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Sinya Aoki

Publications and source records attributed to Sinya Aoki.

At least 91 records · Page 5Linked to original sources
arXiv2018

Most Strange Dibaryon from Lattice QCD

The $ΩΩ$ 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 $m_π\simeq 146$ 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 $B_{ΩΩ} = 1.6 (6) (^{+0.7}_{-0.6}) {\rm MeV}$. These results indicate that the $ΩΩ$ 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.

hep-lat↗
arXiv2018

Flow equation, conformal symmetry and AdS geometry

We argue that the Anti-de-Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.

hep-th↗
arXiv2018

$Λ_c N$ interaction from lattice QCD and its application to $Λ_c$ hypernuclei

The interaction between $Λ_c$ 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 $m_π\simeq 410,~570,~700$ MeV. We study the central potential in $^1S_0$ channel as well as central and tensor potentials in $^3S_1 - $$^3D_1$ channel, and find that the tensor potential for $Λ_c N$ is negligibly weak and central potentials in both $^1S_0$ and $^3S_1 - $$^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 $Λ_c N$ 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 $Λ_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for $Λ_c$ hypernuclei from the $Λ_c$-nucleon potential obtained in lattice QCD, and find that $Λ_c$ hypernuclei can exist for $A \ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the $Λ_c$ hypernuclei.

hep-lat↗
arXiv2018

Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two Dimensions

We study the flow equation for the $\mathcal{N}=1$ supersymmetric $O(N)$ nonlinear sigma model in two dimensions, which cannot be given by the gradient of the action, as evident from dimensional analysis. Imposing the condition on the flow equation that it respects both the supersymmetry and the $O(N)$ symmetry, we show that the flow equation has a specific form, which however contains an undetermined function of the supersymmetric derivatives $D$ and $\bar D$. Taking the most simple choice, we propose a flow equation for this model. As an application of the flow equation, we give the solution of the equation at the leading order in the large $N$ expansion. The result shows that the flow of the superfield in the model is dominated by the scalar term, since the supersymmetry is unbroken in the original model. It is also shown that the two point function of the superfield is finite at the leading order of the large $N$ expansion.

hep-th↗
arXiv2018

Baryon interactions from lattice QCD with physical masses --- strangeness $S=-1$ sector ---

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 $(m_π,m_K)\approx(146,525)$ 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 $ΞΞ$ 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 $ΣN - ΣN$ (the isospin $I=3/2$) diagonal, the $ΛN - ΛN$ diagonal, the $ΛN \rightarrow ΣN$ transition, and the $ΣN - ΣN$ ($I=1/2$) diagonal interactions. Scattering phase shifts for $ΣN$ $(I=3/2)$ system are presented.

hep-lat↗
arXiv2017

Topological susceptibility in 2+1-flavor QCD with chiral fermions

We compute the topological susceptibility $χ_t$ of 2+1-flavor lattice QCD with dynamical Möbius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a "slab" sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass $M_π$ and decay constant $F_π$, we obtain $χ_t$ = 0.227(02)(11)$M_π^2 F_π^2$ at the physical point, where the first error is statistical and the second is systematic.

hep-lat↗
arXiv2017

Axial $U(1)$ symmetry at high temperature in 2-flavor lattice QCD

We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical Möbius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.

hep-lat↗
arXiv2017

$I=2$ $ππ$ scattering phase shift from the HAL QCD method with the LapH smearing

Physical observables, such as the scattering phase shifts and the binding energies, calculated from the non-local HAL QCD potential do not depend on the sink operators used to define the potential. This is called the scheme independence of the HAL QCD method. In practical applications, the derivative expansion of the non-local potential is employed, so that physical observables may receive some scheme dependence at given order of the expansion. In this paper, we compare the $I=2$ $ππ$ scattering phase shifts obtained in the point-sink scheme (the standard scheme in the HAL QCD method) and the smeared-sink scheme (the LapH smearing newly introduced in the HAL QCD method). Although potentials in different schemes have different forms as expected, we find that, for reasonably small smearing size, the resultant scattering phase shifts agree with each other if the next-to-leading order (NLO) term is taken into account. We also find that the HAL QCD potential in the point-sink scheme has negligible NLO term for wide range of energies, which implies a good convergence of the derivative expansion in this case, while the potential in the smeared-sink scheme has non-negligible NLO contribution. Implication of this observation to the future studies of resonance channels (such as the $I=0$ and $1$ $ππ$ scatterings) with smeared all-to-all propagators is briefly discussed. All computations in this paper have been performed at the lattice spacing $a\simeq 0.12$ fm ($1/a \simeq 1.6$ GeV) on a $16^3\times 32$ lattice with the pion mass $m_π\simeq 870$ MeV.

hep-lat↗
arXiv2017

Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and $ΞΞ$ forces --

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 $m_π\simeq 146$ MeV and $m_K \simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$Ξ$ 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 $NΩ$ interaction in $^5S_2$ channel which is relevant to the $NΩ$ pair-momentum correlation in heavy-ion collision experiments.

hep-lat↗
arXiv2017

AdS geometry from CFT on a general conformally flat manifold

We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We explicitly show that the induced metric associated with the primary flow equation becomes AdS whose boundary is the curved manifold. Interestingly, it turns out that such an AdS metric with conformally flat boundary is obtained from the usual Poincare AdS by a simple bulk diffeomorphism transformation. We also demonstrate that the emergence of such an AdS space is guaranteed only by the conformal symmetry at boundary, which converts to the AdS isometry after quantum averaging, as in the case of the flat boundary.

