Flavor Lattice QCD Research Articles

Microscopic origin of criticality at macroscale in QCD chiral phase transition

We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral order parameter (i.e., chiral condensate) and correlations among the energy levels of quarks (i.e., eigenspectra of the massless Dirac operator), which naturally leads to a generalization of the Banks-Casher relation. Based on this novel relation and through (2+1)-flavor lattice QCD calculations using the HISQ action with varying light quark masses in the vicinity of the chiral phase transition, we demonstrate that the correlations among the infrared part of the Dirac eigenspectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.

Attractive N−ϕ interaction and two-pion tail from lattice QCD near physical point

First results on the interaction between the $\ensuremath{\phi}$-meson and the nucleon ($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with nearly physical quark masses. Using the HAL QCD method, the spacetime correlation of the $N\text{\ensuremath{-}}\ensuremath{\phi}$ system in the spin $3/2$ channel is converted into the $N\text{\ensuremath{-}}\ensuremath{\phi}$ scattering phase shift through the interaction potential. The $N\text{\ensuremath{-}}\ensuremath{\phi}$ potential appears to be a combination of a short-range attractive core and a long-range attractive tail. The latter is found to be consistent with the two-pion exchange (TPE) obtained from the interaction between a color-dipole and the nucleon. The resultant scattering length and effective range for ${m}_{\ensuremath{\pi}}=146.4\text{ }\text{ }\mathrm{MeV}$ are ${a}_{0}^{(3/2)}=\ensuremath{-}1.43(23{)}_{\mathrm{stat}}({{\text{ }}_{\ensuremath{-}06}^{+36})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$ and ${r}_{\mathrm{eff}}^{(3/2)}=2.36(10{)}_{\mathrm{stat}}{({\text{ }}_{\ensuremath{-}48}^{+02})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$, respectively. The magnitude of the scattering length is shown to have nontrivial dependence of ${m}_{\ensuremath{\pi}}$ and is sensitive to the existence of the long-range tail from TPE.

Optimized two-baryon operators in lattice QCD

A set of optimized interpolating operators which are dominantly coupled to each eigenstate of two baryons on the lattice is constructed by the HAL QCD method. To test its validity, we consider heavy dibaryons ${\mathrm{\ensuremath{\Omega}}}_{3Q}{\mathrm{\ensuremath{\Omega}}}_{3Q}$ ($Q=s$, $c$) calculated by ($2+1$)-flavor lattice QCD simulations with nearly physical pion mass. The optimized two-baryon operators are shown to provide effective energies of the ground and excited states, separately stable as a function of the Euclidean time. Also they agree with the eigenenergies in a finite lattice box obtained from the leading-order HAL QCD potential $V(\mathbit{r})$ within statistical errors. The overlapping factors between the optimized sink operators and the state created by the wall-type source operator indicate that $V(\mathbit{r})$ can be reliably extracted, no matter whether the spacetime correlation of two baryons is dominated by the ground state or the excited state. It is suggested that the optimized set of operators is useful for variational studies of hadron-hadron interactions.

Static quark-antiquark interactions at nonzero temperature from lattice QCD

We study the interactions of a static quark-antiquark pair at nonzero temperature using realistic $2+1$ flavor lattice QCD calculations. The study consists of two parts. The first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a hard-thermal-loop-inspired fit for the correlation function, Pad\'e rational approximation and the Bayesian reconstruction. We find that our high-statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well-defined ground state spectral peak.

Dibaryon with Highest Charm Number near Unitarity from Lattice QCD.

A pair of triply charmed baryons, Ω_{ccc}Ω_{ccc}, is studied as an ideal dibaryon system by (2+1)-flavor lattice QCD with nearly physical light-quark masses and the relativistic heavy-quark action with the physical charm quark mass. The spatial baryon-baryon correlation is related to their scattering parameters on the basis of the HAL QCD method. The Ω_{ccc}Ω_{ccc} in the ^{1}S_{0} channel, taking into account the Coulomb repulsion with the charge form factor of Ω_{ccc}, leads to the scattering length a_{0}^{C}≃-19 fm and the effective range r_{eff}^{C}≃0.45 fm. The ratio r_{eff}^{C}/a_{0}^{C}≃-0.024, whose magnitude is considerably smaller than that of the dineutron (-0.149), indicates that Ω_{ccc}Ω_{ccc} is located in the unitary regime.

Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field

We present results on the second-order fluctuations of and correlations among net baryon number, electric charge and strangeness in (2+1)-flavor lattice QCD in the presence of a background magnetic field. Simulations are performed using the tree-level improved gauge action and the highly improved staggered quark (HISQ) action with a fixed scale approach ($a\simeq$ 0.117 fm). The light quark mass is set to be 1/10 of the physical strange quark mass and the corresponding pion mass is about 220 MeV at vanishing magnetic field. Simulations are performed on $32^3\times N_\tau$ lattices with 9 values of $N_\tau$ varying from 96 to 6 corresponding to temperatures ranging from zero up to 281 MeV. The magnetic field strength $eB$ is simulated with 15 different values up to $\sim$2.5 GeV$^2$ at each nonzero temperature. We find that quadratic fluctuations and correlations do not show any singular behavior at zero temperature in the current window of $eB$ while they develop peaked structures at nonzero temperatures as $eB$ grows. By comparing the electric charge-related fluctuations and correlations with hadron resonance gas model calculations and ideal gas limits we find that the changes in degrees of freedom start at lower temperatures in stronger magnetic fields. Significant effects induced by magnetic fields on the isospin symmetry and ratios of net baryon number and baryon-strangeness correlation to strangeness fluctuation are observed, which could be useful for probing the existence of a magnetic field in heavy-ion collision experiments.

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

We calculate the light-quark condensate, the strange-quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory (chi PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor chi PT effective potential and condensates can be mapped onto two-flavor chi PT ones by integrating out mesons with strange-quark content (kaons and eta), with renormalized couplings. We compare the results for the light-quark and pion condensates at finite pseudoscalar source with (2+1)-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light-quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

Quark and pion condensates at finite isospin density in chiral perturbation theory

In this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential mu _I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

Scaled variables and the quark-hadron duality

The thermodynamic quantities of the ideal gas of hadrons and the $(2+1)$--flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have unexpectedly revealed that the scaled variables lead to the quark-hadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks $u,d,s$ and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region.

Pion and kaon condensation at zero temperature in three-flavor \u03c7PT at nonzero isospin and strange chemical potentials at next-to-leading order

We consider three-flavor chiral perturbation theory (χPT) at zero temperature and nonzero isospin (μI) and strange (μS) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the π±-condensed phase, the K±-condensed phase, and the {K}^0/{overline{K}}^0 -condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, left|{mu}_Iright|={m}_{pi },left|frac{1}{2}{mu}_I+{mu}_Sright|={m}_K , and left|-frac{1}{2}{mu}_I+{mu}_Sright|={m}_K , respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of μS and in the kaon-condensed phases, it only depends on the combinations pm frac{1}{2}{mu}_I+{mu}_S and not separately on μI and μS. We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent (2 + 1)-flavor lattice QCD data. We find that the three-flavor χPT results are in good agreement with lattice QCD for μI< 200 MeV, however for larger values χPT produces values for observables that are consistently above lattice results. For μI> 200 MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy s-quark, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor χPT can largely be explained by the differences in the experimental values of the low-energy constants.

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.

Charmed baryon\u2013nucleon interaction

We present a comparative study of the charmed baryon–nucleon interaction based on different theoretical approaches. For this purpose, we make use of (i) a constituent quark model tuned in the light-flavor baryon–baryon interaction and the hadron spectra, (ii) existing results in the literature based both on hadronic and quark-level descriptions, (iii) (2+1)-flavor lattice QCD results of the HAL QCD Collaboration at unphysical pion masses and their effective field theory extrapolation to the physical pion mass. There is a general qualitative agreement among the different available approaches to the charmed baryon–nucleon interaction. Different from hadronic models based on one-boson exchange potentials, quark-model based results point to soft interactions without two-body bound states. They also support a negligible channel coupling, due either to tensor forces or to transitions between different physical channels, Lambda _c N – Sigma _c N. Short-range gluon and quark-exchange dynamics generate a slightly larger repulsion in the ^1S_0 than in the ^3S_1Lambda _c N partial wave. A similar asymmetry between the attraction in the two S waves of the Lambda _c N interaction also appears in hadronic approaches. A comparative detailed study of Pauli suppressed partial waves, as the ^1S_0 (I=1/2) and ^3S_1 (I=3/2)Sigma _c N channels, would help to disentangle the short-range dynamics of two-baryon systems containing heavy flavors. The possible existence of charmed hypernuclei is discussed.

NΩ dibaryon from lattice QCD near the physical point

The nucleon(N)-Omega(Ω) system in the S-wave and spin-2 channel (S25) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses (mπ≃146MeV and mK≃525MeV). The time-dependent HAL QCD method is employed to convert the lattice QCD data of the two-baryon correlation function to the baryon-baryon potential and eventually to the scattering observables. The NΩ(S25) potential, obtained under the assumption that its couplings to the D-wave octet-baryon pairs are small, is found to be attractive in all distances and to produce a quasi-bound state near unitarity: In this channel, the scattering length, the effective range and the binding energy from QCD alone read a0=5.30(0.44)(−0.01+0.16)fm, reff=1.26(0.01)(−0.01+0.02)fm, B=1.54(0.30)(−0.10+0.04)MeV, respectively. Including the extra Coulomb attraction, the binding energy of pΩ−(S25) becomes BpΩ−=2.46(0.34)(−0.11+0.04)MeV. Such a spin-2 pΩ− state could be searched through two-particle correlations in p-p, p-nucleus and nucleus-nucleus collisions.

