arXiv subjects
Publications and source records attributed to Takumi Doi.
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.
The interaction between $Λ_c$ 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 $m_π\simeq 410,~570,~700$ MeV. We study the central potential in $^1S_0$ channel as well as central and tensor potentials in $^3S_1 - $$^3D_1$ channel, and find that the tensor potential for $Λ_c N$ is negligibly weak and central potentials in both $^1S_0$ and $^3S_1 - $$^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 $Λ_c N$ 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 $Λ_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for $Λ_c$ hypernuclei from the $Λ_c$-nucleon potential obtained in lattice QCD, and find that $Λ_c$ hypernuclei can exist for $A \ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the $Λ_c$ hypernuclei.
We present our recent results of baryon interactions with strangeness $S=-1$ based on Nambu-Bethe-Salpeter (NBS) correlation functions calculated from lattice QCD with almost physical quark masses corresponding to $(m_π,m_K)\approx(146,525)$ MeV and large volume $(La)^4=(96a)^4\approx$ (8.1 fm)$^4$. In order to perform a comprehensive study of baryon interactions, a large number of NBS correlation functions from NN to $ΞΞ$ are calculated simultaneously by using large scale computer resources. In this contribution, we focus on the strangeness $S=-1$ channels of the hyperon interactions by means of HAL QCD method. Four sets of three potentials (the $^3S_1-^3D_1$ central, $^3S_1-^3D_1$ tensor, and the $^1S_0$ central potentials) are presented for the $ΣN - ΣN$ (the isospin $I=3/2$) diagonal, the $ΛN - ΛN$ diagonal, the $ΛN \rightarrow ΣN$ transition, and the $ΣN - ΣN$ ($I=1/2$) diagonal interactions. Scattering phase shifts for $ΣN$ $(I=3/2)$ system are presented.
Physical observables, such as the scattering phase shifts and the binding energies, calculated from the non-local HAL QCD potential do not depend on the sink operators used to define the potential. This is called the scheme independence of the HAL QCD method. In practical applications, the derivative expansion of the non-local potential is employed, so that physical observables may receive some scheme dependence at given order of the expansion. In this paper, we compare the $I=2$ $ππ$ scattering phase shifts obtained in the point-sink scheme (the standard scheme in the HAL QCD method) and the smeared-sink scheme (the LapH smearing newly introduced in the HAL QCD method). Although potentials in different schemes have different forms as expected, we find that, for reasonably small smearing size, the resultant scattering phase shifts agree with each other if the next-to-leading order (NLO) term is taken into account. We also find that the HAL QCD potential in the point-sink scheme has negligible NLO term for wide range of energies, which implies a good convergence of the derivative expansion in this case, while the potential in the smeared-sink scheme has non-negligible NLO contribution. Implication of this observation to the future studies of resonance channels (such as the $I=0$ and $1$ $ππ$ scatterings) with smeared all-to-all propagators is briefly discussed. All computations in this paper have been performed at the lattice spacing $a\simeq 0.12$ fm ($1/a \simeq 1.6$ GeV) on a $16^3\times 32$ lattice with the pion mass $m_π\simeq 870$ MeV.
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 $m_π\simeq 146$ MeV and $m_K \simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$Ξ$ 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 $NΩ$ interaction in $^5S_2$ channel which is relevant to the $NΩ$ pair-momentum correlation in heavy-ion collision experiments.
Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($ΞΞ$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_π=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.
On the basis of the Lüscher'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 $ΔE$ 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.
A sanity check rules out certain types of obviously false results, but does not catch every possible error. After reviewing such a sanity check for $NN$ bound states with the Lüscher's finite volume formula[1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim in [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013[6,7] exist with the $P$-values of 4--5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansion (ERE) fits in NPL2013 violate the physical pole condition. (iv) Ref.[5] is partly based on new data and analysis different from the original ones[6,7]. (v) A new ERE in Refs.[5,8] does not satisfy the Lüscher's finite volume formula. [1] T. Iritani et al., JHEP 10 (2016) 101. [2] S. Aoki et al., PoS (LATTICE2016) 109. [3] T. Iritani et al., 1703.0720. [4] T. Yamazaki et al., PoS (LATTICE2017) 108. [5] S.R. Beane et al., 1705.09239. [6] S.R. Beane et al., PRD87 (2013) 034506. [7] S.R. Beane et al., PRC88 (2013) 024003. [8] M.L. Wagman et al., 1706.06550.
We present our recent study on baryon-baryon ($BB$) interactions from lattice QCD with almost physical quark masses corresponding to $(m_π,m_K)\approx(146,525)$ MeV and large volume $(La)^4=(96a)^4\approx$ (8.1 fm)$^4$. In order to perform a comprehensive study of $BB$ interactions based on lattice QCD calculation with almost physical masses and to make better use of such large scale computer resources, a large number of $BB$ interactions from $NN$ to $ΞΞ$ are calculated simultaneously. In this report, we focus on the strangeness $S=-1$ channels of the hyperon interactions by means of HAL QCD method. The coupled-channel HAL QCD method is briefly outlined. The snapshots of central and tensor potentials in $^1S_0$ and $^3S_1-^3D_1$ channels are presented for $ΛN$, $ΣN$ (both the isospin $I=1/2, 3/2$) and their coupled-channel systems.
