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Akihiro Shibata

Publications and source records attributed to Akihiro Shibata.

71 records · Page 4Linked to original sources
arXiv2012

Many flavor QCD with N_f=12 and 16

Information of the phase structure of many flavor SU(3) gauge theory is of great interest for finding a theory which dynamically breaks the electro-weak symmetry. We study the SU(3) gauge theory with fermions for $N_f=12$ and 16 in fundamental representation. Both of them, through perturbation theory, reside in the conformal phase. We try to determine the phase of each theory non-perturbatively with lattice simulation and to find the characteristic behavior of the physical quantities in the phase. HISQ type staggered fermions are used to reduce the discretization error which could compromise the behavior of the physical quantity to determine the phase structure at non-zero lattice spacings. Spectral quantities such as bound state masses of meson channel and meson decay constants are investigated with careful finite volume analysis. Our data favor the conformal over chiral symmetry breaking scenario for both $N_f=12$ and 16.

hep-lat↗
arXiv2012

Many flavor QCD as exploration of the walking behavior with the approximate IR fixed point

We present the first report of the LatKMI collaboration on the the lattice QCD simulation performed at the KMI computer, "$φ$", for the cases of 4 flavors and 8 flavors, the latter being expected to be a candidate for the walking technicolor having an approximate scale invariance near the infrared fixed point. The simulation was carried out based on the highly improved staggered quark (HISQ) action. In this proceedings, we report preliminary results on the spectrum, analyzed through the chiral perturbation theory and the finite-size hyperscaling. We observe qualitatively different behavior of the 8-flavor case in contrast to the 4-flavor case which shows clear indication of the hadronic phase as in the usual QCD.

hep-lat↗
arXiv2012

Study of the conformal hyperscaling relation through the Schwinger-Dyson equation

We study corrections to the conformal hyperscaling relation in the conformal window of the large Nf QCD by using the ladder Schwinger-Dyson (SD) equation as a concrete dynamical model. From the analytical expression of the solution of the ladder SD equation, we identify the form of the leading mass correction to the hyperscaling relation. We find that the anomalous dimension, when identified through the hyperscaling relation neglecting these corrections, yields a value substantially lower than the one at the fixed point γ_m^* for large mass region. We further study finite-volume effects on the hyperscaling relation, based on the ladder SD equation in a finite space-time with the periodic boundary condition. We find that the finite-volume corrections on the hyperscaling relation are negligible compared with the mass correction. The anomalous dimension, when identified through the finite-size hyperscaling relation neglecting the mass corrections as is often done in the lattice analyses, yields almost the same value as that in the case of the infinite space-time neglecting the mass correction, i.e., a substantially lower value than γ_m^* for large mass. We also apply the finite-volume SD equation to the chiral-symmetry-breaking phase and find that when the theory is close to the critical point such that the dynamically generated mass is much smaller than the explicit breaking mass, the finite-size hyperscaling relation is still operative. We also suggest a concrete form of the modification of the finite-size hyperscaling relation by including the mass correction, which may be useful to analyze the lattice data.

hep-lat↗
arXiv2010

Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop

We demonstrate that a Jackiw-Nohl-Rebbi solution as the most general two-instanton generates a circular loop of magnetic monopole in four-dimensional Euclidean SU(2) Yang-Mills theory, in contrast to the one-instanton solution in the regular gauge for which no such magnetic monopole loops exist. These results together with our previous result indicate that two-instanton solution and two-meron solution with the same asymptotic behavior in the long distance are responsible for quark confinement based on the dual superconductivity picture.

hep-th↗
arXiv2009

The exact decomposition of gauge variables in lattice Yang-Mills theory

In this paper, we consider lattice versions of the decomposition of the Yang- Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2) and SU(3). As a result, we obtain the general form of the decomposition for SU(N) gauge link variables and confirm the previous results obtained for SU(2) and SU(3).

hep-lat↗
arXiv2009

Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner

We have given a new description of the lattice Yang-Mills theory a la Cho-Faddeev-Niemi-Shabanov, which has enabled us to confirm in a gauge-independent manner "Abelian"-dominance and magnetic-monopole dominance in the Wilson loop average, yielding a gauge-independent dual superconductor picture for quark confinement. In particular, we have given a new procedure (called reduction) for obtaining a gauge-independent magnetic monopole from a given Yang-Mills field. In this talk, we demonstrate how some of known topological configurations in the SU(2) Yang-Mills theory such as merons and instantons generate closed loops of magnetic-monopole current as the quark confiner, both of which are characterized by the gauge-invariant topological index, topological charge (density) and magnetic charge (density), respectively. We also try to detect which type of topological configurations exist in the lattice data involving magnetic-monopole loops generated by Monte Carlo simulation. Here we apply a new geometrical algorithm based on "computational homology" to discriminating each closed loop from clusters of magnetic-monopole current, since the magnetic-monopole current on a lattice is integer valued.

