arXiv subjects
Publications and source records attributed to Sinya Aoki.
We study the various head-on collisions of two bunches of D0-branes and their real-time evolution in the BFSS matrix model in classical limit. For a various matrix size N respecting the 't Hooft scaling, we find quantitative evidence for the formation of a single bound state of D0-branes at late time, which is matrix model thermalization and dual to the formation of a larger black hole.
We investigate the interaction between $Ω$ baryons in the $^1S_0$ channel from 2+1 flavor lattice QCD simulations. On the basis of the HAL QCD method, the $ΩΩ$ potential is extracted from the Nambu-Bethe-Salpeter wave function calculated on the lattice by using the PACS-CS gauge configurations with the lattice spacing $a\simeq 0.09$ fm, the lattice volume $L\simeq 2.9$ fm and the quark masses corresponding to $m_π\simeq 700$ MeV and $m_Ω\simeq 1970$ MeV. The $ΩΩ$ potential has a repulsive core at short distance and an attractive well at intermediate distance. Accordingly, the phase shift obtained from the potential shows moderate attraction at low energies. Our data indicate that the $ΩΩ$ system with the present quark masses may appear close to the unitary limit where the scattering length diverges.
We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2+1-flavor overlap fermion at pion masses m_pi = 380 and 290 MeV. By calculating the I = 1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the $Z_N$ gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the $Z_N$ gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
On the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon forces obtained from lattice QCD simulations, the properties of the medium-heavy doubly-magic nuclei such as 16^O and 40^Ca are investigated. We found that those nuclei are bound for the pseudo-scalar meson mass M_PS ~ 470 MeV. The mass number dependence of the binding energies, single-particle spectra and density distributions are qualitatively consistent with those expected from empirical data at the physical point, although these hypothetical nuclei at heavy quark mass have smaller binding energies than the real nuclei.
We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.
We investigate properties of the $N$(nucleon)-$Ω$(Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness $-3$ channel. We calculate the $NΩ$ potential through the equal-time Nambu-Bethe-Salpeter wave function in 2+1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively $\mathcal{O}(a)$ improved Wilson quark action at the lattice spacing $a\simeq 0.12$ fm on a (1.9 fm)$^{3}\times$ 3.8 fm lattice. The $ud$ and $s$ quark masses in our study correspond to $m_π= 875(1)$ MeV and $m_{K}= 916(1)$ MeV. At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances.By solving the Schrödinger equation with this potential, we find one bound state whose binding energy is $18.9(5.0)(^{+12.1}_{-1.8})$ MeV, where the first error is the statistical one, while the second represents the systematic error.
Recent progresses of lattice QCD studies for hadron spectroscopy and interactions are briefly reviewed. Some emphasis are given on a new proposal for a method, which enable us to calculate potentials between hadrons. As an example of the method, the extraction of nuclear potential in lattice QCD is discussed in detail.
We investigate some aspects of 2-flavor QCD with $m_u\not= m_d$ at low-energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at $m_u=0$ for the fixed $m_d\not=0$, the neutral pion mass becomes zero at two critical values of $m_u$, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the ChPT diverges at these two critical points. We briefly discuss a possibility that $m_u=0$ can be defined by the vanishing the "topological susceptibility. We finally analyze the case of $m_u=m_d=m$ with $θ=π$, which is equivalent to $m_u= - m_d=-m$ with $θ= 0$ by the chiral rotation. In this case, the $η$ condensation occurs at small $m$, violating the CP symmetry spontaneously. Deep in the $η$ condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small $m$ that $m_π^2 = O(m^2)$, which, however, is shown to be consistent with the chiral Ward-Takahashi identities.
Charmed tetraquarks $T_{cc}=(cc\bar{u}\bar{d})$ and $T_{cs}=(cs\bar{u}\bar{d})$ are studied through the S-wave meson-meson interactions, $D$-$D$, $\bar{K}$-$D$, $D$-$D^{*}$ and $\bar{K}$-$D^{*}$, on the basis of the (2+1)-flavor lattice QCD simulations with the pion mass $m_π \simeq $410, 570 and 700 MeV. For the charm quark, the relativistic heavy quark action is employed to treat its dynamics on the lattice. Using the HAL QCD method, we extract the S-wave potentials in lattice QCD simulations, from which the meson-meson scattering phase shifts are calculated. The phase shifts in the isospin triplet ($I$=1) channels indicate repulsive interactions, while those in the $I=0$ channels suggest attraction, growing as $m_π$ decreases. This is particularly prominent in the $T_{cc} (J^P=1^+,I=0)$ channel, though neither bound state nor resonance are found in the range $m_π =410-700$ MeV. We make a qualitative comparison of our results with the phenomenological diquark picture.
