Search

The $\Delta\Delta$ dibaryon resonance $d^\ast (2380)$ with $(J^P, I)=(3^+, 0)$ is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses ($m_\pi =679, 841$ and $1018$ MeV). By using the HAL QCD method, the central $\Delta$-$\Delta$ potential in the ${}^7S_3$ channel is obtained from the lattice data with the lattice spacing $a\simeq 0.121$ fm and the lattice size $L\simeq 3.87$ fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to $d^\ast (2380)$ is formed with the binding energy $25$-$40$ MeV below the $\Delta\Delta$ threshold for the heavy pion masses. The tensor part of the transition potential from $\Delta\Delta$ to $NN$ is also extracted to investigate the coupling strength between the $S$-wave $\Delta\Delta$ system with $J^P=3^+$ and the $D$-wave $NN$ system. Although the transition potential is strong at short distances, the decay width of $d^\ast (2380)$ to $NN$ in the $D$-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study., Comment: 8 pages, 6 figures

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems., Comment: 14 pages, 10 figures; v2: 17 pages, 14 figures, supplementary note added, to be published in Scientific Reports

The $S$-wave $\Lambda\Lambda$ and $N \Xi$ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point ($m_\pi \simeq 146{\rm{MeV}}$ and $m_K \simeq 525{\rm{MeV}}$). Lattice QCD potentials in four different spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The $\Lambda \Lambda$ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The $N\Xi$ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the $N\Xi$ system near unitarity. Relevance to the strangeness=$-2$ hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed., Comment: 16 pages, 8 figures

The momentum correlation functions of baryon pairs, which reflects the baryon-baryon interaction at low energies, are investigated for multi-strangeness pairs ($\Omega\Omega$ and $N\Omega$) produced in relativistic heavy-ion collisions. We calculate the correlation functions based on an expanding source model constrained by single-particle distributions. The interaction potentials are taken from those obtained from recent lattice QCD calculations at nearly physical quark masses. Experimental measurements of these correlation functions for different system sizes will help to disentangle the strong interaction between baryons and to unravel the possible existence of strange dibaryons., Comment: 11 pages, 8 figures (reference format is modified in v2)

The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of $S$-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet $\Lambda_c N$ system calculated in the $(2+1)$-flavor QCD on a $(32a~\mathrm{fm})^3$ lattice at the lattice spacing $a\simeq0.0907$ fm and $m_\pi \simeq 700$ MeV. We find that the $l=0$ component can be successfully extracted by Misner's method from the NBS wave function projected to $A_1^+$ representation of the cubic group, which contains small $l\ge 4$ components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner's method, where the Laplacian can be evaluated analytically for each partial wave component. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner's method works well in lattice QCD with the HAL QCD method but also that the contaminations from higher partial waves in the study of $S$-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in the HAL QCD method with Misner's decomposition, where the utility of this new technique may become clearer., Comment: 22 pages, 10 figures

The nucleon($N$)-Omega($\Omega$) system in the S-wave and spin-2 channel ($^5$S$_2$) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses ($m_\pi \simeq 146$~MeV and $m_K \simeq 525$~MeV). The time-dependent HAL QCD method is employed to convert the lattice QCD data of the two-baryon correlation function to the baryon-baryon potential and eventually to the scattering observables. The $N\Omega$($^5$S$_2$) potential, obtained under the assumption that its couplings to the D-wave octet-baryon pairs are small, is found to be attractive in all distances and to produce a quasi-bound state near unitarity: In this channel, the scattering length, the effective range and the binding energy from QCD alone read $a_0= 5.30(0.44)(^{+0.16}_{-0.01})$~fm, $r_{\rm eff} = 1.26(0.01)(^{+0.02}_{-0.01})$~fm, $B = 1.54(0.30)(^{+0.04}_{-0.10})$~MeV, respectively. Including the extra Coulomb attraction, the binding energy of $p\Omega^-$($^5$S$_2$) becomes $B_{p\Omega^-} = 2.46(0.34)(^{+0.04}_{-0.11})$~MeV. Such a spin-2 $p\Omega^-$ state could be searched through two-particle correlations in $p$-$p$, $p$-nucleus and nucleus-nucleus collisions., Comment: 16 pages, 6 figures, a reference added