hep-th↗
arXiv2017

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

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 ($ΞΞ$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_π=0.51$ 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.

hep-lat↗
arXiv2017

Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with Lüscher's finite volume formula --

On the basis of the Lüscher's finite volume formula, a simple test (consistency check or sanity check) is introduced and applied to inspect the recent claims of the existence of the nucleon-nucleon ($NN$) bound state(s) for heavy quark masses in lattice QCD. We show that the consistency between the scattering phase shifts at $k^2 > 0$ and/or $k^2 < 0$ obtained from the lattice data and the behavior of phase shifts from the effective range expansion (ERE) around $k^2=0$ exposes the validity of the original lattice data, otherwise such information is hidden in the energy shift $ΔE$ of the two nucleons on the lattice. We carry out this sanity check for all the lattice results in the literature claiming the existence of the $NN$ bound state(s) for heavy quark masses, and find that (i) some of the $NN$ data show clear inconsistency between the behavior of ERE at $k^2 > 0$ and that at $k^2 < 0$, (ii) some of the $NN$ data exhibit singular behavior of the low energy parameter (such as the divergent effective range) at $k^2<0$, (iii) some of the $NN$ data have the unphysical residue for the bound state pole in S-matrix, and (iv) the rest of the $NN$ data are inconsistent among themselves. Furthermore, we raise a caution of using the ERE in the case of the multiple bound states. Our finding, together with the fake plateau problem previously pointed out by the present authors, brings a serious doubt on the existence of the $NN$ bound states for pion masses heavier than 300 MeV in the previous studies.

hep-lat↗
arXiv2017

Sanity check for $NN$ bound states in lattice QCD with Lüscher's finite volume formula -- Exposing Symptoms of Fake Plateaux --

A sanity check rules out certain types of obviously false results, but does not catch every possible error. After reviewing such a sanity check for $NN$ bound states with the Lüscher's finite volume formula[1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim in [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013[6,7] exist with the $P$-values of 4--5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansion (ERE) fits in NPL2013 violate the physical pole condition. (iv) Ref.[5] is partly based on new data and analysis different from the original ones[6,7]. (v) A new ERE in Refs.[5,8] does not satisfy the Lüscher's finite volume formula. [1] T. Iritani et al., JHEP 10 (2016) 101. [2] S. Aoki et al., PoS (LATTICE2016) 109. [3] T. Iritani et al., 1703.0720. [4] T. Yamazaki et al., PoS (LATTICE2017) 108. [5] S.R. Beane et al., 1705.09239. [6] S.R. Beane et al., PRD87 (2013) 034506. [7] S.R. Beane et al., PRC88 (2013) 024003. [8] M.L. Wagman et al., 1706.06550.

hep-lat↗
arXiv2017

Entanglement Entropy for 2D Gauge Theories with Matters

We investigate the entanglement entropy in 1+1-dimensional $SU(N)$ gauge theories with various matter fields using the lattice regularization. Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labelled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is associated with "color entanglement", and (3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that entanglement entropies (1) and (2) above indeed appear for various multiple "meson" states in gauge theories with matter fields. Furthermore, we employ transfer matrix formalism for gauge theory with fundamental matter field and analyze its ground state using hopping parameter expansion (HPE), where the hopping parameter $K$ is roughly the inverse square of the mass for the matter. We evaluate the entanglement entropy for the ground state and show that all (1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in higher order than (1) and (2) do. With these results, we discuss how the ground state entanglement entropy in the continuum limit can be understood from the lattice ground state obtained in the HPE.

hep-th↗
arXiv2017

QCD Thermodynamics on the Lattice from the Gradient Flow

To obtain the precise values of the bulk quantities and transport coefficients in quark-gluon-plasma phase, we propose that a direct calculation of the renormalized energy-momentum tensor (EMT) on the lattice using the gradient flow. From one-point function of EMT, authors in Ref.[1] obtained the interaction measure and thermal entropy. The results are consistent with the one obtained by the integral method. Based on the success, we try to measure the two-point function of EMT, which is related to the transport coefficients. Advantages of our method are (1) a clear signal because of the smearing effects of the gradient flow and (2) no need to calculate the wave function renormalization of EMT. In addition, we give a short remark on a comparison of the numerical cost between the positive- and adjoint-flow methods for fermions, needed to obtain the EMT in the (2+1) flavor QCD.

hep-lat↗
arXiv2017

Lambda-Nucleon and Sigma-Nucleon interactions from lattice QCD with physical masses

We present our recent study on baryon-baryon ($BB$) interactions from lattice QCD with almost physical quark masses corresponding to $(m_π,m_K)\approx(146,525)$ 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 $ΞΞ$ 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 $ΛN$, $ΣN$ (both the isospin $I=1/2, 3/2$) and their coupled-channel systems.

hep-lat↗
arXiv2017

Baryon interactions from lattice QCD with physical masses -- Overview and $S = 0, -4$ sectors --

Nuclear forces and hyperon forces are studied by lattice QCD. Simulations are performed with (almost) physical quark masses, $m_π\simeq 146$ 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-$Ξ$ 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.

hep-lat↗