Systems In Lattice QCD Research Articles

Consistency between L\xfcscher\u2019s finite volume method and HAL QCD method for two-baryon systems in lattice QCD

There exist two methods to study two-baryon systems in lattice QCD: the direct method which extracts eigenenergies from the plateaux of the temporal correlation function and the HAL QCD method which extracts observables from the non-local potential associated with the tempo-spatial correlation function. Although the two methods should give the same results theoretically, there have been reported qualitative difference for observables from lattice QCD simulations. Recently, we pointed out in [1, 2] that the separation of the ground state from the excited states is crucial to obtain sensible results in the former, while both states provide useful signals for observables in the latter. In this paper, we identify the contribution of each state in the direct method by decomposing the two-baryon correlation functions into the finite-volume eigenmodes obtained from the HAL QCD method. As in our previous studies, we consider the ΞΞ system in the 1S0 channel at mπ = 0.51 GeV in (2+1)-flavor lattice QCD using the wall and smeared quark sources with spatial extents, La = 3.6, 4.3, 5.8 fm. We demonstrate that the “pseudo-plateau” at early time slices (t = 1 ∼ 2 fm) from the smeared source in the direct method indeed originates from the contamination of the excited states, and the plateau with the ground state saturation is realized only at t > 5 ∼ 15 fm corresponding to the inverse of the lowest excitation energy. We also demonstrate that the two-baryon operator can be optimized by utilizing the finite-volume eigenmodes, so that (i) the finite-volume energy spectra from the HAL QCD method agree with those from the temporal correlation function with the optimized operators and (ii) the correct finite-volume spectra would be accessed in the direct method only if highly optimized operators are employed. Thus we conclude that the long-standing issue on the consistency between Lüscher’s finite volume method and the HAL QCD method for two baryons is now resolved at least for this particular system considered here: they are consistent with each other quantitatively only if the excited contamination is properly removed in the former.

Tetraquark and Pentaquark Systems in Lattice QCD

Motivated by the recent experimental discoveries of multi-quark candidates, e.g., the $\Theta^+(1540)$, we study multi-quark systems in lattice QCD. First, we perform accurate mass measurements of low-lying 5Q states with $J=1/2$ and I=0 in both positive- and negative-parity channels in anisotropic lattice QCD. The lowest positive-parity 5Q state is found to have a large mass of about 2.24GeV after the chiral extrapolation. To single out the compact 5Q state from $NK$ scattering states, we develop a new method with the hybrid-boundary condition (HBC), and find no evidence of the compact 5Q state below 1.75GeV in the negative-parity channel. Second, we perform the first study of the multi-quark potential in lattice QCD to clarify the inter-quark interaction in multi-quark systems. The 5Q potential $V_{\rm 5Q}$ for the QQ-${\rm \bar{Q}}$-QQ system is found to be well described by the ``OGE Coulomb plus multi-Y Ansatz": the sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term based on the flux-tube picture. The 4Q potential $V_{\rm 4Q}$ for the QQ-${\rm \bar{Q}\bar{Q}}$ system is also described by the OGE Coulomb plus multi-Y Ansatz, when QQ and $\rm \bar Q \bar Q$ are well separated. The 4Q system is described as a "two-meson" state with disconnected flux tubes, when the nearest quark and antiquark pair is spatially close. We observe a lattice-QCD evidence for the ``flip-flop'', i.e., the flux-tube recombination between the connected 4Q state and the ``two-meson'' state. On the confinement mechanism, the lattice QCD results indicate the flux-tube-type linear confinement in multi-quark hadrons.

Coupled-channel approach to strangeness S = -2 baryon-bayron interactions in lattice QCD

The baryon-baryon interactions with strangeness S = -2 with the flavor SU(3) breaking are calculated for the first time by using the HAL QCD method extended to coupled channel system in lattice QCD. The potential matrices are extracted from the Nambu-Bethe-Salpeter wave functions obtained by the 2+1 flavor gauge configurations of CP-PACS/JLQCD Collaborations with a physical volume of 1.93 fm cubed and with m_pi/m_K = 0.96, 0.90, 0.86. The spatial structure and the quark mass dependence of the potential matrix in the baryon basis and in the SU(3) basis are investigated.

Multi-hadron systems in lattice QCD

I present an overview of recent progress in the study of multi-hadron systems in lattice QCD. After reviewing the recent developments that are beginning to enable nuclear physics to be studied from the underlying theory of the Standard Model, I discuss the recent results that have been obtained in multi-hadron systems. I also explore the difficulties particular to lattice QCD calculations of such systems and emphasise the issues that remain to be resolved.

Variational study of the flux tube recombination in the two quarks and two antiquarks system in lattice QCD

The color fields in a system composed by two static quarks and two static antiquarks are studied. We use a variational method, to probe not only the ground state but also the first excited state. These results permit us to observe and interpret the flux tube recombination in the mesons-to-mesons and the tetraquark-to-mesons transitions, for both states. The results are compared with previous results for the static potential and the Casimir scaling predictions.

