arXiv subjects

Takumi Doi

Publications and source records attributed to Takumi Doi.

At least 37 records · Page 2Linked to original sources

arXiv2022

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 $Ω_{3Q}Ω_{3Q}$ ($Q=s,c$) 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 to the eigenenergies in a finite lattice box obtained from the leading-order HAL QCD potential $V({\boldsymbol{r}})$ within statistical errors. The overlapping factors between the optimized sink operators and the state created by the wall-type source operator indicate that $V( \boldsymbol{r})$ 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.

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arXiv2022

Nuclear force with LapH smearing

The nuclear forces are determined by combining the HAL QCD method and a new type of source smearing technique. The new smearing is a projection to a space spanned by the lowest-lying eigenvectors of the free Laplacian operator on a lattice, which enables efficient calculation of hadron correlators at an affordable cost by utilizing the hadron-level momentum conservations. We find that this new approach reduces the statistical and systematic errors in the resultant nuclear forces.

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arXiv2021

Finite volume analysis on systematics of the derivative expansion in HAL QCD method

We study the convergence of the derivative expansion in HAL QCD method from the finite volume analysis. Employing the (2+1)-flavor lattice QCD data obtained at nearly physical light quark masses $(m_π, m_K) \simeq (146, 525)$ MeV and the physical charm quark mass, we study two representative systems, $ΩΩ$ and $Ω_{ccc}Ω_{ccc}$ in the $^1S_0$ channel, where both systems were found to have a shallow bound state in our previous studies. The HAL QCD potentials are determined at the leading-order in the derivative expansion, from which finite-volume eigenmodes are obtained. Utilizing the eigenmode projection, we find that the correlation functions are dominated by the ground state (first excited state) in the case of $ΩΩ$ ($Ω_{ccc}Ω_{ccc}$). In both $ΩΩ$ and $Ω_{ccc}Ω_{ccc}$, the spectra obtained from eigenmode-projected temporal correlators are found to be consistent with those from the HAL QCD potential for both the ground and first excited state. These results show that the derivative expansion is well converged in these systems, and also provide a first explicit evidence that the HAL QCD method enables us to reliably extract the binding energy of the ground state even from the correlator dominated by excited scattering states.

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arXiv2021

Most charming dibaryon near unitarity

We present a first study on a pair of triply charmed baryons, $Ω_{ccc}Ω_{ccc}$ in the $^1S_0$ channel, on the basis of the HAL QCD method. The measurements are perfomed on the $(2+1)$-flavor lattice QCD configurations with nearly physical light-quark masses and physical charm-quark mass. We show that the system with the Coulomb repulsion taking into account the charge form factor of $Ω_{ccc}$ leads to the scattering length $a^\mathrm{C}_0\simeq-19$ fm and the effective range $r^\mathrm{C}_\mathrm{eff}\simeq0.45$ fm, which indicates $Ω_{ccc}Ω_{ccc}$ is located in the unitary regime.

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arXiv2021

Emergence of the rho resonance from the HAL QCD potential

In this article, we report the $ρ$ resonance study using the HAL QCD method. We calculate the $I=1$ $ππ$ potential at $m_π \approx 0.41$ GeV by a combination of the one-end trick, sequential propagator and covariant approximation averaging (CAA). Thanks to those techniques, we determine the non-local $I=1$ $ππ$ potential at the next-to-next-to-leading order (N$^2$LO) of the derivative expansion for the first time and obtain the pole of the S-matrix corresponding to the $ρ$ resonance. We also discuss the comparison between our result and a previous calculation, done by Lüscher's method.

hep-lat↗

arXiv2021

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 ${^1S_0}$ channel taking into account the Coulomb repulsion with the charge form factor of $Ω_{ccc}$ leads to the scattering length $a^{\rm C}_0\simeq -19~\text{fm}$ and the effective range $r^{\rm C}_{\mathrm{eff}}\simeq 0.45~\text{fm}$. The ratio $r^{\rm C}_{\mathrm{eff}}/a^{\rm C}_0 \simeq -0.024$, whose magnitude is considerably smaller than that of the dineutron ($-0.149$), indicates that $Ω_{ccc}Ω_{ccc}$ is located in the unitary regime.

