the effective mass of the off-diagonal gluon field in the MA gauge with ${\rm U(1)}_3 \times {\rm U(1)}_8$ Landau gauge fixing in SU(3) quenched lattice QCD on $16^4$ at $β$=5.7, 5.8 and 6.0. The off-diagonal gluon component behaves as a massive vector boson with the approximate effective mass $M_{\rm off} = 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and its propagation is limited within a short range. We thus show the origin of infrared Abelian dominance in terms of short-range propagation of off-diagonal gluons. We also investigate the functional form of the off-diagonal gluon propagator. We find that the functional form is well described by the four-dimensional Euclidean Yukawa-type function ${\rm exp}\{-m_{\rm off} r\}/r$ with $m_{\rm off} = 1.3 -1.4 {\rm GeV}$ for $r = 0.1- 0.8{\rm fm}$. This also indicates that the spectral function has a negative region.

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arXiv2012

Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $β$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}} \simeq 1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$ for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region.

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arXiv2012

Stringy excitation and role of UV gluons in lattice QCD

Using SU(3) quenched lattice QCD, we study ground-state and low-lying even-parity excited-state potentials of quark-antiquark systems in terms of the gluon-momentum component in the Coulomb gauge. By introducing UV-cut in the gluon-momentum space, we investigate the "UV-gluon sensitivity" of the ground-state and excited-state potentials and the stringy excitation quantitatively. Even after cutting off high-momentum gluon component above 1.5GeV, the IR part of the ground-state potential is almost unchanged. On the other hand, the change of excited-state potential is more significant by the cut of UV-gluons. However, even after the removal of UV-gluons, the magnitude of the low-lying gluonic excitation remains to be of the order of 1GeV.

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arXiv2012

Dirac-mode expansion analysis for Polyakov loop

To clarify the relation between chiral symmetry breaking and color confinement, we investigate the Polyakov loop in terms of the Dirac eigenmodes in SU(3) lattice QCD. We analyze the low-lying (IR) and UV Dirac-mode contribution to the Polyakov loop, respectively, using the Dirac-mode expansion method. In the confined phase, the Polyakov loop $< L_P >$ remains almost zero and $Z_3$ center symmetry is thus unbroken, even after removing low-lying Dirac-modes, which are responsible to chiral symmetry breaking. In the confined phase, the Polyakov loop $< L_P >$ also remains almost zero by UV Dirac-modes cut. In addition to the confined phase, we analyze the Polyakov loop in the deconfined phase and its temperature dependence. The behavior of the Polyakov loop $< L_P >$ is found to be almost unchanged by the cut of low-lying or UV Dirac-modes in both confined and deconfined phases.

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arXiv2012

Lattice QCD analysis for Faddeev-Popov eigenmodes in terms of gluonic momentum components in the Coulomb gauge

We analyze the relation between Faddeev-Popov eigenmodes and gluon-momentum components in the Coulomb gauge using SU(3) lattice QCD. In the Coulomb gauge, the color-Coulomb energy is largely enhanced by near-zero Faddeev-Popov eigenmodes, which would lead to the confining potential. By the ultraviolet-momentum gluon cut, the color-Coulomb energy and the Faddeev-Popov spectrum are almost unchanged. In contrast to the ultraviolet insensitivity, the color-Coulomb energy and the Faddeev-Popov eigenmodes drastically change by infrared-momentum gluon cut. Without infrared gluons, the color-Coulomb energy tends to become non-confining, and near-zero Faddeev-Popov eigenmodes vanish. We also investigate the full FP eigenmodes, and find that infrared gluons widely influence both high and low Faddeev-Popov eigenmodes.

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arXiv2012

Gauge-Invariant Formalism with a Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking

Using the eigen-mode of the QCD Dirac operator $\Slash D=γ^μD^μ$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on $6^4$ at $β$=5.6. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the slope parameter corresponding to the string tension or the confinement force is almost unchanged. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the $Z_3$-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold for between confinement and chiral symmetry breaking in QCD.

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arXiv2012

Relevant Gluonic Momentum for Confinement and Gauge-Invariant Formalism with Dirac-mode Expansion

We investigate the relevant gluon-momentum region for confinement in lattice QCD on $16^4$ at $β$=5.7, 5.8 and 6.0, based on the Fourier expansion. We find that the string tension $σ$, i.e., the confining force, is almost unchanged even after removing the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, the confinement property originates from the low-momentum gluon component below 1.5GeV, which is the upper limit to contribute to $σ$. In the relevant region, smaller gluon momentum component is more important for confinement. Next, we develop a manifestly gauge-covariant expansion of the QCD operator such as the Wilson loop, using the eigen-mode of the QCD Dirac operator $γ^μD^μ$. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD on $6^4$ at $β$=5.6. As a remarkable fact, the confinement force is almost unchanged even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. This indicates that one-to-one correspondence does not hold for between confinement and chiral symmetry breaking in QCD.

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arXiv2011

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

We study quark-pair creations in strong color electromagnetic 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.

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arXiv2011

Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a possible gauge for the quark potential model

We investigate "instantaneous interquark potential", an interesting gauge-dependent quantity defined from the spatial correlator $<\mathrm{Tr} [U_4^\dagger(s)U_4(s')]>$ of the temporal link-variable $U_4$, in detail in generalized Landau gauge using SU(3) quenched lattice QCD. While the instantaneous potential has no linear part in the Landau gauge, in the Coulomb gauge, it is expressed by the Coulomb plus linear potential, where the slope is 2-3 times larger than the physical string tension, and the lowest energy state is considered to be a gluon-chain state. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and it approximately reproduces the physical interquark potential in a specific intermediate gauge, which we call "$λ_C$-gauge". This $λ_C$-gauge is expected to provide a quark-potential-model picture, where dynamical gluons do not appear. We also investigate $T$-length terminated Polyakov-line correlator and its corresponding "finite-time potential" in generalized Landau gauge.

