The ΔΔ dibaryon resonance <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> with <math><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>,</mo><mi>I</mi><mo>)</mo><mo>=</mo><mo>(</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></math> is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses (<math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>679</mn><mo>,</mo><mn>841</mn></math> and 1018 MeV). By using the HAL QCD method, the central Δ-Δ potential in the <math><mmultiscripts><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>7</mn></mrow></mmultiscripts></math> channel is obtained from the lattice data with the lattice spacing <math><mi>a</mi><mo>≃</mo><mn>0.121</mn></math> fm and the lattice size <math><mi>L</mi><mo>≃</mo><mn>3.87</mn></math> fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> 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 <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup></math> and the D-wave NN system. Although the transition potential is strong at short distances, the decay width of <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> 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.

Japan

Shinya Gongyo

Kenji Sasaki

Takaya Miyamoto

Sinya Aoki

Takumi Doi

Tetsuo Hatsuda

Yoichi Ikeda

Takashi Inoue

Noriyoshi Ishii

(2380) dibaryon from lattice QCD

The nucleon(N)-Omega(Ω) system in the S-wave and spin-2 channel (<math><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts></math>) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses (<math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≃</mo><mn>146</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and <math><msub><mrow><mi>m</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>≃</mo><mn>525</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>). 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 <math><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts><mo>)</mo></math> 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 <math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>5.30</mn><mo>(</mo><mn>0.44</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow><mrow><mo>+</mo><mn>0.16</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>fm</mtext></math>, <math><msub><mrow><mi>r</mi></mrow><mrow><mi>eff</mi></mrow></msub><mo>=</mo><mn>1.26</mn><mo>(</mo><mn>0.01</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow><mrow><mo>+</mo><mn>0.02</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>fm</mtext></math>, <math><mi>B</mi><mo>=</mo><mn>1.54</mn><mo>(</mo><mn>0.30</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.10</mn></mrow><mrow><mo>+</mo><mn>0.04</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>, respectively. Including the extra Coulomb attraction, the binding energy of <math><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mmultiscripts><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>5</mn></mrow></mmultiscripts><mo>)</mo></math> becomes <math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><mn>2.46</mn><mo>(</mo><mn>0.34</mn><mo>)</mo><mo>(</mo><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.11</mn></mrow><mrow><mo>+</mo><mn>0.04</mn></mrow></msubsup><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>. Such a spin-2 <math><mi>p</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup></math> state could be searched through two-particle correlations in p-p, p-nucleus and nucleus-nucleus collisions.

Takumi Iritani

Iran

Faisal Etminan

Ω dibaryon from lattice QCD near the physical point

The <math><mrow><mi>Ξ</mi><mi>Ξ</mi></mrow></math> interaction in the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channel is studied to examine the convergence of the derivative expansion of the nonlocal HAL QCD potential at the next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math>). We find that (i) the leading order potential from the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> analysis provides the scattering phase shifts accurately at low energies, (ii) the full <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> potential provides only a 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 <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>LO</mi></mrow></math> 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 we find that they are well under control for this particular system.

Hidekatsu Nemura

Systematics of the HAL QCD potential at low energies in lattice QCD

We invalidate the arguments given in [T. Yamazaki and Y. Kuramashi, Phys. Rev. D 96, 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 on “Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory”

The <math><mi>Ω</mi><mi>Ω</mi></math> system in the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channel (the most strange dibaryon) is studied on the basis of the (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor lattice QCD simulations with a large volume <math><mrow><mo>(</mo><mn>8.1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> and nearly physical pion mass <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>146</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> at a lattice spacing of <math><mi>a</mi><mo>≃</mo><mn>0.0846</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length <math><msub><mi>a</mi><mn>0</mn></msub><mo>=</mo><mn>4.6</mn><mo>(</mo><mn>6</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.5</mn></mrow><mrow><mo>+</mo><mn>1.2</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, the effective range <math><msub><mi>r</mi><mi>eff</mi></msub><mo>=</mo><mn>1.27</mn><mo>(</mo><mn>3</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.03</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, and the binding energy <math><msub><mi>B</mi><mrow><mi>Ω</mi><mi>Ω</mi></mrow></msub><mo>=</mo><mn>1.6</mn><mo>(</mo><mn>6</mn><mo>)</mo><msubsup><mo>(</mo><mrow><mo>−</mo><mn>0.6</mn></mrow><mrow><mo>+</mo><mn>0.7</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. These results indicate that the <math><mi>Ω</mi><mi>Ω</mi></math> 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.

Most Strange Dibaryon from Lattice QCD

We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

Kai Watanabe

Current matrix element in HAL QCD’s wavefunction-equivalent potential method

Physical observables, such as the scattering phase shifts and binding energy, calculated from the non-local HAL QCD potential do not depend on the sink operators used to define the potential. In practical applications, the derivative expansion of the non-local potential is employed, so that physical observables may receive some scheme dependence at a given order of the expansion. In this paper, we compare the 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 a negligible NLO term for a wide range of energies, which implies good convergence of the derivative expansion, while the potential in the smeared-sink scheme has a non-negligible NLO contribution. The implications of this observation for future studies of resonance channels (such as the and scatterings) with smeared all-to-all propagators are briefly discussed.

Daisuke Kawai

I = 2 π π scattering phase shift from the HAL QCD method with the LapH smearing

Baryon–baryon interactions with strangeness with flavor SU(3) breaking are calculated for the first time by using the HAL QCD method extended to the coupled-channel system in lattice QCD. The potential matrices are extracted from the Nambu–Bethe–Salpeter wave functions obtained by the -flavor gauge configurations of the CP-PACS JLQCD Collaborations with a physical volume of and with . The spatial structure and the quark mass dependence of the potential matrix in the baryon basis and in the SU(3) basis are investigated.

Keiko Murano

Coupled-channel approach to strangeness S 2 baryon–bayron interactions in lattice QCD

We investigate the interaction between baryons in the channel from -flavor lattice quantum chromodynamics (QCD) simulations. On the basis of the HAL QCD method, the potential is extracted from the Nambu–Bethe–Salpeter wave function calculated on the lattice by using the PACS-CS gauge configurations with a lattice spacing of fm, a lattice volume of fm, and quark masses corresponding to MeV and MeV. The potential has a repulsive core at short distances and an attractive well at intermediate distances. Accordingly, the phase shift obtained from the potential shows moderate attraction at low energies. Our data indicate that the system with the present quark masses may appear close to the unitary limit where the scattering length diverges.

Masanori Yamada

Omega-Omega interaction from 2+1-flavor lattice quantum chromodynamics

Charmed tetraquarks Tcc=(ccu¯d¯) and Tcs=(csu¯d¯) are studied through the S-wave meson–meson interactions, D – D , K¯ – D , D – D⁎ and K¯ – D⁎ , on the basis of the (2+1) -flavor lattice QCD simulations with the pion mass mπ≃410 , 570 and 700 MeV. For the charm quark, the relativistic heavy quark action is employed to treat its dynamics on the lattice. Using the HAL QCD method, we extract the S-wave potentials in lattice QCD simulations, from which the meson–meson scattering phase shifts are calculated. The phase shifts in the isospin triplet ( I=1 ) channels indicate repulsive interactions, while those in the I=0 channels suggest attraction, growing as mπ decreases. This is particularly prominent in the Tcc(JP=1+,I=0) channel, though neither bound state nor resonance are found in the range mπ=410–700 MeV . We make a qualitative comparison of our results with the phenomenological diquark picture.