arXiv subjects

Sinya Aoki

Publications and source records attributed to Sinya Aoki.

At least 145 records · Page 8Linked to original sources

arXiv2012

Chiral symmetry restoration and eigenvalue density of Dirac operator

We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings to avoid possible ultra-violet(UV) divergences. Studying multi-point correlation functions in various channels in the thermodynamical limit, we obtain stronger constraints than those found in the previous studies that not only the eigenvalue density at the origin but also 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.

hep-lat↗

arXiv2012

Phase structure of finite density QCD with a histogram method

We study the phase structure of QCD in the $T-μ$ plane using a histogram method and the reweighting technique by performing phase quenched simulations of two-flavor QCD with RG-improved gauge action and O($a$) improved Wilson quark action. Taking the effects of the complex phase of the quark determinant using the cumulant expansion method, we calculate the probability distribution function of plaquette and phase-quenched determinant as a function of $T$ and $μ$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function.

hep-lat↗

arXiv2012

The neutral pion decay and the chiral anomaly on the lattice

We perform a lattice QCD calculation of the π^0\toγγtransition form factor and the associated decay width. We use a Euclidean time integral of the relevant three-point function to compute the decay amplitude for two-photon final state, which is a non-QCD state. We use the all-to-all quark propagator technique to carry out this integral as well as to include the disconnected quark diagram contributions. We execute the calculation using the overlap fermion formulation, which ensures the exact chiral symmetry on the lattice and produces the chiral anomaly through the Jacobian of the chiral transformation. We examine various sources of systematic effects except for possible discretization effect. Our final results for the form factor and the decay width reproduce the ABJ anomaly in the chiral limit and agree with the experimental measurements at the physical pion mass with a precision of a few percent.

hep-lat↗

arXiv2012

Two-photon decay of the neutral pion in lattice QCD

We perform non-perturbative calculation of the π^0 to γγ transition form factor and the associated decay width using lattice QCD. The amplitude for two-photon final state, which is not an eigenstate of QCD, is extracted through an Euclidean time integral of the relevant three-point function. We utilize the all-to-all quark propagator technique to carry out this integral as well as to include the disconnected quark diagram contributions. The overlap fermion formulation is employed on the lattice to ensure exact chiral symmetry on the lattice. After examining various sources of systematic effects except for possible discretization effect, we obtain Γ=7.83(31)(49) eV for the pion decay width, where the first error is statistical and the second is our estimate of the systematic error.

hep-lat↗

arXiv2012

Toward an understanding of short distance repulsions among baryons in QCD -- NBS wave functions and operator product expansion --

We report on our recent attempts to determine the short distance behaviors of general 2-baryon and 3-baryon forces, which are defined from the Nambu-Bethe-Salpeter(NBS) wave function, by using the operator product expansion and a renormalization group analysis in QCD. We have found that the repulsion at short distance increases as the number of valence quarks increases or when the number of different flavors involved decreases. This global tendency suggests a Pauli suppression principle among quark fields at work.

hep-lat↗

arXiv2012

Lattice QCD approach to Nuclear Physics

We review recent progress of the HAL QCD method which was recently proposed to investigate hadron interactions in lattice QCD. The strategy to extract the energy-independent non-local potential in lattice QCD is explained in detail. The method is applied to study nucleon-nucleon, nucleon-hyperon, hyperon-hyperon and meson-baryon interactions. Several extensions of the method are also discussed.

hep-lat↗

arXiv2012

Topological susceptibility and axial symmetry at finite temperature

We consider the simulation of finite temperature QCD with two flavors of dynamical overlap fermions in order to study the suppression of the axial U(1) symmetry breaking at the chiral phase transition point. As a preliminary study, pure gauge simulations are performed to investigate how fixing the topology affects physical quantities like the topological susceptibility, $χ_t$, at finite temperature, showing that it is possible to reconstruct known results from the fixed topology sector. First results on the degeneracy of meson correlators in the high temperature QGP sector are shown.

hep-lat↗

arXiv2012

Matrix Theory for Baryons: An Overview of Holographic QCD for Nuclear Physics

We provide, for non-experts, a brief overview of holographic QCD and a review of a recent proposal of matrix-description of multi-baryon systems in holographic QCD. Based on the matrix model, we derive the baryon interaction at short distances in multi-flavor holographic QCD. We show that there is a very universal repulsive core of inter-baryon forces for generic number of flavors. This is consistent with a recent lattice QCD analysis for N_f = 2, 3 where repulsive core looks universal. We also provide a comparison of our results with the lattice QCD and the operator product expansion (OPE) analysis.

hep-th↗

arXiv2012

Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice

Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave-function are utilized to extract non-local hadron-hadron potential. "The ground state saturation", which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the 1S_0 channel.

hep-lat↗

arXiv2012

Numerical study of QCD phase diagram at high temperature and density by a histogram method

We study the QCD phase structure at high temperature and density adopting a histogram method. Because the quark determinant is complex at finite density, the Monte-Carlo method cannot be applied directly. We use a reweighting method and try to solve the problems which arise in the reweighting method, i.e. the sign problem and the overlap problem. We discuss the chemical potential dependence of the probability distribution function in the heavy quark mass region and examine the applicability of the approach in the light quark region.

