Potential In Lattice QCD Research Articles

Phenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets

The study of heavy quarkonium suppression in heavy-ion collisions represents an important source of information about the properties of the quark-gluon plasma produced in such collisions. In a previous paper, we have considered how to model the evolution of a quarkonium in such a way that the solution of the resulting equations evolves toward the correct thermal equilibrium distribution for a homogeneous and static medium. We found that it is crucial to take into account the energy gap between singlet and octet configurations when the temperature is not much greater than this energy gap. In this paper, we explore in more detail the phenomenological consequences of this observation in the more realistic situation of an expanding system. We consider two different scenarios, based on the same approximation scheme, but on different choices of parameters. In the first case, we rely on a Hard Thermal Loop approximation, while the second case is based on a recent determination of the static potential in lattice QCD. In both cases, we compute the decay width and the nuclear modification factor, both taking the energy gap into account and ignoring it. We find that the impact on the predictions is as large in the expanding medium as it is in the static case. Our conclusion is that this energy gap should be taken into account in phenomenological studies.

Lattice QCD and Baryon-Baryon Interactions: HAL QCD Method

In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories such as QCD. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we formulate a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the L\"uscher's formula. We give several theoretical and numerical evidences that the conventional method combined with the naive plateau fitting for the finite volume energies in the literature so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious problem can be avoided in the HAL QCD method by defining the potential in an energy-independent way. We also discuss systematics of the HAL QCD method, in particular errors associated with a truncation of the derivative expansion. Thirdly, we present several results obtained from the HAL QCD method, which include (central) nuclear force, tensor force, spin-orbital force, and three nucleon force. We finally show the latest results calculated at the nearly physical pion mass, $m_\pi \simeq 146$ MeV, including hyperon forces which lead to form $\Omega\Omega$ and $N\Omega$ dibaryons.

ΛΛ and NΞ interactions from lattice QCD near the physical point

The S-wave ΛΛ and NΞ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point (mπ≃146MeV and mK≃525MeV). Lattice QCD potentials in four different spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The ΛΛ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The NΞ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the NΞ system near unitarity. Relevance to the strangeness = −2 hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed.

Phenomenological view on baryon-baryon potentials from lattice QCD simulations

A qualitative discussion on the range of the potentials as they result from the phenomenological meson-exchange picture and from lattice simulations by the HAL QCD Collaboration is presented. For the former pion- and/or $\eta$-meson exchange are considered together with the scalar-isoscalar component of correlated $\pi\pi /K \bar K$ exchange. It is observed that the intuitive expectation for the behavior of the baryon-baryon potentials for large separations, associated with the exchange of one and/or two pions, does not always match with the potentials extracted from the lattice simulations. Only in cases where pion exchange provides the longest ranged contribution, like in the $\Xi N$ system, a reasonable qualitative agreement between the phenomenological and the lattice QCD potentials is found for baryon-baryon separations of $r \gtrsim 1$ fm. For the $\Omega N$ and $\Omega\Omega$ interactions where isospin conservation rules out one-pion exchange a large mismatch is observed, with the potentials by the HAL QCD Collaboration being much longer ranged and much stronger at large distances as compared to the phenomenological expectation. This casts some doubts on the applicability of using these potentials in few- or many-body systems.

Doubly heavy tetraquark resonances in lattice QCD

We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. We compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for l = 1, decaying into two B mesons, with quantum numbers I(JP) = 0(1−), mass and decay width .

Recent Applications of Self-Consistent Green’s Function Theory to Nuclei

We discuss recent ab initio calculations based on self-consistent Green’s function theory. It is found that a simple extension of the formalism to account for two-nucleon scattering outside the model space allows to calculate non-soft interactions. With this, it is possible to make predictions for Lattice QCD potentials, obtained so far at pion masses of mπ = 0.47 GeV/c2. More traditional calculations that use saturating chiral EFT forces yield a good description of nuclear responses and nucleon knockout spectroscopy.