We extend the HAL QCD approach, with which potentials between two hadrons can be obtained in QCD at energy below inelastic thresholds, to inelastic and multi-particle scatterings. We first derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles, in terms of the one-shell $T$-matrix consrainted by the unitarity of quantum field theories. We show that its asymptotic behavior contains phase shifts and mixing angles of $n$ particle scatterings. This property is one of the essential ingredients of the HAL QCD scheme to define "potential" from the NBS wave function in quantum field theories such as QCD. We next construct energy independent but non-local potentials above inelastic thresholds, in terms of these NBS wave functions. We demonstrate an existence of energy-independent coupled channel potentials with a non-relativistic approximation, where momenta of all particles are small compared with their own masses. Combining these two results, we can employ the HAL QCD approach also to investigate inelastic and multi-particle scatterings.
In the previous work, we have shown that the SU(2) chiral symmetry recovered above the critical temperature gives a strong constraint on the Dirac eigenvalue spectrum and this constraint is strong enough for a set of anomalous U(1) chiral symmetry breaking operators to vanish in the thermodynamical and chiral limits. We use this condition as an input and impose a constraint on the Landau low energy effective theory of QCD. The only constraint we can set is that the mass splitting term between the pion and eta meson should vanish. All the singlet/non-singlet scalar/pseudo-scalar mesons contribute to the effective theory. We evaluate the renormalization group $β$-function for the effective theory using the $ε$-expansion at one loop level, but find no stable infra-red fixed point except for the trivial Gaussian one. The chiral phase transition seems to be of first order.
We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for the nucleon-nucleon potentials.
Quark mass dependence of the equation of state (EOS) for nucleonic matter is investigated, on the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon interaction extracted from lattice QCD simulations. We observe saturation of nuclear matter at the lightest available quark mass corresponding to the pseudoscalar meson mass ~ 469 MeV. Mass-radius relation of the neutron stars is also studied with the EOS for neutron-star matter from the same nuclear force in lattice QCD. We observe that the EOS becomes stiffer and thus the maximum mass of neutron star increases as the quark mass decreases toward the physical point.
We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles in quantum field theories. To deal with $n$-particles in the center of mass flame coherently, we introduce the Jacob coordinates of $n$ particles and then combine their $3(n-1)$ coordinates into the one spherical coordinate in $D=3(n-1)$ dimensions. We parametrize on-shell $T$-matrix for $n$-particle system of scalar fields at low energy, using the unitarity constraint of the $S$-matrix. We then express asymptotic behaviors of the NBS wave function for $n$ particles at low energy, in terms of parameters of $T$-matrix, and show that the NBS wave function carry the information of $T$-matrix such as phase shifts and mixing angles of the $n$-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of $n$-particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define "potential" from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCD's definition of potentials for 3 or more nucleons(baryons) in terms the NBS wave functions.
We examine the axial U(1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, (i.e.) the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a $16^3\times 8$ lattice with two flavors of dynamical quarks represented by the overlap fermion formalism. Chiral symmetry and its violation due to the axial anomaly is manifestly realized with this formulation, which is a prerequisite for the study of the effective restoration of the axial U(1) symmetry. In order to avoid discontinuity in the gauge configuration space, which occurs for the exactly chiral lattice fermions, the simulation is confined in a fixed topological sector. It induces finite volume effect, which is well described by a formula based on the Fourier transform from the $θ$-vacua. We confirm this formula at finite temperature by calculating the topological susceptibility in the quenched theory. Our two flavor simulations show degeneracy of the meson correlators and a gap in the Dirac operator spectral density, which implies that the axial U(1) symmetry is effectively restored in the chirally symmetric phase.
We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, which ensures the exact "chiral" symmetry at finite lattice spacings. Studying multi-point correlation functions in various channels and taking their thermodynamical limit (and then taking the chiral limit), we obtain stronger constraints than those found in the previous studies: both the eigenvalue density at the origin and its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons, suggesting that the 2nd order chiral phase transition with the O(4) scaling is not realized in 2 flavor QCD. Possible lattice artifacts when non-chiral lattice Dirac operator is employed are briefly discussed.
We construct energy independent but non-local potentials above inelastic thresholds, in terms of Nambu-Bethe-Salpeter wave functions defined in quantum field theories such as QCD. As an explicit example, we consider NN --> NN + n pi scattering processes for n=0,1,2,.... We show an existence of energy-independent coupled channel potentials with a non-relativistic approximation, where momenta of all particles are small compared with their own masses. In the case of two-body inelastic scatterings such as Lambda Lambda --> Lambda Lambda, N Xi, Sigma Sigma, on the other hand, we show that energy-independent potentials can be constructed without relying on non-relativistic approximations. We also propose a method to extract these potentials using time-dependence of general correlation functions.