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A novel approach is proposed to link the charge symmetry breaking (CSB) nuclear interaction and the low-energy constants in quantum chromodynamics (QCD) for the first time by matching the CSB effect in nuclear matter. Resulting CSB interaction is applied to study the Okamoto-Nolen-Schiffer anomaly on the energy differences of mirror nuclei by taking $ {}^{17} \mathrm{F} $-$ {}^{17} \mathrm{O} $, $ {}^{15} \mathrm{O} $-$ {}^{15} \mathrm{N} $, $ {}^{41} \mathrm{Sc} $-$ {}^{41} \mathrm{Ca} $, and $ {}^{39} \mathrm{Ca} $-$ {}^{39} \mathrm{K} $ as typical examples. The magnitude and sign of the QCD-based CSB interactions are found to resolve the anomaly successfully within theoretical uncertainties., 5 pages, 2 figures, 6 tables in the main text; 5 pages, 2 figures, 2 tables in the supplemental material

This review aims at providing an extensive discussion of modern constraints relevant for dense and hot strongly interacting matter. It includes theoretical first-principle results from lattice and perturbative QCD, as well as chiral effective field theory results. From the experimental side, it includes heavy-ion collision and low-energy nuclear physics results, as well as observations from neutron stars and their mergers. The validity of different constraints, concerning specific conditions and ranges of applicability, is also provided.

We theoretically examine a continuity between atomic and molecular Fermi superfluids in a Bose-Fermi mixture near the Feshbach resonance. Considering a two-channel model describing the Feshbach resonance between Fermi and Bose atoms, we have constructed the mean-field framework based on the perturbative expansion of the Feshbach atom-dimer coupling. The resulting effective Hamiltonian exhibits not only the continuity between atom-atom to molecule-molecule Cooper pairings but also becomes equivalent to the two-band-superconductor model with Suhl-Matthias-Walker type pair-exchange coupling. We demonstrate how these atomic and molecular Fermi superfluids coexist within the two-band-like superfluid theory. The pair-exchange coupling and resulting superfluid gaps are found to be strongly enhanced near the Feshbach resonance due to the interplay between the infrared singularity of Bogoliubov phonons and their Landau damping arising from the coupling with fermions. The pair-exchange coupling can be probed via the observation of the intrinsic Josephson effect between atomic and molecular superfluids., 13 pages, 5 figures

We investigate the distribution of energy-momentum tensor (EMT) around a static quark in the deconfined phase of SU(3) Yang-Mills theory. The EMT defined through the gradient-flow formalism is used for the numerical analysis of the EMT distribution around the Polyakov loop with the continuum extrapolation. Using EMT, one can study the mechanical distortion of the color gauge field induced by the static charge. We find substantial separation in the absolute values of the EMT eigenvalues which is not observed in Maxwell theory. The separation grows as temperature is lowered toward the critical temperature. The lattice data also indicate the thermal screening at long distance and the perturbative behavior at short distance., 8 pages, 11 figures, Proceedings of the 38th International Symposium on Lattice Field Theory, 26-30 July 2021

The $S$-wave $\Lambda\Lambda$ and $N \Xi$ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point ($m_\pi \simeq 146{\rm{MeV}}$ and $m_K \simeq 525{\rm{MeV}}$). 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 $\Lambda \Lambda$ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The $N\Xi$ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the $N\Xi$ 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., Comment: 16 pages, 8 figures

The momentum correlation functions of baryon pairs, which reflects the baryon-baryon interaction at low energies, are investigated for multi-strangeness pairs ($\Omega\Omega$ and $N\Omega$) produced in relativistic heavy-ion collisions. We calculate the correlation functions based on an expanding source model constrained by single-particle distributions. The interaction potentials are taken from those obtained from recent lattice QCD calculations at nearly physical quark masses. Experimental measurements of these correlation functions for different system sizes will help to disentangle the strong interaction between baryons and to unravel the possible existence of strange dibaryons., Comment: 11 pages, 8 figures (reference format is modified in v2)

The properties of open strange meson K1± in nuclear matter are estimated in the QCD sum rule approach. We obtain a relation between the in-medium mass and width of K1− (K1+) in nuclear matter, and show that the upper limit of the mass shift is as large as −249 (−35) MeV. The spectral modification of the K1 meson is possible to be probed by using kaon beams at J-PARC. Such measurement together with that of K⁎ will shed light on how chiral symmetry is partially restored in nuclear matter.