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arXiv2011

Fast vacuum decay into particle pairs in strong electric and magnetic fields

We discuss fermion pair productions in strong electric and magnetic fields. We point out that, in the case of massless fermions, the vacuum persistency probability per unit time and volume is zero in the strong electric and magnetic fields, while it is finite when the magnetic field is absent. The contribution from the lowest Landau level (LLL) dominates this phenomenon. We also discuss dynamics of the vacuum decay, using an effective theory of the LLL projection, taking into account the back reaction.

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arXiv2010

Lattice QCD Study for Gluon Propagator and Gluon Spectral Function

We study the gluon propagator in the Landau gauge in SU(3) lattice QCD at $β$=5.7, 5.8 and 6.0 at the quenched level. The Euclidean Landau-gauge gluon propagator $D(r)\equiv D_{μμ}^{aa}(x)/24$ is found to be well described by four-dimensional Yukawa-type function $e^{-mr}/r$ in the infrared and intermediate region of $r \equiv (x_μx_μ)^{1/2}$ = 0.1 $\sim$ 1.0fm. The infrared effective gluon mass is obtained as $m \simeq$ 600MeV. Associated with the 4D Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $ρ(ω)$ of the gluon field. Remarkably, the obtained gluon spectral function $ρ(ω)$ is almost negative definite, except for a positive $δ$-functional peak at $ω=m$. Since the Yukawa-type propagation indicates a three-dimensional space-time character, we consider a hypothesis of an effective dimensional reduction by generalized Parisi-Sourlas mechanism in a stochastic color-magnetic vacuum of infrared QCD.

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arXiv2010

Lattice QCD analysis for instantaneous interquark potential in generalized Landau gauge

Using generalized Landau gauge, we study the continuous change of gluon properties from the Landau gauge toward the Coulomb gauge in SU(3) lattice QCD. We investigate "instantaneous interquark potential", which is defined by the spatial correlation of the temporal link-variable $U_4$ and is an interesting gauge-dependent concept. In the Coulomb gauge, the instantaneous potential is expressed by the Coulomb plus linear potential, where the slope is, however, 2-3 times as large as the physical string tension. In the Landau gauge, the instantaneous potential has no linear part. We find that the linear part is continuously growing by varying gauge from the Landau gauge toward the Coulomb gauge. We also find that the instantaneous potential approximately reproduces the physical interquark potential in a specific intermediate gauge, $λ_C$-gauge. This $λ_C$-gauge is expected to be a useful gauge for modeling effective theories such as the quark potential model.

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arXiv2009

Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

We study the gluon propagator $D_{μν}^{ab}(x)$ in the Landau gauge in SU(3) lattice QCD at $β$ = 5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as $400 \sim 600$MeV for $r \equiv (x_αx_α)^{1/2} = 0.5 \sim 1.0$ fm. Through the functional-form analysis of $D_{μν}^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gauge gluon propagator $D_{μμ}^{aa}(r)$ is well described by the Yukawa-type function $e^{-mr}/r$ with $m \simeq 600$MeV for $r = 0.1 \sim 1.0$ fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator $\tilde D_{μμ}^{aa}(p^2)$ with $(p^2)^{1/2}= 0.5 \sim 3$ GeV is found to be well approximated with a new-type propagator of $(p^2+m^2)^{-3/2}$, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $ρ(ω)$ of the gluon field. The mass parameter $m$ turns out to be the effective gluon mass in the infrared region of $\sim$ 1fm. As a remarkable fact, the obtained gluon spectral function $ρ(ω)$ is almost negative-definite for $ω>m$, except for a positive $δ$-functional peak at $ω=m$.

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arXiv2009

Lattice QCD Analysis for Gluons

Nonperturbative properties of gluons are studied in SU(3) lattice QCD at the quenched level. The first subject is a functional-form analysis of the gluon propagator $D_{μν}^{ab}(x)$ in the Landau gauge. We find that the gluon propagator $D_{μμ}^{aa}(r)$ obtained in lattice QCD is well described by the four-dimensional (4D) Yukawa-type function $e^{-mr}/r$ with $m \simeq 600$MeV for the Euclidean 4D distance $r = 0.1 \sim 1.0$ fm. In momentum space, the gluon propagator $\tilde D_{μμ}^{aa}(p^2)$ ($p= 0.5 \sim 3$ GeV) is found to be well approximated with a new-type propagator of $(p^2+m^2)^{-3/2}$, which corresponds to 4D Fourier image of the Yukawa-type function. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $ρ(ω)$ of the gluon field. The mass parameter $m$ turns out to be the infrared effective mass of gluons. The obtained gluon spectral function $ρ(ω)$ is almost negative-definite for $ω>m$, except for a positive $δ$-functional peak at $ω=m$. The second subject is a lattice-QCD determination of the relevant gluonic momentum-component for color confinement. As a remarkable fact, the string tension is found to be almost unchanged even after cutting off the high-momentum gluon component above 1.5 GeV in the Landau gauge. In fact, the relevant gluonic scale for color confinement is concluded to be below 1.5 GeV.

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