ρ resonance from the I = 1 ππ potential in lattice QCD

We calculate the phase shift for the I = 1 ππ scattering in 2+1 flavor lattice QCD at mπ = 410 MeV, using all-to-all propagators with the LapH smearing. We first investigate the sink operator independence of the I = 2 ππ scattering phase shift to estimate the systematics in the LapH smearing scheme in the HAL QCD method at mπ = 870 MeV. The difference in the scattering phase shift in this channel between the conventional point sink scheme and the smeared sink scheme is reasonably small as long as the next-toleading analysis is employed in the smeared sink scheme with larger smearing levels. We then extract the I = 1 ππ potential with the smeared sink operator, whose scattering phase shift shows a resonant behavior (ρ resonance). We also examine the pole of the S-matrix corresponding to the ρ resonance in the complex energy plane.

Tetraquark resonances computed with static lattice QCD potentials and scattering theory

We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. As a proof of concept we focus on systems with isospin I = 0, but consider different relative angular momenta l of the heavy b quarks. We compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for l = 1, decaying into two B mesons, with quantum numbers I(JP) = 0(1−), mass [see formula in PDF] MeV and decay width [see formula in PDF] MeV.

Udb¯b¯ tetraquark resonances with lattice QCD potentials and the Born-Oppenheimer approximation

We study tetraquark resonances with lattice QCD potentials computed for a static bbar bbar pair in the presence of two lighter quarks u d, the Born-Oppenheimer approximation and the emergent wave method. As a proof of concept we focus on the system with isospin I = 0, but consider different relative angular momenta l of the heavy quarks bbar bbar. For l=0 a bound state has already been predicted with quantum numbers I(JP) = 0(1+). Exploring various angular momenta we now compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a tetraquark resonance for l =1, decaying into two B mesons, with quantum numbers I(JP) = 0(1-), mass m = 10 \, 576^{+4}_{-4} MeV} and decay width Gamma = 112^{+90}_{-103} MeV.

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.

Lattice quantum chromodynamical 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.

Phase of quark determinant in lattice QCD with finite chemical potential

We investigate the phase of the quark determinant with finite chemical potential in lattice QCD using both analytic and numerical methods. Applying the winding expansion and the hopping parameter expansion to the logarithm of the determinant, we show that the absolute value of the phase has an upper bound that grows with the spatial volume but decreases exponentially with an increase in the temporal extent of the lattice. This analytic but approximate result is confirmed with a numerical study in four-flavor QCD in which the phase is calculated exactly. Since the phase is well controlled on lattices with larger time extents, we try the phase reweighting method in a region beyond $\ensuremath{\mu}/T=1$ where the Taylor expansion method cannot be applied. Working in four-flavor QCD, we find a first-order like behavior on a ${6}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice at $\ensuremath{\mu}/T\ensuremath{\approx}0.8$ which was previously observed by the Kentucky group with the canonical method. We also show that the winding expansion has a nice convergence property beyond $\ensuremath{\mu}/T=1$. We expect that this expansion is useful to study the high density region of the QCD phase diagram at low temperatures.

First study of the three-gluon static potential in lattice QCD

We estimate the potential energy for a system of three static gluons in lattice QCD. This is relevant for the different models of three-body glueballs that have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different color structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is performed in a ${24}^{3}\ifmmode\times\else\texttimes\fi{}48$ periodic Lattice, with $\ensuremath{\beta}=6.2$ and $a\ensuremath{\sim}0.072\text{ }\text{ }\mathrm{fm}$.

“Gluelump” spectrum and adjoint source potential in lattice QCD 3

We calculate the potential between “quarks” which are in the adjoint representation of SU(2) color in the three-dimensional lattice theory. We work in the scaling region of the theory and at large quark separations R. We also calculate the masses M Qg of color-singlet bound states formed by coupling an adjoint quark to adjoint glue (“gluelumps”). Good scaling behavior is found for the masses of both magnetic (angular momentum J = 0) and electric ( J = 1) gluelumps, and the magnetic gluelump is found to be the lowest-lying state. It is naively expected that the potential for adjoint quarks should saturate above a separation R scr where it becomes energetically favorable to produce a pair of gluelumps. We obtain a good estimate of the naive screening distance R scr. However we find little evidence of saturation in the potential out to separations R of about 1.5 R scr.

Improved determination of the heavy-quark potential in lattice QCD.