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 properties of open strange meson $K_1^\pm$ in nuclear matter are estimated in the QCD sum rule approach. We obtain a relation between the in-medium mass and width of $K_1^-$ ($K_1^+$) in nuclear matter, and show that the upper limit of the mass shift is as large as -249 (-35) MeV. The spectral modification of the $K_1$ meson is possible to be probed by using kaon beams at J-PARC. Such measurement together with that of $K^*$ will shed light on how chiral symmetry is partially restored in nuclear matter., 12 pages, 3 figures, accepted for publication in Phys. Lett. B

The interaction between $\Lambda_c$ and a nucleon ($N$) is investigated by employing the HAL QCD method in the (2+1)-flavor lattice QCD on a $(2.9~\mathrm{fm})^3$ volume at $m_\pi \simeq 410,~570,~700$ MeV. We study the central potential in $^1S_0$ channel as well as central and tensor potentials in $^3S_1 - $$^3D_1$ channel, and find that the tensor potential for $\Lambda_c N$ is negligibly weak and central potentials in both $^1S_0$ and $^3S_1 - $$^3D_1$ 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 $\Lambda_c N$ system is attractive and has a similar strength in $^1S_0$ and $^3S_1$ 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 $\Lambda_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for $\Lambda_c$ hypernuclei from the $\Lambda_c$-nucleon potential obtained in lattice QCD, and find that $\Lambda_c$ hypernuclei can exist for $A \ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the $\Lambda_c$ hypernuclei., Comment: 27 pages, 10 figures, 4 tables

We investigate properties of the N(nucleon)–Ω(Omega)N(nucleon)–Ω(Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness −3 channel. We calculate the NΩ potential through the equal-time Nambu–Bethe–Salpeter wave function in 2+12+1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively O(a)O(a) improved Wilson quark action at the lattice spacing a≃0.12a≃0.12 fm on a (1.9 fm)3×(1.9 fm)3× 3.8 fm lattice. The ud and s quark masses in our study correspond to mπ=875(1) MeVmπ=875(1) MeV and mK=916(1) MeVmK=916(1) MeV. At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances. By solving the Schrödinger equation with this potential, we find one bound state whose binding energy is View the MathML source18.9(5.0)(−1.8+12.1) MeV, where the first error is the statistical one, while the second represents the systematic error.

The possible exotic meson Z_{c}(3900), found in e^{+}e^{-} reactions, is studied by the method of coupled-channel scattering in lattice QCD. The interactions among πJ/ψ, ρη_{c}, and D[over ¯]D^{*} channels are derived from (2+1)-flavor QCD simulations at m_{π}=410-700 MeV. The interactions are dominated by the off-diagonal πJ/ψ-D[over ¯]D^{*} and ρη_{c}-D[over ¯]D^{*} couplings, which indicates that the Z_{c}(3900) is not a usual resonance but a threshold cusp. Semiphenomenological analyses with the coupled-channel interaction are also presented to confirm this conclusion.

Baryon–baryonpotentials 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 Mps=469–1171 MeV. The NN scattering phase-shifts and the mass of H-dibaryon in the flavor SU(3) limit are extracted from the resultant potentials by solving the Schrödinger equation. The NN phase-shifts 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 JP=0+ channel with the binding energy of about 26 MeV for the lightest quark mass Mps=469 MeV. Effect of flavor SU(3) symmetry breaking on the H-dibaryon is estimated by solving the coupled-channel Schrödinger equation for Μ–NΞ–ΣΣ with the physical baryon masses and the potential matrix obtained in the SU(3) limit: a resonant H-dibaryon is found between Μ and NΞ thresholds in this treatment.