Prediction of the BottomoniumD-Wave Spectrum from Full Lattice QCD

We calculate the full spectrum of D-wave states in the Υ system in lattice QCD for the first time, by using an improved version of nonrelativistic QCD on coarse and fine "second-generation" gluon field configurations from the MILC Collaboration that include the effect of up, down, strange, and charm quarks in the sea. By taking the 2S-1S splitting to set the lattice spacing, we determine the (3)D2-1S splitting to 2.3% and find agreement with experiment. Our prediction of the fine structure relative to the (3)D2 gives the (3)D3 at 10.181(5) GeV and the (3)D1 at 10.147(6) GeV. We also discuss the overlap of (3)D1 operators with (3)S1 states.

Two-nucleon bound states in quenched lattice QCD

We address the issue of bound state in the two-nucleon system in lattice QCD. Our study is made in the quenched approximation at the lattice spacing of a = 0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state and the free two-nucleon state by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads us to the conclusion that the measured ground states for not only spin triplet but also singlet channels are bounded. Furthermore the existence of the bound state is confirmed by investigating the properties of the energy for the first excited state obtained by 2x2 diagonalization method. The scattering lengths for both channels are evaluated by applying the finite volume formula derived by Luscher to the energy of the first excited states.

Multipion Systems in Lattice QCD and the Three-Pion Interaction

The ground-state energies of 2, 3, 4, and 5 pi(+)'s in a spatial volume V approximately (2.5 fm)(3) are computed with lattice QCD. By eliminating the leading contribution from three-pi(+) interactions, particular combinations of these n-pi(+) ground-state energies provide precise extractions of the pi(+)pi(+) scattering length in agreement with that obtained from calculations involving only two pi(+)'s. The three-pi(+) interaction can be isolated by forming other combinations of the n-pi(+) ground-state energies. We find a result that is consistent with a repulsive three-pi(+) interaction for m_(pi) less, similar352 MeV.

Electroweak properties of two-nucleon systems in lattice QCD

We discuss a method by which lattice QCD simulations can be used to determine the electroweak properties of two-nucleon systems. In particular, we demonstrate that numerical calculations of two-particle energy levels in a finite volume immersed in background electroweak fields can determine the deuteron magnetic moment, the cross-section for thermal neutron capture n p → d γ and the cross-section for neutrino breakup of the deuteron, ν d → n p ν . The last of these processes is only poorly constrained experimentally and will provide a large source of uncertainty in future extractions of neutrino mass and mixing parameters from the Sudbury Neutrino Observatory.

Detailed analysis of the gluonic excitation in the three-quark system in lattice QCD

We study the excited-state potential and the gluonic excitation in the static three-quark (3Q) system using $\mathrm{S}\mathrm{U}(3)$ lattice QCD with ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ at $\ensuremath{\beta}=5.8$ and 6.0 at the quenched level. For about 100 different patterns of spatially-fixed 3Q systems, we accurately extract the excited-state potential ${V}_{3\mathrm{Q}}^{\mathrm{e}.\mathrm{s}.}$ together with the ground-state potential ${V}_{3\mathrm{Q}}^{\mathrm{g}.\mathrm{s}.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks. The gluonic excitation energy $\ensuremath{\Delta}{E}_{3\mathrm{Q}}\ensuremath{\equiv}{V}_{3\mathrm{Q}}^{\mathrm{e}.\mathrm{s}.}\ensuremath{-}{V}_{3\mathrm{Q}}^{\mathrm{g}.\mathrm{s}.}$ is found to be about 1 GeV at the typical hadronic scale. This large gluonic excitation energy is conjectured to give a physical reason of the success of the quark model for low-lying hadrons even without explicit gluonic modes. We investigate the functional form of $\ensuremath{\Delta}{E}_{3\mathrm{Q}}$ in terms of the 3Q location. The lattice data of $\ensuremath{\Delta}{E}_{3\mathrm{Q}}$ are relatively well reproduced by the ``inverse Mercedes Ansatz'' with the ``modified Y-type flux-tube length,'' which indicates that the gluonic excitation mode is realized as a complicated bulk excitation of the whole 3Q system.

An improvement in DS-BiCGstab( l) and its application for linear systems in lattice QCD

An improved algorithm of the DS-BiCGstab( l) method (IDSL) is proposed. The DS-BiCGstab( l) method (DSL) selects the value of l dynamically for the BiCGstab( l) method, but it does not always select a proper value for l in terms of its convergence. From this viewpoint, this research has focused on converging behavior with the BiCGstab( l) method, and the DSL has been improved. Several numerical results in lattice QCD show that this improvement leads dynamic selection of l to a value relevant to the convergence than the DSL without a substantial increase in the calculating costs.

Lattice QCD simulation of meson exchange forces.

We present the formalism for investigating the {ital {bar Q}q{bar Q}q} system in lattice QCD. This system serves as a model for describing exchange forces between heavy, static hadrons. We use this formalism to calculate the exchange potential from gauge configurations which incorporate the effects of dynamical quarks. Our data can be interpreted as giving preliminary results on the range of the nuclear force.