hep-lat↗
arXiv2008

A new description of lattice Yang-Mils theory and non-Abelian monopoles as the quark confiner

We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant magnetic monopoles which are inherent in the Wilson loop operator. For SU(3) there are two options: the minimal option with a single type of non-Abelian magnetic monopole characterized by the maximal stability subgroup $\tilde{H}=U(2)=SU(2)\times U(1)$, and the maximal one with two types of Abelian magnetic monopoles characterized by the maximal torus subgroup $\tilde{H}=U(1)\times U(1)$. The maximal option corresponds to a gauge independent reformulation of the Abelian projection represented by the conventional MAG. In the minimal option, we have successfully performed the numerical simulation of the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation, and the infrared dominance of a decomposed field variable for correlation functions after demonstrating the preservation of color symmetry which was explicitly broken by the conventional MAG.

hep-lat↗
arXiv2008

Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.

hep-th↗
arXiv2008

Proving Abelian dominance in the Wilson loop operator

We give a gauge-independent definition of Abelian dominance in the Wilson loop operator and a constructive proof of the Abelian dominance through a non-Abelian Stokes theorem via lattice regularization. We obtain a necessary and sufficient condition for the Abelian dominance in the Wilson loop operator in the fundamental representation. In the continuum limit, the gauge field is decomposed such that the Abelian dominance is given as an exact operator relation, leading to the exact (100%) Abelian dominance. On a lattice, we estimate the deviation from the exact Abelian dominance due to non-zero lattice spacing. In order to obtain the best Abelian dominance on a lattice by minimizing the deviation, we discuss how to decompose the gauge field variable into the dominant part and the remaining one to be decoupled on a lattice.

hep-th↗
arXiv2006

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

hep-th↗
arXiv2003

Non-perturbative propagators and dimension 2 condensate in Yang-Mills theory

We have found ultraviolet asymptotic slutions of the Schwinger-Dyson equation for the gluon and ghost propagators which have simultaneously the perturbative logarithmic correction and the non-perturbative $1/p^2$ power correction. By including the perturbative corrections, the power correction reproduces exactly the leading OPE result suggesting the existence of dimension two condensate.

hep-lat↗
arXiv1998

Chiral Phase Transition of QCD at Finite Temperature and Density from Schwinger-Dyson Equation

We study the chiral phase transition of QCD at finite temperature and density by numerically solving Schwinger-Dyson equation for the quark propagator with the improved ladder approximation in the Landau gauge. Using the solution we calculate a pion decay constant from a generalized version of Pagels-Stokar formula. Chiral phase transition point is determined by analyzing an effective potential for the quark propagator. We find solutions for which chiral symmetry is broken while the value of the effective potential is larger than that for the chiral symmetric vacuum. These solutions correspond to meta-stable states, and the chiral symmetric vacuum is energetically favored. We present a phase diagram on the general temperature--chemical potential plane, and show that phase transitions are of first order in wide range.

hep-ph↗
arXiv1997

The Pion Decay Constants and the Rho-Meson Mass at Finite Temperature in the Hidden Local Symmetry

We study the temperature dependence of the pion decay constant and rho-meson mass in the hidden local symmetry model at one loop. Using the standard imaginary time formalism, we include the thermal effect of rho meson as well as that of pion. We show that the pion gives a dominant contribution to the pion decay constant and rho-meson contribution slightly decreases the critical temperature. The rho-meson pole mass increases as T^4/m_ρ^2 at low temperature dominated by the pion-loop effect. At high temperature, although the pion-loop effect decreases the rho-meson mass, the rho-loop contribution overcomes the pion-loop contribution and rho-meson mass increases with temperature. We also show that the conventional parameter a is stable as the temperature increases.

hep-ph↗
arXiv1993

Phase Structure of the Gauged Yukawa Model

Based on the ladder Schwinger-Dyson equation, we investigate phase struc- ture of the gauged Yukawa model possessing a global $SU(2)_L \times SU(2)_R$ symmetry and an unbroken (vector-like) gauge symmetry. We show that even when we tune the squared mass of the scalar boson in the Lagrangian to be positive, there still exists the dynamical chiral symmetry breaking due to fermion pair condensate (VEV of the composite scalar) triggered by the strong Yukawa coupling larger than a certain critical value. We find a "nontrivial ultraviolet fixed line" and "renormalized trajectories" in the three-dimensional coupling space of the Yukawa coupling, the gauge cou- pling and the "hopping parameter" of the elementary scalar field. Presence of the gauge coupling is crucial to existence of the fixed line. Implications of the result for the lattice calculation and the top quark condensate model are also discussed.

hep-ph↗