By a new approach introducing a "3-window model" and constructing phenomenologically an equation of state for the hadron-quark (HQ) transition region, possible maximum mass of neutron stars (NSs) is discussed. It is found that neutron stars (NSs) with HQ transition core are able to have a mass exceeding two-solar mass, consistent with massive NSs recently observed., 3 pages, 1 figure

We investigate the interaction between $\Omega$ baryons in the $^1S_0$ channel from 2+1 flavor lattice QCD simulations. On the basis of the HAL QCD method, the $\Omega\Omega$ potential is extracted from the Nambu-Bethe-Salpeter wave function calculated on the lattice by using the PACS-CS gauge configurations with the lattice spacing $a\simeq 0.09$ fm, the lattice volume $L\simeq 2.9$ fm and the quark masses corresponding to $m_\pi \simeq 700$ MeV and $m_\Omega \simeq 1970$ MeV. The $\Omega\Omega$ potential has a repulsive core at short distance and an attractive well at intermediate distance. Accordingly, the phase shift obtained from the potential shows moderate attraction at low energies. Our data indicate that the $\Omega\Omega$ system with the present quark masses may appear close to the unitary limit where the scattering length diverges., Comment: 9 pages, 4 figures, 1 table

We investigate properties of the $N$(nucleon)-$\Omega$(Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness $-3$ channel. We calculate the $N\Omega$ potential through the equal-time Nambu-Bethe-Salpeter wave function in 2+1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively $\mathcal{O}(a)$ improved Wilson quark action at the lattice spacing $a\simeq 0.12$ fm on a (1.9 fm)$^{3}\times$ 3.8 fm lattice. The $ud$ and $s$ quark masses in our study correspond to $m_{\pi}= 875(1)$ MeV and $m_{K}= 916(1)$ MeV. At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances.By solving the Schr\"{o}dinger equation with this potential, we find one bound state whose binding energy is $18.9(5.0)(^{+12.1}_{-1.8})$ MeV, where the first error is the statistical one, while the second represents the systematic error., Comment: 14 pages, 6 figures. Minor corrections made and some references added. A published version in the Gerry Brown Memorial issue of Nucl. Phys. A (2014)

A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed temperature are calculated directly on 32^3 x (6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor (T_{mu nu}^R(x)) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t-dependence of the flowed data., 5 pages, 3 figures; comments and references added (v2), included erratum and all figures are revised (v3)

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., 43 pages, 23 figures, to appear in Progress of Theoretical and Experimental Physics (PTEP), Special Issue :A: Computational Approach in particle, Nuclear and Astrophysics

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., 13 pages, 6 figures

We study the phase structure of QCD in the $T-\mu$ 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 $\mu$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function., Comment: 7 pages, 13 figures, contribution to "The 30th International Symposium on Lattice Field Theory", June 24-29, 2012, Cairns, Australia

The Nambu-Bethe-Salpeter (NBS) wave function for two nucleons on the lattice has been shown to yield a non-local and energy-independent nucleon-nucleon (NN) potential, U(r,r'). In practice, the derivative expansion of U(r,r') is currently employed to determine the potential at low energies. In this report, we study the magnitude of non-locality to check the convergence of such a derivative expansion. With quenched lattice QCD at m_\pi = 530MeV, we compare the NN potentials at the center of mass energy E ~ 0 MeV and at E ~ 45 MeV. We also investigate the angular momentum dependence of the spin singlet potential, by comparing the potentials in 1S0 and 1D2 channels. We find that the non-locality and the angular momentum dependence in the above energy range are negligible within statistical errors., Comment: 7pages, 2figures. Talk presented at The XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy

We study the QCD phase structure in the three-flavor Nambu-Jona-Lasinio model, incorporating the interplay between the chiral and diquark condensates induced by the axial anomaly. We demonstrate that for an appropriate range of parameters of the model, the interplay leads to the low temperature critical point in the phase structure predicted by a previous Ginzburg-Landau analysis. We also show that a Bose-Einstein condensate (BEC) of diquark molecules emerges in the intermediate density region, and as a result, a BEC-BCS crossover is realized with increasing quark chemical potential., 9 pages, 9 figures