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.

The proton–Ω correlation function in Au + Au collisions at [formula omitted

We present the first measurement of the proton–Ω correlation function in heavy-ion collisions for the central (0–40%) and peripheral (40–80%) Au + Au collisions at sNN=200 GeV by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Predictions for the ratio of peripheral collisions to central collisions for the proton–Ω correlation function are sensitive to the presence of a nucleon–Ω bound state. These predictions are based on the proton–Ω interaction extracted from (2+1)-flavor lattice QCD calculations at the physical point. The measured ratio of the proton–Ω correlation function between the peripheral (small system) and central (large system) collisions is less than unity for relative momentum smaller than 40 MeV/c. Comparison of our measured correlation ratio with theoretical calculation slightly favors a proton–Ω bound system with a binding energy of ∼ 27 MeV.

Flavor diagonal tensor charges of the nucleon from ( 2+1+1 )-flavor lattice QCD

We present state-of-the-art results for the matrix elements of flavor diagonal tensor operators within the nucleon state. The calculation of the dominant connected contribution is done using eleven ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark (HISQ) action with 2+1+1 dynamical flavors. The calculation of the disconnected contributions is done using seven (six) ensembles for the strange (light) quarks. These high-statistics simulations allowed us to address various systematic uncertainties. A simultaneous fit in the lattice spacing and the light-quark mass is used to extract the tensor charges in the continuum limit and at $M_\pi=135$ MeV. Results for the proton in the $\overline{MS}$ scheme at 2~GeV are: $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$. Implications of these results for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed.

Most Strange Dibaryon from Lattice QCD.

The ΩΩ system in the ^{1}S_{0} channel (the most strange dibaryon) is studied on the basis of the (2+1)-flavor lattice QCD simulations with a large volume (8.1 fm)^{3} and nearly physical pion mass m_{π}≃146 MeV at a lattice spacing of a≃0.0846 fm. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length a_{0}=4.6(6)(_{-0.5}^{+1.2}) fm, the effective range r_{eff}=1.27(3)(_{-0.03}^{+0.06}) fm, and the binding energy B_{ΩΩ}=1.6(6)(_{-0.6}^{+0.7}) MeV. These results indicate that the ΩΩ system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.

ΛcN interaction from lattice QCD and its application to Λc hypernuclei

The interaction between Λc and a nucleon (N) is investigated by employing the HAL QCD method in the (2+1)-flavor lattice QCD on a (2.9fm)3 volume at mπ≃410,570,700 MeV. We study the central potential in S01 channel as well as central and tensor potentials in S13−3D1 channel, and find that the tensor potential for ΛcN is negligibly weak and central potentials in both S01 and S13−3D1 channels are almost identical with each other except at short distances. Phase shifts and scattering lengths calculated with these potentials show that the interaction of ΛcN system is attractive and has a similar strength in S01 and S13 channels at low energies (i.e. the kinetic energy less than about 40 MeV). While the attractions are not strong enough to form two-body bound states, our results lead to a possibility to form Λc hypernuclei for sufficiently large atomic numbers (A). To demonstrate this, we derive a single-folding potential for Λc hypernuclei from the Λc-nucleon potential obtained in lattice QCD, and find that Λc hypernuclei can exist for A≥12 with the binding energies of a few MeV. We also estimate the Coulomb effect for the Λc hypernuclei.

The η′ meson at the physical point with Nf = 2 Wilson twisted mass fermions

We present results for the η′ meson and the topological susceptibility in Nf = 2 flavour lattice QCD. The results are obtained using Wilson twisted mass fermions at maximal twist with pion masses ranging from 340 MeV down to the physical point. A comparison to literature values is performed giving a handle on discretisation effects.

PΞ− Correlation in Relativistic Heavy Ion Collisions with Nucleon-Hyperon Interaction from Lattice QCD

On the basis of the pΞ− interaction extracted from (2+1)-flavor lattice QCD simulations at the physical point, the momentum correlation of p and Ξ− produced in relativistic heavy ion collisions is evaluated. CSL(Q) defined by a ratio of the momentum correlations between the systems with different source sizes is shown to be largely enhanced at low momentum due to the strong attraction between p and Ξ− in the I = J = 0 channel. Thus, measuring this ratio at RHIC and LHC and its comparison to the theoretical analysis will give a useful constraint on the pΞ− interaction.