We study the asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave functions, which are important for the HAL QCD potential method to extract hadron interactions, in the case that a bound state exists in the system. We consider the complex scalar particles, two of which lead to the formation of a bound state. In the case of the two-body system, we show that the NBS wave functions for the bound state as well as scattering states in the asymptotic region behave like the wave functions in quantum mechanics, which carry the information of the binding energy as well as the scattering phase shift. This analysis theoretically establishes under some conditions that the HAL QCD potential can correctly reproduce not only the scattering phase shift but also the binding energy. As an extension of the analysis, we also study the asymptotic behaviors of all possible NBS wave functions in the case of the three-body systems, two of which can form a bound states., Comment: 16 pages; published version

The $\Xi\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the convergence of the derivative expansion of the non-local HAL QCD potential at the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order potential from the N$^2$LO analysis gives the scattering phase shifts accurately at low energies, (ii) the full N$^2$LO potential gives only small correction to the phase shifts even at higher energies below the inelastic threshold, and (iii) the potential determined from the wall quark source at the leading order analysis agrees with the one at the N$^2$LO analysis except at short distances, and thus, it gives correct phase shifts at low energies. We also study the possible systematic uncertainties in the HAL QCD potential such as the inelastic state contaminations and the finite volume artifact for the potential and find that they are well under control for this particular system., Comment: 23 pages, 13 figures

We present our recent results of baryon interactions with strangeness $S=-1$ based on Nambu-Bethe-Salpeter (NBS) correlation functions calculated from lattice QCD with almost physical quark masses corresponding to $(m_\pi,m_K)\approx(146,525)$ MeV and large volume $(La)^4=(96a)^4\approx$ (8.1 fm)$^4$. In order to perform a comprehensive study of baryon interactions, a large number of NBS correlation functions from NN to $\Xi\Xi$ are calculated simultaneously by using large scale computer resources. In this contribution, we focus on the strangeness $S=-1$ channels of the hyperon interactions by means of HAL QCD method. Four sets of three potentials (the $^3S_1-^3D_1$ central, $^3S_1-^3D_1$ tensor, and the $^1S_0$ central potentials) are presented for the $\Sigma N - \Sigma N$ (the isospin $I=3/2$) diagonal, the $\Lambda N - \Lambda N$ diagonal, the $\Lambda N \rightarrow \Sigma N$ transition, and the $\Sigma N - \Sigma N$ ($I=1/2$) diagonal interactions. Scattering phase shifts for $\Sigma N$ $(I=3/2)$ system are presented., Comment: Talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spain, 8 pages, 17 figures, references added, typos corrected, arXiv admin note: text overlap with arXiv:1702.00734

We present the latest lattice QCD results for baryon interactions obtained at nearly physical quark masses. $N_f = 2+1$ nonperturbatively ${\cal O}(a)$-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of $(96a)^4 \simeq (8.1\mbox{fm})^4$ with $a^{-1} \simeq 2.3$ GeV, where $m_\pi \simeq 146$ MeV and $m_K \simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$\Xi$ systems in $^1S_0$ channel and $^3S_1$-$^3D_1$ coupled channel, and extract central and tensor interactions by the HAL QCD method. We also present the results for the $N\Omega$ interaction in $^5S_2$ channel which is relevant to the $N\Omega$ pair-momentum correlation in heavy-ion collision experiments., Comment: Talk given at 35th International Symposium on Lattice Field Theory (Lattice 2017), Granada, Spain, 18-24 Jun 2017, 8 pages, 9 figures. arXiv admin note: text overlap with arXiv:1702.01600

The interaction between $\Lambda_c$ and a nucleon ($N$) is investigated by employing the HAL QCD method in the (2+1)-flavor lattice QCD on a $(2.9~\mathrm{fm})^3$ volume at $m_\pi \simeq 410,~570,~700$ MeV. We study the central potential in $^1S_0$ channel as well as central and tensor potentials in $^3S_1 - $$^3D_1$ channel, and find that the tensor potential for $\Lambda_c N$ is negligibly weak and central potentials in both $^1S_0$ and $^3S_1 - $$^3D_1$ channels are almost identical with each other except at short distances. Phase shifts and scattering lengths calculated with these potentials show that the interaction of $\Lambda_c N$ system is attractive and has a similar strength in $^1S_0$ and $^3S_1$ channels at low energies (i.e. the kinetic energy less than about $40$ MeV). While the attractions are not strong enough to form two-body bound states, our results lead to a possibility to form $\Lambda_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for $\Lambda_c$ hypernuclei from the $\Lambda_c$-nucleon potential obtained in lattice QCD, and find that $\Lambda_c$ hypernuclei can exist for $A \ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the $\Lambda_c$ hypernuclei., Comment: 27 pages, 10 figures, 4 tables

