The Determination of the Quark-Gluon Mixed Condensate (anti-Q sigma G Q) from Lattice QCD

We study the quark-gluon mixed condensate g, using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with \beta = 6.0, and perform the measurement of the mixed condensate at 16 points in each gauge configuration for each current quark mass of m_q=21, 36, 52 MeV. Using the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g / \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large value of the mixed condensate suggests its importance in the operator product expansions in QCD. We study also chiral restoration at finite temperature in terms of the mixed condensate, which is another chiral order parameter. We present the lattice QCD results of the mixed condensate at finite temperature.Comment: 5 pages, Talk given at Tokyo-Adelaide Joint Workshop on Quarks, Astrophysics and Space physics, Tokyo, Japan, Jan.6 - Jan.10, 200

Comment on "Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory"

We invalidate the arguments given in [T.Yamazaki and Y.Kuramashi, Phys. Rev. D96, 114511 (2017)] over the HAL QCD method for hadron-hadron interactions on the lattice. We also pose questions on the practical usefulness of the method proposed in this reference.Comment: 3 pages. Version accepted for publication in Physical Review

Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with L\"uscher's finite volume formula --

On the basis of the L\"uscher's finite volume formula, a simple test (consistency check or sanity check) is introduced and applied to inspect the recent claims of the existence of the nucleon-nucleon ($NN$) bound state(s) for heavy quark masses in lattice QCD. We show that the consistency between the scattering phase shifts at $k^2 > 0$ and/or $k^2 < 0$ obtained from the lattice data and the behavior of phase shifts from the effective range expansion (ERE) around $k^2=0$ exposes the validity of the original lattice data, otherwise such information is hidden in the energy shift $\Delta E$ of the two nucleons on the lattice. We carry out this sanity check for all the lattice results in the literature claiming the existence of the $NN$ bound state(s) for heavy quark masses, and find that (i) some of the $NN$ data show clear inconsistency between the behavior of ERE at $k^2 > 0$ and that at $k^2 < 0$, (ii) some of the $NN$ data exhibit singular behavior of the low energy parameter (such as the divergent effective range) at $k^2<0$, (iii) some of the $NN$ data have the unphysical residue for the bound state pole in S-matrix, and (iv) the rest of the $NN$ data are inconsistent among themselves. Furthermore, we raise a caution of using the ERE in the case of the multiple bound states. Our finding, together with the fake plateau problem previously pointed out by the present authors, brings a serious doubt on the existence of the $NN$ bound states for pion masses heavier than 300 MeV in the previous studies.Comment: 39 pages, 16 figures, and 11 tables, title changed, references and comment adde

Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and ΞΞ\Xi\Xi forces --

We present the latest lattice QCD results for baryon interactions obtained at nearly physical quark masses. $N_f = 2+1$ nonperturbatively ${\cal O}(a)$-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of (96a)^4 \simeq (8.1\mbox{fm})^4 with $a^{-1} \simeq 2.3$ GeV, where $m_\pi \simeq 146$ MeV and $m_K \simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$\Xi$ systems in $^1S_0$ channel and $^3S_1$-$^3D_1$ coupled channel, and extract central and tensor interactions by the HAL QCD method. We also present the results for the $N\Omega$ interaction in $^5S_2$ channel which is relevant to the $N\Omega$ pair-momentum correlation in heavy-ion collision experiments.Comment: Talk given at 35th International Symposium on Lattice Field Theory (Lattice 2017), Granada, Spain, 18-24 Jun 2017, 8 pages, 9 figures. arXiv admin note: text overlap with arXiv:1702.0160

Most Strange Dibaryon from Lattice QCD

The $\Omega\Omega$ system in the $^1S_0$ 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 $m_{\pi}\simeq 146$ MeV at a lattice spacing $a\simeq 0.0846$ fm. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length $a_0 = 4.6 (6)(^{+1.2}_{-0.5}) {\rm fm}$, the effective range $r_{\rm eff} = 1.27 (3)(^{+0.06}_{-0.03}) {\rm fm}$ and the binding energy $B_{\Omega \Omega} = 1.6 (6) (^{+0.7}_{-0.6}) {\rm MeV}$. These results indicate that the $\Omega\Omega$ 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.Comment: 6 pages and 4 figure

NΩN\Omega dibaryon from lattice QCD near the physical point

The nucleon($N$)-Omega($\Omega$) system in the S-wave and spin-2 channel ($^5$S$_2$) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses ($m_\pi \simeq 146$~MeV and $m_K \simeq 525$~MeV). 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 $N\Omega$($^5$S$_2$) 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 $a_0= 5.30(0.44)(^{+0.16}_{-0.01})$~fm, $r_{\rm eff} = 1.26(0.01)(^{+0.02}_{-0.01})$~fm, $B = 1.54(0.30)(^{+0.04}_{-0.10})$~MeV, respectively. Including the extra Coulomb attraction, the binding energy of $p\Omega^-$($^5$S$_2$) becomes $B_{p\Omega^-} = 2.46(0.34)(^{+0.04}_{-0.11})$~MeV. Such a spin-2 $p\Omega^-$ state could be searched through two-particle correlations in $p$-$p$, $p$-nucleus and nucleus-nucleus collisions.Comment: 16 pages, 6 figures, a reference adde