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arXiv2021

Emergence of the $ρ$ resonance from the HAL QCD potential in lattice QCD

We investigate the $I=1$ $ππ$ interaction using the HAL QCD method in lattice QCD. We employ the (2+1)-flavor gauge configurations on $32^3 \times 64$ lattice at the lattice spacing $a \approx 0.0907$ fm and $m_π \approx 411$ MeV, in which the $ρ$ meson appears as a resonance state. We find that all-to-all propagators necessary in this calculation can be obtained with reasonable precision by a combination of three techniques, the one-end trick, the sequential propagator, and the covariant approximation averaging (CAA). The non-local $I=1$ $ππ$ potential is determined at the next-to-next-to-leading order (N$^2$LO) of the derivative expansion for the first time, and the resonance parameters of the $ρ$ meson are extracted. The obtained $ρ$ meson mass is found to be consistent with the value in the literature, while the value of the coupling $g_{ρππ}$ turns out to be somewhat larger. The latter observation is most likely attributed to the lack of low-energy information in our lattice setup with the center-of-mass frame. Such a limitation may appear in other P-wave resonant systems and we discuss possible improvement in future. With this caution in mind, we positively conclude that we can reasonably extract the N$^2$LO potential and resonance parameters even in the system requiring the all-to-all propagators in the HAL QCD method, which opens up new possibilities for the study of resonances in lattice QCD.

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arXiv2021

Hybrid Quantum Annealing via Molecular Dynamics

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

quant-ph↗

arXiv2020

$d^\ast (2380)$ dibaryon from lattice QCD

The $ΔΔ$ dibaryon resonance $d^\ast (2380)$ with $(J^P, I)=(3^+, 0)$ is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses ($m_π=679, 841$ and $1018$ MeV). By using the HAL QCD method, the central $Δ$-$Δ$ potential in the ${}^7S_3$ channel is obtained from the lattice data with the lattice spacing $a\simeq 0.121$ fm and the lattice size $L\simeq 3.87$ fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to $d^\ast (2380)$ is formed with the binding energy $25$-$40$ MeV below the $ΔΔ$ threshold for the heavy pion masses. The tensor part of the transition potential from $ΔΔ$ to $NN$ is also extracted to investigate the coupling strength between the $S$-wave $ΔΔ$ system with $J^P=3^+$ and the $D$-wave $NN$ system. Although the transition potential is strong at short distances, the decay width of $d^\ast (2380)$ to $NN$ in the $D$-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.

hep-lat↗

arXiv2020

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 Lüscher'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, $m_π\simeq 146$ MeV, including hyperon forces which lead to form $ΩΩ$ and $NΩ$ dibaryons.

hep-lat↗

arXiv2020

Partial wave decomposition on the lattice and its applications to the HAL QCD method

The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of $S$-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet $Λ_c N$ system calculated in the $(2+1)$-flavor QCD on a $(32a~\mathrm{fm})^3$ lattice at the lattice spacing $a\simeq0.0907$ fm and $m_π\simeq 700$ MeV. We find that the $l=0$ component can be successfully extracted by Misner's method from the NBS wave function projected to $A_1^+$ representation of the cubic group, which contains small $l\ge 4$ components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner's method, where the Laplacian can be evaluated analytically for each partial wave component. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner's method works well in lattice QCD with the HAL QCD method but also that the contaminations from higher partial waves in the study of $S$-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in the HAL QCD method with Misner's decomposition, where the utility of this new technique may become clearer.