The $\Omega\Omega$ system in the $^1S_0$ channel (the most strange dibaryon) is studied on the basis of the (2+1)-flavor lattice QCD simulations with a large volume (8.1 fm)$^3$ and nearly physical pion mass $m_{\pi}\simeq 146$ MeV at a lattice spacing $a\simeq 0.0846$ fm. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length $a_0 = 4.6 (6)(^{+1.2}_{-0.5}) {\rm fm}$, the effective range $r_{\rm eff} = 1.27 (3)(^{+0.06}_{-0.03}) {\rm fm}$ and the binding energy $B_{\Omega \Omega} = 1.6 (6) (^{+0.7}_{-0.6}) {\rm MeV}$. These results indicate that the $\Omega\Omega$ system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions., Comment: 6 pages and 4 figures

We discuss free Dirac fermions rotating uniformly inside a cylindrical cavity in the presence of background magnetic field parallel to the cylinder axis. We show that in addition to the known bulk states the system contains massive edge states with the masses inversely proportional to the radius of the cylinder. The edge states appear at quantized threshold values of the fermion mass. In the limit of infinite fermion mass the masses of the edge states remain finite but, generally, nonzero as contrasted to the bulk states whose masses become infinite. The presence of magnetic field affects the spectrum of both bulk and edge modes, and the masses of the edge states may vanish at certain values of magnetic field. The moment of inertia of Dirac fermions is non-monotonically increasing, oscillating function of magnetic field. The oscillations are well pronounced in a low-temperature domain and they disappear at high temperatures., Comment: 19 pages, 13 figures

In order to avoid unphysical causality-violating effects any rigidly rotating system must be bounded in directions transverse to the axis of rotation. We demonstrate that this requirement implies substantial dependence of properties of relativistically rotating system on the boundary conditions. We consider a system of interacting fermions described by the Nambu-Jona-Lasinio model in a space bounded by cylindrical surface of finite radius. In order to confine the fermions inside the cylinder we impose "chiral" MIT boundary conditions on its surface. These boundary conditions are parameterized by a continuous chiral angle \Theta. We find that at any value of \Theta the chiral restoration temperature T_c decreases as a quadratic function of the angular frequency \Omega. However, the position and the slope of the critical curve T_c = T_c(\Omega) in the phase diagram depends noticeably on the value of the chiral angle., Comment: 10 pages, 9 figures

The strangeness $S=-2$ baryon-baryon interaction is investigated directly from the fundamental theory of the strong interaction, QCD. The HAL QCD method enables us to extract baryon interactions from the Nambu-Bethe-Salpeter wave functions without using any experimental information. We present our latest result on the $S = -2$ baryon interactions and discuss the H-dibaryon state using potentials which are calculated by using the (almost) physical point gauge configurations with large lattice volume of$(8.1{\rm{fm}})^4$ generated on the K-computer., Comment: 7 pages, 4 figures. Talk given at 34th International Symposium on Lattice Field Theory (Lattice 2016), Southampton, UK, 24-30 Jul 2016

We present lattice QCD results of baryon-baryon potentials in S=-3 sector, i.e., \Xi\Sigma (I=3/2) potentials and \Xi\Lambda-\Xi\Sigma coupled channel potentials (I=1/2) by using the 2+1 flavor gauge configurations with almost the physical quark masses generated on 96^4 lattice with 1/a \simeq 2.3 GeV and L = 96a \simeq 8.1 fm where m_pi \simeq 146 MeV and m_K \simeq 525 MeV. These potentials are obtained based on the time-dependent HAL QCD method with a non-relativistic approximation. Qualitative behaviors of the results are found to be consistent with those in the flavor SU(3) limit., Comment: 7 pages, 21 figures. Talk given at the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, Southampton, United Kingdom