A new iterative procedure in fitting data is proposed which can properly correct small nonlinear effects. Applying this procedure to fit the Polyakov loop correlation functions previously obtained in lattice QCD simulations, we are able to eliminate the finite-size boundary effects and obtain the quark potential functions themselves, instead of just parameters for the potentials. The quality of the fits is improved significantly. The potential functions obtained at $\ensuremath{\beta}=6.0\ensuremath{-}6.2$ scale in fine detail, providing important further support of the scaling. The improved estimates of the string tension satisfy the asymptotic scaling within 97%. In comparison with experiments, the obtained value $\frac{\sqrt{\ensuremath{\sigma}}}{{\ensuremath{\Lambda}}_{L}}=79\ifmmode\pm\else\textpm\fi{}3$ indicates ${\ensuremath{\Lambda}}_{\mathrm{MS}}=449\ifmmode\pm\else\textpm\fi{}17$ MeV, where MS denotes the minimal subtraction scheme. The coupling constant $\ensuremath{\alpha}=0.43\ifmmode\pm\else\textpm\fi{}0.03$ agrees very well with experiments, and is also in excellent agreement with the theoretical value $\frac{\ensuremath{\pi}}{8}=0.39$, assuming that the long-distance behavior of QCD can be effectively described by the Neveu-Schwarz string theory.

Computing quark potential on a parallel supercomputer

Computing the quark potential in lattice QCD on a state-of-the-art parallel computer — the 128 node Caltech/JPL MarkIIIfp Hypercube — achieves a sustained speed of 600 megaflops, and leads to excellent physics results. We describe various aspects of the computation with particular emphasis on the practical experiences on the parallel implementation and performance analysis of the MarkIIIfp Hypercube.

Asymptotic scaling of the heavy-quark potential in lattice QCD.

The scaling behavior of the heavy-quark $q\overline{q}$ potential is studied by measuring Wilson-line operator-operator correlations via extensive simulations on large lattices. By using large size loops (up to 16\ifmmode\times\else\texttimes\fi{}12) and extracting the potential at large distance $R\ensuremath{\ge}4$ we find that the string tension satisfies the two-loop asymptotic scaling within about 95% accuracy at the coupling $\ensuremath{\beta}=6.0$ 6.1, 6.2 and $\ensuremath{\alpha}$ remains a constant. Thus the scaling of the string tension sets in at around $\ensuremath{\beta}=6$. The obtained values $\frac{\sqrt{\ensuremath{\sigma}}}{{\ensuremath{\Lambda}}_{L}}=78\ifmmode\pm\else\textpm\fi{}4$ and $\ensuremath{\alpha}\ensuremath{\simeq}0.54\ifmmode\pm\else\textpm\fi{}0.11$ agree well with the potential-model analysis on the $c\overline{c}$ and $b\overline{b}$ systems. Among the existing underlying string theories, our results favor the Neveu-Schwarz string theory.

Dynamical quark effects on heavy-quark spin-dependent potential in lattice QCD

A full QCD simulation was carried out for the spin-dependent force for the heavy quark spectroscopy using the Kogut-Susskind quark action with the gauge coupling β=5.6 on a 10 3×20 lattice at m q a=0.1 and 0.05. The effect of vacuum quark loops on the spin-dependent potential is absorbed into the shift of the bare gauge coupling. This implies that the spin-dependent potential would be still insufficient to describe the excited spectra of J/Ψ and ϒ families in terms of the non-relativistic potential model, contrary to the conjecture sometimes made in the literature. The present result ensures that the inclusion of the vacuum quark loop does not affect the mass splitting patterns of hadron multiplets in the quenched calculation.

Dynamical quark effects on the hadronic spectrum and q [formula omitted]-potential in lattice QCD

The results of a calculation which incorporates virtual quark-antiquark pairs at a coupling of β=5.7 and quark mass of 0.05 are compared with those of two quenched simulations at β=5.895 and 6. The inclusion of the dynamical quark produces no effects in the hadron mass spectrum besides an overall shift in the coupling. In contrast, the Wilson lopp factors show a non-trivial effect, in the form of a flattening of the heavy quark potential. All three studies were carried out on a 10 3·32 lattice.