Full QCD Simulations Research Articles

Chiral magnetic effect in a lattice model

We study analytically the one-loop contribution to the chiral magnetic effect (CME) using lattice regularization with a Wilson fermion field. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical value of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher-order corrections from QCD dynamics is also assessed.

Justification of the complex Langevin method with the gauge cooling procedure

Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus we demonstrate explicitly that the gauge cooling can be used as a viable technique to satisfy the convergence conditions for the complex Langevin method. We also discuss the "gauge cooling" in 0-dimensional systems such as vector models or matrix models.

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams

We study the possible significance of four-quark states in the iso-singlet scalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full lattice QCD simulations on an $8^3 \times 16$ lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetra-quark operators together with singly disconnected diagrams. In the computation of the singly disconnected diagrams we employ the $Z_2$-noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an essential role in propagators of tetraquark and molecular operators.

Progress in complex Langevin simulations of full QCD at non-zero density

Progress in the application of the complex Langevin method to full QCD at non-zero chemical potential is reported. The method evades the sign problem which makes naive simulations at nonzero density impossible. The procedure 'gauge cooling' is used to stabilize the simulations at small enough lattice spacings. The method allows simulations also at high densities, all the way up to saturation. Simulations in a systematic hopping parameter expansion are also performed and good convergence is observed, validating the full as well as the expanded simulations.

Heavy dense QCD and nuclear matter from an effective lattice theory

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, \kappa, whose action is correct to \kappa^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as gap between the onset of isospin and baryon condensation.

Bottomonium from lattice QCD as a probe of the Quark-Gluon Plasma

We study the temperature dependence of bottomonium for temperatures in the range 0.4Te < T < 2.1Tc, using non-relativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for Nf = 2 light flavors. We consider the behaviour of the correlators in Euclidean space, we analyze the associated spectral functions and we study the dependence on the momentum. Our results are amenable to a successful comparison with effective field theories. They help build a coherent picture of the behaviour of bottomonium in the plasma, consistent which the current LHC results.

Charmonium potentials: Matching perturbative and lattice QCD

Central and spin–spin potentials for charmonium, constructed from Nambu–Bethe–Salpeter amplitudes in lattice simulations of full QCD, are matched with results from perturbative QCD at an appropriate distance scale. This matching is made possible by defining the perturbative potentials through Fourier transforms with a low-momentum cutoff. The central (spin-independent) potential is compared with potentials derived from an expansion in powers of the inverse quark mass. A well-controlled continuation of the charmonium spin–spin potential from lattice QCD to short distances is performed. The mass splittings of the charmonium singlet and triplet states below the open charm threshold, obtained from the matched spin–spin potential, are in good agreement with the experimental values.

Hadron interactions from lattice QCD

After a brief review on the recent progress in lattice QCD simulations, we discuss the nucleon and hyperon interactions obtained from the Nambu–Bethe–Salpeter amplitude on the lattice. Bound H-dibaryon in the flavor-SU(3) limit of QCD is also investigated on the basis of 3-flavor full QCD simulations.

BoundHDibaryon in Flavor SU(3) Limit of Lattice QCD

The flavor-singlet H dibaryon, which has strangeness -2 and baryon number 2, is studied by the approach recently developed for the baryon-baryon interactions in lattice QCD. The flavor-singlet central potential is derived from the spatial and imaginary-time dependence of the Nambu-Bethe-Salpeter wave function measured in N(f)=3 full QCD simulations with the lattice size of L≃2,3,4 fm. The potential is found to be insensitive to the volume, and it leads to a bound H dibaryon with the binding energy of 30-40 MeV for the pseudoscalar meson mass of 673-1015 MeV.

Bottomonium above Deconfinement in Lattice Nonrelativistic QCD

We study the temperature dependence of bottomonium for temperatures in the range 0.4T(c) < T < 2.1T(c), using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for Nf = 2 light flavors on a highly anisotropic lattice. We find that the Υ is insensitive to the temperature in this range, while the χb propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behavior consistent with nearly free dynamics at T ≃ 2T(c).

Critical slowing down and error analysis in lattice QCD simulations

We study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical critical exponent of about 5 in pure gauge theory. We also consider Wilson loops which we can demonstrate to decouple from the modes which slow down the topological charge. Quenched observables are studied and a comparison to simulations of full QCD is made. In order to deal with the slow modes in the simulation, we propose a method to incorporate the information from slow observables into the error analysis of physical observables and arrive at safer error estimates.

Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice

We investigate baryon-baryon (BB) interactions in the 3-flavor full QCD simulations with degenerate quark masses for all flavors. The BB potentials in the orbital S-wave are extracted from the Nambu-Bethe-Salpeter wave functions measured on the lattice. We observe strong flavor-spin dependences of the BB potentials at short distances. In particular, a strong repulsive core exists in the flavor-octet and spin-singlet channel (the 8s representation), while an attractive core appears in the flavor singlet channel (the 1 representation). We discuss the relation of such flavor-spin dependence with the Pauli exclusion principle at the quark level. The possible existence of an H-dibaryon resonance above the ΛΛ threshold is also discussed.

K N Potential and Θ+ in Lattice QCD

We study the s-wave KN interactions in the isospin I = 0, 1 channels and associated exotic state Theta+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to mpi = 871 MeV. The s-wave KN potentials are obtaine d from the Bethe-Salpeter amplitudes. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I = 1 potential. The I = 0 potential is found to have attractive well at mid range. The KN scattering phase shift s are calculated and compared with the experimental data.

Kaon-Nucleon potential from lattice QCD

We study the KN interactions in the I(J^{\pi})=0(1/2^-) and 1(1/2^-) channels and associated exotic state \Theta^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_{\pi}=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 potential is found to have attractive well at mid range. From these potentials, the $KN$ scattering phase shifts are calculated and compared with the experimental data.

FROM LATTICE QCD TO NUCLEAR FORCE

After a brief introduction to the phenomenological nucleon-nucleon (NN) potentials, the basic formulation of deriving the NN potential from lattice QCD simulations on the basis of the equal-time Bethe-Salpeter wave function is presented. The resultant non-local NN potential and its derivative expansion are discussed. Ongoing and planned studies on the lattice with quenched and full QCD simulations are summarized.

SOME RECENT LATTICE QCD RESULTS FROM THE CSSM

Recent CSSM Lattice Collaboration studies of hadron electromagnetic structure and the exotic hadron spectrum are highlighted. The momentum dependence of quark and gluon propagators revealed in lattice simulations of full QCD are also illustrated.

2 + 1 flavor simulations of QCD with improved staggered quarks

The MILC collaboration has been performing realistic simulations of full QCD with 2+1 flavors of improved staggered quarks. Our simulations allow for controlled continuum and chiral extrapolations. I present results for the light pseudoscalar sector: masses and decay constants, quark masses and Gasser-Leutwyler low-energy constants. In addition I will present some results for heavy-light mesons, decay constants and semileptonic form factors, obtained in collaboration with the HPQCD and Fermilab lattice collaborations. Such calculations will help in the extraction of CKM matrix elements from experimental measurements.

Two-flavor QCD thermodynamics using anisotropic lattices

Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale-setting simulations, which determine the Karsch coefficients, allows for the calculation of the equation of state at finite temperatures.

Finite-size effects in lattice QCD with dynamical Wilson fermions

As computing resources are limited, choosing the parameters for a full lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible. Aiming to push unquenched simulations with the Wilson action towards the computationally expensive regime of small quark masses we address the question whether one can possibly save computing time by extrapolating results from small lattices to the infinite volume, prior to the usual chiral and continuum extrapolations. In the present work the systematic volume dependence of simulated pion and nucleon masses is investigated and compared with a long-standing analytic formula by L\"uscher and with results from chiral perturbation theory (ChPT). We analyze data from hybrid Monte Carlo simulations with the standard (unimproved) two-flavor Wilson action at two different lattice spacings of $a\ensuremath{\approx}0.08$ and 0.13 fm. The quark masses considered correspond to approximately 85% and 50% (at the smaller $a$) and 36% (at the larger $a$) of the strange quark mass. At each quark mass we study at least three different lattices with $L/a=10$ to 24 sites in the spatial directions ($L=0.85--2.08\text{ }\text{ }\mathrm{fm}$). We find that an exponential ansatz fits the volume dependence of the pion masses well, but with a coefficient about an order of magnitude larger than the theoretical leading-order prediction. In the case of the nucleon we observe a remarkably good agreement between our lattice data and a recent formula from relativistic baryon ChPT.

Meson-Meson Potentials from Lattice QCD and Inverse Scattering

Potentials between light-light and heavy-light mesons are computed from meson-meson Green’s functions in the framework of quenched lattice QCD with Kogut-Susskind fermions. Comparisons with a full QCD simulation and a simulation using an O(a 2) tree-level and tadpole improved gauge action show that dynamic quarks and lattice discretization errors have no drastic influence. Calculations from inverse scattering theory propose a similar shape for $$K\bar K$$ potentials, whereas a good qualitative agreement with ππ potentials could not be obtained.