Nuclear forces and hyperon forces are studied by lattice QCD. Simulations are performed with (almost) physical quark masses, $m_\pi \simeq 146$ MeV and $m_K \simeq 525$ MeV, where $N_f=2+1$ nonperturbatively ${\cal O}(a)$-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of $(96a)^4 \simeq (8.1\mbox{fm})^4$ with $a^{-1} \simeq 2.3$ GeV. In this report, we give the overview of the theoretical framework and present the numerical results for two-nucleon forces ($S=0$) and two-$\Xi$ forces ($S=-4$). Central forces are studied in $^1S_0$ channel, and central and tensor forces are obtained in $^3S_1$-$^3D_1$ coupled channel analysis., Comment: Talk given at 34th International Symposium on Lattice Field Theory (Lattice 2016), Southampton, UK, 24-30 Jul 2016, 7 pages, 8 figures

We present our recent study on baryon-baryon ($BB$) interactions from lattice QCD with almost physical quark masses corresponding to $(m_\pi,m_K)\approx(146,525)$ MeV and large volume $(La)^4=(96a)^4\approx$ (8.1 fm)$^4$. In order to perform a comprehensive study of $BB$ interactions based on lattice QCD calculation with almost physical masses and to make better use of such large scale computer resources, a large number of $BB$ interactions from $NN$ to $\Xi\Xi$ are calculated simultaneously. In this report, we focus on the strangeness $S=-1$ channels of the hyperon interactions by means of HAL QCD method. The coupled-channel HAL QCD method is briefly outlined. The snapshots of central and tensor potentials in $^1S_0$ and $^3S_1-^3D_1$ channels are presented for $\Lambda N$, $\Sigma N$ (both the isospin $I=1/2, 3/2$) and their coupled-channel systems., Comment: Talk presented at the 34th annual International Symposium on Lattice Field Theory (LATTICE 2016), 24-30 July 2016, University of Southampton, UK, 7 pages, 13 figures

We study rotating fermionic matter at finite temperature in the framework of the Nambu-Jona-Lasinio model. In order to respect causality the rigidly rotating system must be bound by a cylindrical boundary with appropriate boundary conditions that confine the fermions inside the cylinder. We show the finite geometry with the MIT boundary conditions affects strongly the phase structure of the model leading to three distinct regions characterized by explicitly broken (gapped), partially restored (nearly gapless) and spontaneously broken (gapped) phases at, respectively, small, moderate and large radius of the cylinder. The presence of the boundary leads to specific steplike irregularities of the chiral condensate as functions of coupling constant, temperature and angular frequency. These steplike features have the same nature as the Shubnikov-de Haas oscillations with the crucial difference that they occur in the absence of both external magnetic field and Fermi surface. At finite temperature the rotation leads to restoration of spontaneously broken chiral symmetry while the vacuum at zero temperature is insensitive to rotation ("cold vacuum cannot rotate"). As the temperature increases the critical angular frequency decreases and the transition becomes softer. A phase diagram in angular frequency-temperature plane is presented. We also show that at fixed temperature the fermion matter in the chirally restored (gapless) phase has a higher moment of inertia compared to the one in the chirally broken (gapped) phase., Comment: 30 pages, 14 figures; v2: misprints corrected

Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($\Xi\Xi$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{\pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions., Comment: 32 pages, 13 figures, minor corrections, published version, typos corrected

We describe an efficient algorithm to compute a large number of baryon-baryon interactions from $NN$ to $\Xi\Xi$ by means of HAL QCD method, which lays the groundwork for the nearly physical point lattice QCD calculation with volume $(96a)^4\approx$($8.2$fm)$^4$. Preliminary results of $\Lambda N$ potential calculated with quark masses corresponding to ($m_{\pi}$,$m_{K}$)$\approx$(146,525)MeV are presented., Comment: Talk given at the 12th International Conference on Hypernuclear and Strange Particle Physics (HYP2015), Sendai, Japan, 7-12 September, 2015, 4 pages, 3 figures