Nuclear forces and hyperon forces are studied by lattice QCD. Simulations are performed with (almost) physical quark masses, $m_π\simeq 146$ MeV and $m_K \simeq 525$ MeV, where $N_f=2+1$ 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. In this report, we give the overview of the theoretical framework and present the numerical results for two-nucleon forces ($S=0$) and two-$Ξ$ forces ($S=-4$). Central forces are studied in $^1S_0$ channel, and central and tensor forces are obtained in $^3S_1$-$^3D_1$ coupled channel analysis.
The strangeness $S=-2$ baryon-baryon interaction is investigated directly from the fundamental theory of the strong interaction, QCD. The HAL QCD method enables us to extract baryon interactions from the Nambu-Bethe-Salpeter wave functions without using any experimental information. We present our latest result on the $S = -2$ baryon interactions and discuss the H-dibaryon state using potentials which are calculated by using the (almost) physical point gauge configurations with large lattice volume of$(8.1{\rm{fm}})^4$ generated on the K-computer.
We present lattice QCD results of baryon-baryon potentials in S=-3 sector, i.e., ΞΣ(I=3/2) potentials and ΞΛ-ΞΣcoupled channel potentials (I=1/2) by using the 2+1 flavor gauge configurations with almost the physical quark masses generated on 96^4 lattice with 1/a \simeq 2.3 GeV and L = 96a \simeq 8.1 fm where m_pi \simeq 146 MeV and m_K \simeq 525 MeV. These potentials are obtained based on the time-dependent HAL QCD method with a non-relativistic approximation. Qualitative behaviors of the results are found to be consistent with those in the flavor SU(3) limit.
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 interaction among $πJ/ψ$, $ρη_{c}$ and $\bar{D}D^{*}$ channels is derived from (2+1)-flavor QCD simulations at $m_π=410$-$700$ MeV. The interaction is dominated by the off-diagonal $πJ/ψ$-$\bar{D}D^{*}$ and $ρη_{c}$-$\bar{D}D^{*}$ couplings, which indicates that the $Z_{c}(3900)$ is not a usual resonance but a threshold cusp. Semi-phenomenological analyses with the coupled-channel interaction are presented to confirm this conclusion.
For the attractive interaction, the Lüscher's finite volume formula gives the phase shift at negative squared moment $k^2<0$ for the ground state in the finite volume, which corresponds to the analytic continuation of the phase shift at $k^2<0$ in the infinite volume. Using this fact, we reexamine behaviors of phase shifts at $k^2 <0$ obtained directly from plateaux of effective energy shifts in previous lattice studies for two nucleon systems on various volumes. We have found that data, based on which existences of the bound states are claimed, show singular behaviors of the phase shift at $k^2<0$, which seem incompatible with smooth behaviors predicted by the effective range expansion. This, together with the fake plateau problem for the determination of the energy shift, brings a serious doubt on existences of the $NN$ bound states claimed in previous lattice studies at pion masses heavier than 300 MeV.
Lattice QCD calculations of baryon forces are performed for the first time with (almost) physical quark masses. $N_f = 2+1$ dynamical clover fermion gauge configurations are generated at the lattice spacing of $a \simeq 0.085$ fm on a $(96 a)^4 \simeq (8.2 {\rm fm})^4$ lattice with quark masses corresponding to $(m_π, m_K) \simeq (146, 525)$ MeV. Baryon forces are calculated using the time-dependent HAL QCD method. In this report, we study $ΞΞ$ and $NN$ systems both in $^1S_0$ and $^3S_1$-$^3D_1$ channels, and the results for the central and tensor forces as well as phase shifts in the $ΞΞ$ $(^1S_0)$ channel are presented.
We describe an efficient algorithm to compute a large number of baryon-baryon interactions from $NN$ to $ΞΞ$ by means of HAL QCD method, which lays the groundwork for the nearly physical point lattice QCD calculation with volume $(96a)^4\approx$($8.2$fm)$^4$. Preliminary results of $ΛN$ potential calculated with quark masses corresponding to ($m_π$,$m_{K}$)$\approx$(146,525)MeV are presented.
We present the lattice QCD studies for baryon-baryon interactions for the first time with (almost) physical quark masses. $N_f = 2+1$ gauge configurations are generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quark action with stout smearing on the lattice of $(96 a)^4 \simeq (8.2 {\rm fm})^4$ with $a \simeq 0.085$ fm, where $m_π\simeq 146$ MeV and $m_K \simeq 525$ MeV. Baryon forces are calculated from Nambu-Bethe-Salpeter (NBS) correlation functions using the time-dependent HAL QCD method. In this report, we first give the general overview of the theoretical frameworks essential to the physical point calculation of baryon forces. We then present the numerical results for the two-nucleon central and tensor forces in $^3S_1$-$^3D_1$ coupled channel and the central force in $^1S_0$ channel. In particular, a clear signal is obtained for the tensor force.
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.