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arXiv2020

The HAL QCD potential in $I=1$ $ππ$ system with the $ρ$ meson bound state

In this paper, we investigate the HAL QCD potential in the $I=1$ $ππ$ scattering using the hybrid method for all-to-all propagators, in which a propagator is approximated by low-eigenmodes and the remaining high-eigenmode part is stochastically estimated. To verify the applicability of the hybrid method to systems containing quark creation$/$annihilation contributions such as the $ρ$ meson, we calculate the $I=1$ $ππ$ potential with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $(m_π,m_ρ) \approx (870, 1230)$ MeV, in which the $ρ$ meson appears as a deeply-bound state. While we find that the naive stochastic evaluations for quark creation$/$annihilation contributions lead to extremely large statistical fluctuations, additional noise reduction methods enable us to obtain a sufficiently precise potential, which shows a strong attractive force. We also confirm that the binding energy and $k^3 \cot δ$ obtained from our potential are roughly consistent with an existing $ρ$ meson bound state, within a large systematic error associated with our calculation, whose possible origin is also discussed.

hep-lat↗

arXiv2020

$ΛΛ$ and N$Ξ$ interactions from Lattice QCD near the physical point

The $S$-wave $ΛΛ$ and $N Ξ$ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point ($m_π\simeq 146{\rm{MeV}}$ 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 $ΛΛ$ 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.

hep-lat↗

arXiv2019

$I=2$ $ππ$ potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $ππ$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_π \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $ππ$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $ρ$ meson by the HAL QCD potential with the hybrid method.

hep-lat↗

arXiv2019

$NΩ$ dibaryon from lattice QCD near the physical point

The nucleon($N$)-Omega($Ω$) 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 ($m_π\simeq 146$~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 $NΩ$($^5$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 $pΩ^-$($^5$S$_2$) becomes $B_{pΩ^-} = 2.46(0.34)(^{+0.04}_{-0.11})$~MeV. Such a spin-2 $pΩ^-$ state could be searched through two-particle correlations in $p$-$p$, $p$-nucleus and nucleus-nucleus collisions.

hep-lat↗

arXiv2019

Consistency between Lüscher's 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 correlator and the HAL QCD method which extracts observables from the non-local potential associated with the tempo-spatial correlator. Although the two methods should give the same results theoretically, qualitatively different results have been reported. Recently, we pointed out 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 in the latter. In this paper, we identify the contribution of each state in the direct method by decomposing the two-baryon correlators into the finite-volume eigenmodes obtained from the HAL QCD method. We consider the $ΞΞ$ system in the $^1$S$_0$ channel at $m_π= 0.51$ GeV in 2+1 flavor lattice QCD using the wall and smeared quark sources. 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 true 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 optimized temporal correlator and (ii) the correct 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 the Lüscher's finite volume method and the HAL QCD method for two baryons is now resolved: They are consistent with each other quantitatively only if the excited contamination is properly removed in the former.

hep-lat↗

arXiv2019

Systematics of the HAL QCD Potential at Low Energies in Lattice QCD

The $ΞΞ$ interaction in the $^1$S$_0$ channel is studied to examine the convergence of the derivative expansion of the non-local HAL QCD potential at the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order potential from the N$^2$LO analysis gives the scattering phase shifts accurately at low energies, (ii) the full N$^2$LO potential gives only small correction to the phase shifts even at higher energies below the inelastic threshold, and (iii) the potential determined from the wall quark source at the leading order analysis agrees with the one at the N$^2$LO analysis except at short distances, and thus, it gives correct phase shifts at low energies. We also study the possible systematic uncertainties in the HAL QCD potential such as the inelastic state contaminations and the finite volume artifact for the potential and find that they are well under control for this particular system.

hep-lat↗

arXiv2018

Most Strange Dibaryon from Lattice QCD

The $ΩΩ$ 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 $m_π\simeq 146$ 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 $B_{ΩΩ} = 1.6 (6) (^{+0.7}_{-0.6}) {\rm MeV}$. 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.

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