We discuss that a low-energy effective Lagrangian relying on SO(3) $\rightarrow$ SO(2) is applicable for a ferrimagnet as well as a ferromagnet and an antiferromagnet. The analysis of the particle states shows that there exist not only massless modes with the dispersion relations $\omega \propto |\bm{k}|,\, |\bm{k}|^2$, i.e., the so-called type-I and type-II Nambu-Goldstone modes, respectively, but also gapped modes with $\omega \propto m^2+|\bm{k}|^2$. We clarify how the coefficients of the terms with one time derivative and those with two time derivatives in the effective Lagrangian determine the order parameters specifying whether the system is in a ferromagnetic, antiferromagnetic or ferrimagnetic state; we stress that the gapped mode related to the spontaneous symmetry breaking appears only in the ferrimagnetic system and not in the ferromagnetic and antiferromagnetic systems. We also establish the power counting scheme and calculate the scattering amplitudes and thereby the scattering lengths between the two Nambu-Goldstone bosons. We show that the scattering length of the gapped mode is finite and proportional to the gap. This characteristic property of the gapped NG mode can be used to discriminate it from gapped excitations which originate in other mechanisms. Finally, we study the effects of the explicit symmetry breaking that are given by an external magnetic field and a single-ion anisotropy, and show that the external magnetic fields do not have any effects on the scattering amplitudes in all the spin systems as was known for the ferromagnet system. In contrast, the anisotropy does affect the scattering amplitudes, the phase shift, and the scattering length except for spin 1/2 systems. This result supports the possibility of the Efimov effect in spin systems discussed in previous studies., Comment: 26pages, 0 figures; published in Progress of Theoretical and Experimental Physics (PTEP)

The possible exotic meson $Z_{c}(3900)$, found in $e^+ e^-$ reactions, is studied by the method of coupled-channel scattering in lattice QCD. The interaction among $\pi J/\psi$, $\rho \eta_{c}$ and $\bar{D}D^{*}$ channels is derived from (2+1)-flavor QCD simulations at $m_{\pi}=410$-$700$ MeV. The interaction is dominated by the off-diagonal $\pi J/\psi$-$\bar{D}D^{*}$ and $\rho \eta_{c}$-$\bar{D}D^{*}$ couplings, which indicates that the $Z_{c}(3900)$ is not a usual resonance but a threshold cusp. Semi-phenomenological analyses with the coupled-channel interaction are presented to confirm this conclusion., Comment: 5 pages, 6 figures

Lattice QCD calculations of baryon forces are performed for the first time with (almost) physical quark masses. $N_f = 2+1$ dynamical clover fermion gauge configurations are generated at the lattice spacing of $a \simeq 0.085$ fm on a $(96 a)^4 \simeq (8.2 {\rm fm})^4$ lattice with quark masses corresponding to $(m_\pi, m_K) \simeq (146, 525)$ MeV. Baryon forces are calculated using the time-dependent HAL QCD method. In this report, we study $\Xi\Xi$ and $NN$ systems both in $^1S_0$ and $^3S_1$-$^3D_1$ channels, and the results for the central and tensor forces as well as phase shifts in the $\Xi\Xi$ $(^1S_0)$ channel are presented., Comment: Talk given at the 12th International Conference on Hypernuclear and Strange Particle Physics (HYP2015), Sendai, Japan, 7-12 Sep 2015, 4 pages, 6 figures

We present the lattice QCD studies for baryon-baryon interactions for the first time with (almost) physical quark masses. $N_f = 2+1$ gauge configurations are generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quark action with stout smearing on the lattice of $(96 a)^4 \simeq (8.2 {\rm fm})^4$ with $a \simeq 0.085$ fm, where $m_\pi \simeq 146$ MeV and $m_K \simeq 525$ MeV. Baryon forces are calculated from Nambu-Bethe-Salpeter (NBS) correlation functions using the time-dependent HAL QCD method. In this report, we first give the general overview of the theoretical frameworks essential to the physical point calculation of baryon forces. We then present the numerical results for the two-nucleon central and tensor forces in $^3S_1$-$^3D_1$ coupled channel and the central force in $^1S_0$ channel. In particular, a clear signal is obtained for the tensor force., Comment: Talk given at 33rd International Symposium on Lattice Field Theory (Lattice 2015), Kobe, Japan, 14-18 Jul 2015, 7 pages, 5 figures