hep-lat↗

arXiv2012

Exploring Three-Nucleon Forces in Lattice QCD

Three-nucleon forces (3NF) are investigated from two-flavor lattice QCD simulations. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF in the same framework. As a first exploratory study, we extract 3NF in which three nucleons are aligned linearly with an equal spacing. This is the simplest geometrical configuration which reduces the huge computational cost of calculating the NBS wave function. Quantum numbers of the three-nucleon system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel). Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m_π= 1.13 GeV. We find repulsive 3NF at short distance in the triton channel. Several sources of systematic errors are also discussed.

hep-lat↗

arXiv2012

Two-Baryon Potentials and H-Dibaryon from 3-flavor Lattice QCD Simulations

Baryon-baryon potentials are obtained from 3-flavor QCD simulations with the lattice volume L ~ 4 fm, the lattice spacing a ~ 0.12 fm, and the pseudo-scalar-meson mass M_ps =469 - 1171 MeV. The NN scattering phase shift and the mass of H-dibaryon in the flavor SU(3) limit are extracted from the resultant potentials by solving the Schrodinger equation. The NN phase shift in the SU(3) limit is shown to have qualitatively similar behavior as the experimental data. A bound H-dibaryon in the SU(3) limit is found to exist in the flavor-singlet J^P=0^+ channel with the binding energy of about 26 MeV for the lightest quark mass M_ps = 469 MeV. Effect of flavor SU(3) symmetry breaking on the H-dibaryon is estimated by solving the coupled-channel Schrodinger equation for Lambda Lambda - N Xi - Sigma Sigma with the physical baryon masses and the potential matrix obtained in the SU(3) limit: a resonant H-dibaryon is found between Lambda Lambda and N Xi thresholds in this treatment.

hep-lat↗

arXiv2011

Revisiting symmetries of lattice fermions via spin-flavor representation

Employing the spin-flavor representation, we investigate the structures of the doubler-mixing symmetries and the mechanisms of their spontaneous breakdown in four types of lattice fermion formulation. We first revisit the $U(4)\timesU(4)A$ symmetries of the naive fermion with the vanishing bare mass m, and re-express them in terms of the spin-flavor representation. We apply the same method to the Wilson fermion, which possesses only the U(1) vector symmetry for general values of m. For a special value of m, however, there emerges an additional U(1) symmetry to be broken by pion condensation. We also explore two types of minimally doubled fermion, and discover a similar kind of symmetry enhancement and its spontaneous breakdown.

hep-lat↗

arXiv2011

Short distance repulsion in 3 nucleon forces from perturbative QCD

We investigate the short distance behavior of 3 nucleon forces (3NF) defined through Nambu--Bethe--Salpeter wave functions, using the operator product expansion(OPE) and calculating anomalous dimensions of 9--quark operators in perturbative QCD. As is the case of NN forces previously considered, we show that 3NF have repulsions at short distance at 1--loop, which becomes exact in the short distance limit thanks to the asymptotic freedom of QCD. Moreover these behaviors are universal in the sense that they do not depend on the energy of the NBS wave function for 3 nucleons.

hep-lat↗

arXiv2011

Chiral perturbation theory for twisted mass QCD at small quark mass

We study the lattice cutoff ($a$) and quark mass dependences of pion masses and decay constants in the $N_f = 2$ twisted mass QCD, using the Wilson chiral perturbation theory to the next leading order (NLO). In order to investigate the region near zero quark mass, we introduce the power counting scheme where $O(a^2, am)$ terms are included in the tree level effective Lagrangian. At the NLO of this power counting scheme, we calculate the charged pion mass and decay constant as a function of the lattice cutoff as well as the twisted quark mass at the maximal twist. In this paper, we adopt two different definitions for the maximal twist. We confirm that the difference between the two appears as the $O(a^2)$ effects so that the automatic $O(a)$ improvement is realized for both definitions.

hep-lat↗

arXiv2011

Hadron interactions in lattice QCD

Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract $NN$ potentials, hyperon potentials and the meson-baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.

hep-lat↗

arXiv2011

Interpolation between the epsilon and p regimes

We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional epsilon and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum modes of Nambu-Goldstone bosons are, however, treated separately and partly integrated out to all orders as in the epsilon expansion. In this new scheme, the theory remains infra-red finite even in the chiral limit, while the chiral-logarithmic effects are kept present. We calculate the two-point function in the pseudoscalar channel and show that the correlator has a constant contribution in addition to the conventional hyperbolic cosine function of time t. This constant term rapidly disappears in the p regime but it is indispensable for a smooth convergence of the formula to the epsilon regime result. Our calculation is useful to precisely estimate the finite volume effects in lattice QCD simulations on the pion mass Mpi and kaon mass MK, as well as their decay constants Fpi and FK.

hep-lat↗

arXiv2011

Extraction of Hadron Interactions above Inelastic Threshold in Lattice QCD

We propose a new method to extract hadron interactions above inelastic threshold from the Nambu-Bethe-Salpter amplitude in lattice QCD. We consider the scattering such as $A+B\rightarrow C+D$, where $A,B,C,D$ are names of different 1-particle states. An extension to cases where particle productions occur during scatterings is also discussed.

hep-lat↗