We discuss the dark matter in the hidden gauge theory. We propose a scenario where the mini-inflation dilutes the dark matter density. This scenario is consistent with the current baryon number asymmetry., Comment: 4 pages, 3 figures, Contribution to the proceedings of Toyama International Workshop on Higgs as a Probe of New Physics (HPNP2015), February 2015, Toyama, Japan

Using SU(2) lattice QCD in two dimensions, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge (MAG) with U(1)$_3$ Landau gauge fixing. These propagators are investigated both in momentum space and coordinate space. The Monte Carlo simulation is performed at $\beta=7.99, 30.5,$ and $120$ on $62^2, 128^2,$ and $256^2$ at the quenched level. In the momentum space, the transverse component of the diagonal gluon propagator shows suppression with increasing $\beta$ in the infrared region and the dressing function at $\beta=120$ has a maximum at $p^2 \simeq 4$GeV, while the transverse component of the off-diagonal gluon propagator does not show the $\beta$-dependence and the dressing function does not have a maximum. This behavior indicates that the effect of the Gribov copies is found for the diagonal gluon, consistent with the result obtained by the Gribov-Zwanziger action in the MAG. In addition, this behavior supports that the Abelian dominance is not found in two dimensions. In the coordinate space, the diagonal gluon propagator decreases as $\beta$ increases at long distance. In particular, at $\beta=120$ the diagonal propagator decreases more rapidly with increasing distance than the off-diagonal propagator. These behaviors also indicate the presence of Gribov copies and no Abelian dominance in two dimensions. Furthermore, we also study these propagators at zero-spatial-momentum. The result suggests that all of the spectral functions of diagonal and off-diagonal gluons would have negative regions and thus they show the violation of the Kallen-Lehmann representation.

The cosmological scenario of the dark matter generated in the hidden gauge theory based on the grand unification is discussed. It is found that the stability of the dark matter halo of our Galaxy and the cosmic ray observation constrain, respectively, the dark matter mass and the unification scale between the standard model and the hidden gauge theory sectors. To obtain a phenomenologically consistent thermal evolution, the entropy of the standard model sector needs to be increased. We therefore propose a scenario where the mini-inflation is induced from the potential coupled to the Standard model sector, in particular the Higgs sector. This scenario makes consistent the current dark matter density as well as the baryon-to-photon ratio for the case of pion dark matter. For the glueball or heavy pion of hidden gauge theory, an additional mini-inflation in the standard model sector before the leptogenesis is required. We also propose the possibility to confirm this scenario by known prospective experimental approaches., Comment: 6 pages, 5 figures

We study the phase structure of SU(2) gauge-Higgs model in two dimensions using lattice simulations. We show the result for the plaquette expectation value, static potential, and W propagator. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. The behavior of the plaquette expectation value is consistent with a smooth cross-over in accordance with the Fradkin-Shenker-Osterwalder-Seiler theorem. In the confinement-like region, the static potential seems to rise linearly with string breaking at large distances, while in the Higgs-like region there seems to be a massive behavior which means that the BEH mechanism occurs. The correlation length obtained from the W propagator has a finite maximum between these phases, which supports no second-order phase transition. Based on these results, we suggest that there is no phase transition in two dimensions.

First, we develop the counting rule for Nambu-Goldstone bosons to the system including two-time derivative terms. In this case, the type-II Nambu-Goldstone bosons may appear along with the massive Nambu-Goldstone ones. The number of the bosons is not reduced in contrast to the system without two-time derivative terms. We also investigate the reduction of the degrees of freedom from the perspective of the Dirac-Bergmann theory of constraints and reproduce the counting rule for Nambu-Goldstone bosons without Lorentz invariance. Then, we construct the generic Higgs model and study a Higgs phenomenon with these Nambu-Goldstone bosons on the basis of the Dirac-Bergmann theory. We show that the gauge fields in this system absorb all of the Nambu-Goldstone bosons such as the type-I, type-II and massive ones., Comment: version accepted in Phys. Rev. D

We study numerically the phase structure and the gluon propagator of the SU(2) gauge-Higgs model in two dimensions. First, we calculate gauge-invariant quantities, in particular the static potential from Wilson Loop, the W propagator, and the plaquette expectation value. Our results suggest that a confinement-like region and a Higgs-like region appear even in two dimensions. In the confinement-like region, the static potential rises linearly, with string breaking at large distances, while in the Higgs-like region, it is of Yukawa type, consistent with a Higgs-type mechanism. The correlation length obtained from the W propagator has a finite maximum between these regions. The plaquette expectation value shows a smooth cross-over consistent with the Fradkin-Shenker-Osterwalder-Seiler theorem. From these results, we suggest that there is no phase transition in two dimensions. We also calculate a gauge-dependent order parameter in Landau gauge. Unlike gauge invariant quantities, the gauge non-invariant order parameter has a line of discontinuity separating these two regions. Finally we calculate the gluon propagtor. We infer from its infrared behavior that the gluon propagator would vanish at zero momentum in the infinite-volume limit, consistent with an analytical study., Comment: accepted in JHEP

We construct the local Gribov-Zwanziger action for SU(2) Euclidean Yang-Mills theories in the maximally Abelian (MA) gauge with U(1)$_3$ Landau gauge fixing based on the Zwanziger's work in the Landau gauge. By the restriction of the functional integral region to the Gribov region in the MA gauge, we give the nonlocal action. We localize the action with new fields and obtain the action with the shift of the new scalar fields, which has the terms, corresponding to the localized action of the horizon function in the MA gauge. The diagonal gluon propagator in the MA gauge at tree level behaves like the propagator from Gribov-Zwanziger action in the Landau gauge and shows the violation of Kallen-Lehmann representation.

In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian (MA) gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on $16^4$ at $\beta$=6.0 and $32^4$ at $\beta$=5.8 and 6.0 at the quenched level. In the four-dimensional Euclidean space-time, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}} \simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}} \simeq 1\mathrm{GeV}$ in the region of $r =0.4-1.0$fm. In the momentum space, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}} \simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}} \simeq 1\mathrm{GeV}$ in the region of $p <1.1$GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by $Z/(p^2+m^2)^\nu$ with fit parameters, $Z, m$ and $\nu$ in the region of $p <3.0$GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions., Comment: Continues and extends arXiv:1207.4377

Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$, 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 calculations. 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 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 between confinement and chiral symmetry breaking in QCD., Comment: 8 pages, 20 figures, Prepared for Conference: Quark Confinement and the Hadron Spectrum X (Confinement X)

In order to investigate the direct relation between confinement and chiral symmetry breaking in QCD, we investigate the Polyakov loop in terms of the Dirac eigenmodes in both confined and deconfined phases. Using the Dirac-mode expansion method in SU(3) lattice QCD, we analyze the contribution of low-lying and higher Dirac-modes to the Polyakov loop, respectively.In the confined phase below T_c, after removing low-lying Dirac-modes, the chiral condensate $< \bar{q} q>$ is largely reduced, however, the Polyakov loop remains almost zero and Z_3-center symmetry is unbroken. These results indicate that the system is still in the confined phase without low-lying Dirac-modes. By higher Dirac-modes cut, the Polyakov loop also remains almost zero below T_c. We also analyze the Polyakov loop in the deconfined phase above T_c. We find that the Polyakov loop and Z_3-symmetry behavior are insensitive to low-lying and higher Dirac-modes in both confined and deconfined phases., Comment: 8 pages, 4 figures, talk given at Quark Confinement and the Hadron Spectrum X, 8-12 October 2012, TUM Campus Garching, Munich, Germany

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 $\beta$=5.7, 5.8 and 6.0 and $32^4$ at $\beta=$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., Comment: arXiv admin note: substantial text overlap with arXiv:1211.0116, arXiv:1207.4377

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 $\beta$=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., Comment: arXiv admin note: substantial text overlap with arXiv:1207.4377

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., Comment: 7 pages, 4 figures, talk given at 30th International Symposium on Lattice Field Theory Lattice 2012, Cairns, Australia, June 24-29, 2012

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 $\beta$=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.

Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$, 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 $\beta$=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.

We investigate the relevant gluon-momentum region for confinement in lattice QCD on $16^4$ at $\beta$=5.7, 5.8 and 6.0, based on the Fourier expansion. We find that the string tension $\sigma$, 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 $\sigma$. 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 $\gamma^\mu D^\mu$. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD on $6^4$ at $\beta$=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., Comment: for Proceedings of International Workshop on QCD Green's Functions, Confinement, and Phenomenology, Trento, Sep 5-9, 2011